common core workbook iwb common corewm01_27_15.pdf · education time courseware inc. copyright 2014...

Copyright © 2014

Education Time Courseware, Inc.

John R. Mazzarella

Richard G. Schiller

COMMON CORE

Workbook

Education Time Courseware Inc. Copyright 2014

AUTHORS: v2.1

John Mazzarella Adjunct Professor Mathematics, Molloy College

Mathematics Teacher (Retired)

Richard Schiller Adjunct Professor Mathematics, Molloy College

Mathematics Teacher, St. John the Baptist DHS

COPYRIGHT 2014

Education Time Courseware, Inc.

83 Twin Lane North

Wantagh, NY 11793

PHONE: (516) 784-7925

ISBN: 0-943749-86-8

COMMON CORE WORKBOOK


Table of contents:

Study Guide ................................................................................................................................................. 7

Unit 1 – Analyzing Graphs of Functions .................................................................................................. 10

Homework 1: Foundations - Domain and Range (A-REI.10,F-IF.1,F-IF.2) ................................. 10

Homework 2: Piecewise Linear Functions (F-IF.4, F-IF.7.b, N-Q.2) ............................................. 12

Homework 3: Foundations: Graphs of Quadratic Functions (A-CED2)...................................... 15

Homework 4: Analyzing Graphs of Quadratics/Rate of Change (A-CED2, F-IF.7.a) ................. 16

Homework 5: Foundations: Graphs of Exponential Functions (A-CED.2) .................................. 20

Homework 6: Analyzing Exponential Graphs (F-IF.2) ................................................................... 21

Homework 7: Two Graphing Stories (F-IF.2,.6,.7) .......................................................................... 23

Homework 8: Unit 1 Review .............................................................................................................. 25

Unit 2 - Algebraic Expressions ................................................................................................................. 30

Homework 1: Foundations - Signed Numbers (A.SEE.1B, A-SSE.2, A-APR.1) ........................... 30

Homework 2: Foundations: Algebraic Expressions /Order of Operation (A-SSE.1B,A-SEE.2) ... 32

Homework 3: –Distributive, Commutative & Associative Properties (A-SEE.1B, A-SEE.2) .... 34

Homework 4: Expressions (A-SSE.1A, A-SSE.1B, A-SSE-2) ......................................................... 37


Homework 6: Cumulative Review Questions (Unit 2) ..................................................................... 42

Unit 3 –Polynomials .................................................................................................................................. 44

Homework 1: Addition and Subtraction of Polynomials (A-SSE.2, A-APR.1) ............................ 44

Homework 2: Multiplication and Division of Polynomials (A-SSE.2, A-APR.1) .......................... 46

Homework 3: Exponents – Review of basic properties (N-RN.1) ................................................... 48

Homework 4: Zero, Negative and Fractional Exponents (N-RN.1) ............................................... 49

Homework 5: Removing Parentheses (A-APR.1, A-SSE.2) ............................................................ 50

Homework 6: Modeling (A-SSE.2, A-APR.1)................................................................................... 51

Homework 7: Geometric Applications (A-SSE.2, A-APR.1) .......................................................... 54


Homework 9: Cumulative Review Questions (Unit 3) ..................................................................... 58

Unit 4 –Foundations - Radicals ................................................................................................................. 61

Homework 1: Add/Subtract Radicals (A-REL.4A, N-RN.2) .......................................................... 61

Homework 2: Multiplication / Division of Radicals (A-REL.4A, N-RN.3) .................................... 63

Unit 5 – Solving Equations and Inequalities ............................................................................................. 66

Homework 1: Solving Linear Equations (A-CED.1, A-REI.3) ....................................................... 66

Homework 2: Foundations: Fractional, Decimal and Literal Equations (A-CED.1, A-REI.1,.3) .. 67

Homework 3: True and False Equations (A-CED.1, A-REI.1,.3) .................................................. 69

Homework 4: Applications /Fractional Equations (A-CED.1, A-REI.1,2,.3) ................................ 70

Homework 5: Foundation: Inequality Expressions (A-CED.1, A-REI.1,.3) ................................. 73


Homework 6: Foundations: Inequality Word Problems (A-CED.1, A-REI.1,.3) ......................... 74

Homework 7: Solving Inequalities (A-CED.1, A-REI.1, A-REI.3) ................................................ 75

Homework 8: Inequalities Joined by “AND” or “OR” (A-CED.1, A-REI.1,.3) ........................... 76


Homework 10: Cumulative Review Questions (Unit 5) .................................................................. 79

Unit 6 – Solution Sets to Equations with Two Variables ..........................................................................81

Homework 1: Foundations: Verbal Problems (A-CED.1, A-CED.2, A.REI.3) ............................ 81

Homework 2: Foundations: Graphing Linear Functions (F-IF.2) ................................................. 84

Homework 3: Graphs of Linear Equations (A-CED.1, A-CED.2, A.REI.3) ................................. 85

Homework 4: Foundations–Graphs of Simultaneous Equations (A-REI.6, A-REI.10, F-IF.1) .. 87

Homework 5: Simultaneous Equations Algebraically (A-REI.6,12) .............................................. 89

Homework 6: System of Inequalities (A-REI.6, A-REI.12) ............................................................ 92

Homework 7: Applications of Systems (N-Q.1, A-SSE.1A,A-CED1,2,3) ...................................... 94

Homework 8 - Rates and Algebra Solutions (N-Q.1, A-SSE.1A, A-CED.1, .2, .3) ........................ 97

Homework 9 - Unit 6 Review ............................................................................................................. 98

Homework 10: Cumulative Review Questions (Unit 6) .................................................................. 99

Unit 7 – Statistics .....................................................................................................................................102

Homework 1: Foundations: Relationships (S.ID.2,S-IC.1) .......................................................... 102

Homework 2: Foundations: Histograms, Box & Whisker, Stem & Leaf (S-ID.1, S-ID.2) ........ 103

Homework 3: Distributions and Their Shapes (S-ID.1, S-ID.2, S-ID.3) ...................................... 105

Homework 4: Describing the Center of a Distribution (S-ID.2) ................................................... 108

Homework 5: Interpreting the Mean as a Balance Point (S-ID.1,2,3) ......................................... 111

Homework 6: Summarizing Deviations from the Mean (S-ID.2) ................................................. 114

Homework 7: Measuring Variability for Symmetrical Distributions (S-ID.2) ........................... 115

Homework 8: Interpreting the Standard Deviation (S-ID.2, S-ID.5, S-ID.9) ............................. 117

Homework 9: Skewed Distributions (Interquartile Range) (S-ID.1, S-ID.2, S-ID.3, S-ID.4) .... 119

Homework 10: Comparing Distributions (S-ID.1, S-ID.2, S-ID.3) .............................................. 121

Homework 11: Bivariate Categorical Data & Relative Frequencies (S-ID.5, S-ID.9) ................ 123

Homework 12: Relationships between Two Numerical Variables (S-ID.5, S-ID.6) ................... 125

Homework 13: Modeling Relationships with a Line (S-ID.6, S-ID.7, S-ID.8, S-ID.9) ................ 129

Homework 14: Interpreting Residuals from a Line (S-ID.6, S-ID.7, S-ID.8, S-ID.9)................ 131

Homework 15: Analyzing Residuals & Correlations (S-ID.6, S-ID.7, S-ID.8, S-ID.9) ............... 135

Homework 16: Unit 7 Review .......................................................................................................... 139

Homework 17: Cumulative Review Unit 7 ..................................................................................... 144

Unit 8 – Sequences...................................................................................................................................148

Homework 1: Integer Sequences ( F-IF.2,F-IF.3,F-BF.1A,F-BF.2,F-LE.2) ................................ 148


Homework 2: Recursive Formulas for Sequences (F-IF.3) ........................................................... 151

Homework 3: Arithmetic Sequences (F-IF3, F-BF.1, F-BF.2) ...................................................... 153

Homework 4: Geometric Sequences (A-SSE.4, F-BF.1, F-LE.2) ................................................. 155

Homework 5: Investment Applications (F-LE.5) ........................................................................... 156

Homework 6: Exponential Growth & Exponential Decay (F-LE.1C, F-LE.2, F-LE.5, F-BF.1) ..... 158

Homework 7: Review for Unit 8 Test .............................................................................................. 160

Unit 9 – Functions and Interval Notation ................................................................................................ 162

Homework 1: Patterns in Linear Equations (F-IF.2, F-IF.4, F-IF.7)........................................... 162

Homework 2: Modeling Linear Equations (F-IF.2, F-IF.4, F-IF.7) ............................................. 163

Homework 3: Evaluating Functions (F-IF.1, F-IF.2) .................................................................... 166

Homework 4: Foundations - Functions (F-IF.1, F-IF.2) ............................................................... 171

Homework 5: Unit 9 Review Questions .......................................................................................... 174

Homework 6: Cumulative Review Questions (Unit 9) ................................................................... 176

Unit 10 – The Graph of Functions .......................................................................................................... 179

Homework 1: Interpreting the Graph of a Function (F-IF.1, F-IF.2, F-IF.4, F-IF.6) ............... 179

Homework 2 –Graphing Functions/ Programming Code ( F-IF.1,F-IF.2, F-IF.7,F-LE.2) ........ 181

Homework 3 – Piecewise Functions (F-IF.6, F-IF.7, F-BF.3) ....................................................... 185

Homework 4 – Transformations of Functions with Parent Graphs (F-IF.4, F-BF.3) ................ 187

Homework 5: Transformations of Functions – Sketching Graphs (F-IF.4, F-BF.3, F-LE.2, F-IF.7) 190

Homework 6 - Concept Connectors (F-IF.4, F-BF.3, F-LE.2) ...................................................... 193

Homework 7: Foundations – Slopes of Linear Equations (F-IF.4, F-IF.6).................................. 194

Homework 8: Unit 10 Review .......................................................................................................... 196

Homework 9: Cumulative Review Questions (Unit 10) ................................................................. 198

Unit 11 – Foundations – Rational Expressions ....................................................................................... 200

Homework 1: Rational Expressions ( & ) (A-APR.1, A-APR.2, A-APR.6, A-APR.7) ........ 200

Homework 2: Rational Expressions (Addition & Subtraction) (A-APR.1, A-APR.7) ............... 202

Homework 3: Solving Fractional Equations (A-ARP.1, A-ARP.7, A-REI.2).............................. 204

Unit 12 – Quadratic Functions ................................................................................................................ 206

Homework 1: Factoring Polynomial Expressions (A.SSE.2) ........................................................ 206

Homework 2: Geometric Applications using Polynomials (A-APR.1, A-APR.7, F-BF.1A, F-IF.8A) .. 208

Homework 3: Factoring Strategies (A-APR.1, A-APR.7, F-BF.1A, F-IF.8A, A-SEE.3) ............ 210

Homework 4: Solving Quadratic Equations (A-SSE.3, A-APR.3, A-REI.4B, F-IF.8) ............... 212

Homework 5: Solving Quadratic Equations (A-SSE.3, A-APR.3, A-REI.4B, F-IF.8) ............... 213

Homework 6: Creating Quadratic Equations (A-APR.3, A-REI.4B, F-IF.8, F-BF.1, F-LE.3) ........ 214

Homework 7: Graphs of Quadratic Functions (A-APR.3, A-REI.4B, F-IF.8A, F-IF.7C) ......... 215

Homework 8: Graphing Functions from Factored Form (A-APR.3, A-REI.4B, F-IF.8A, F-IF.7C) .... 217


Homework 9: Interpreting Quadratic Functions (F-LE.3 A-REI.4B, F-IF.8A, F-IF.7C) ........ 220

Homework 10: Completing the Square (A-SSE.3B, A-REI.4a, b, F-IF8) ................................... 222

Homework 11: Solving by Completing the Square (A-SSE.3B, A-REI.4a, b, F-IF8)................ 223

Homework 12: Solving Equations by Formula (A-REI.4B, A-SSE.3, A-APR.3, F-IF.8) ........... 224

Homework 13: Applying the Discriminant (A-REI.4B, A-SSE.3, A-APR.3, F-IF.8) ................. 225

Homework 14: Vertex Form /Standard Form (F-IF.8a, A-REI.4B, A-SSE.3) ........................... 227

Homework 15: Graphing Root Functions ((F-IF.4, F-BF.3, F-LE.2, F-IF.7)) ........................... 229

Homework 16: Translating Functions (F-IF.4, F-BF.3, F-LE.2, F-IF.7) .................................... 231

Homework 16: Review for Unit 12 Test ......................................................................................... 235

Homework 17: Cumulative Review Questions (Unit 12) .............................................................. 238

Full Year Practice Test 1 .......................................................................................................................243

Full Year Practice Test 2..........................................................................................................................250 Practice Test 3 ..........................................................................................................................................257

Practice Test 4 ..........................................................................................................................................264


Study Guide

Properties of Real Numbers

Addition Multiplication

Commutative: a + b = b + a a•b = b•a

Associative: a + (b + c) = (a + b) + c a(bc)=(ab)c

Distributive: a(b + c) = ab + ac

Identity: a + 0 = a a•1 = a

Inverse: a + (-a) = 0 a•1

a= 1

Zero Property: a•0 = 0

Scientific Notation:

9.4 ×103 = 9400 9.4× 10

-3 = .0094

Absolute Value

| 3 | = 3 | - 3 | = 3

TO SOLVE EQUATIONS :

Remove parentheses( DISTRIBUTE)

Remove decimals or fractions

Combine LIKETERMS on the same sideof the= sign

Movethe required variable to the same sideof the=

ISOLATE thevariableby additionor subtraction

Then DIVIDE by thecoefficient of thevariabletoend

LITERAL EQUATIONS:

ISOLATE the REQUIRED VARIABLE:

Example: Solve for a:

ab + c = d

- c = - c

ab = d - c

ab d c

b b

d ca

b

INEQUALITIES

ISOLATE the REQUIRED VARIABLE

Same process as equations

NOTE: ONE MAJOR INEQUALITY FACT

WHEN MULTIPLY or DIVIDE both sides by

A NEGATIVE NUMBER

MUST CHANGE the DIRECTION of the

INEQUALITY

Example. -3x ≤ 15

Divide both sides by -3

x ≥ - 5

3 15

3 3

x

INTERVAL NOTATION

( 2 , 5 ) represents 2 < x < 5

[ 2, 5 ] represents 2 ≤ x ≤ 5

[ 2, 5 ) represents 2 ≤ x < 5

MULTIPLICATION ( FOIL or DISTRIBUTE)

( x + 4) ( x – 2) = x2 – 2x + 4x – 8

= x2 + 2x + 8

( a + b)2 = (a + b)( a + b)= a

2 + 2ab + b

2

( a – b)2 = ( a – b)( a – b) = a

2 – 2ab + b

2

( a – b)( a + b) = a2 – ab + ab + b

2 = a

2 – b

2

EXPONENTS

xa •x

b= x

a+b x

0 = 1

aa-b

b

x= x

x x

-2 =

2

1

x

(xa)b = x

ab

(xy)a = x

a•x

b (-5)

2 ≠ -5

2


EQUATIONS OF LINES m = slope

y = mx + b slope – intercept form

y – y1 = m(x – x1) point – slope form

SLOPE:

2 1

2 1

y yvertical change risem

hoeizontal change run x x

PARALLEL LINES have EQUAL SLOPES

PERPENDICULAR LINES slopes are NEGATIVE

RECIPROCALS

SYSTEMS of EQUATIONS:

y – 3x = 3 SUBSTITUTE one variable into the second equation.

y + 3x = 9 ADD or SUBTRACT to eliminate a variable.

INEQUALITY SYSTEMS – graph EQUALITY , DOTTED(< or >),

or SOLID (≤ or ≥)lines and SHADE the SOLUTION side.

LINEAR QUADRATIC SYSTEM:

SUBSTITUTE linear into the quadratic and solve.

FACTORING

1) Look for GCF First (greatest

common factor number or variable)

2) Difference of TWO perfect squares

A2 – B

2

3) Trinomial x2 + Ax + M

( 2 #’s add to A and multiply to M)

( x # ) ( x # )

QUADRATIC EQUATIONS

Set = 0 x2 – 2x – 8 = 0

Factor ( x – 4) ( x + 2) = 0

T chart x – 4 = 0 | x + 2 = 0

Solve for x x = 4 x = - 2

These are the ROOTS of the equation.

PARABOLAS

y = ax2 + bx + c

Axis of Symmetry x = b

a

Roots are the x intercepts, where the

parabola crosses the X AXIS

FRACTIONS

UNDEFINED: N

Dwhen D = 0

2

5x is undefined when x = 5 (D = 0)

ADDITION/ SUBTRACTION

Need COMMON DENOMINATOR

3 4

2 3

3 3 2 4

3 2 2 3

9 8 17

6 6 6

x x

x x

x x x

MULTIPLICATION

“MULTIPLY ACROSS” 2 5 10

3 7 21

DIVISION

“INVERT and MULTIPLY”

2 5 2 7 14

3 7 3 5 15

ALWAYS FACTOR FIRST!

FUNCTIONS

Every x value is assigned ONE and ONLY ONE y value.

{ (2,3), (4,5), (6,8) } YES { (2,3) , (4,5), ( 2, 8)} NO

f(x) = 2x+1 find f(3) = 2(3) + 1 = 7

A GRAPH that passes the VERTICAL LINE TEST is a function.

DIRECT VARIATION

Occurs if one variable increases then the other increases also or if

one variable decreases, the other variable decreases also.

Expressed as y = kx or k =y

x where k is called the CONSTANT of

VARIATION.

EXPONENTIAL GROWTH and DECAY

GROWTH: y = a(base)x where a is positive and the base is

greater than 1. ( Growth RATE is greater than 100%)

DECAY: y = a(base)x where a is positive and the base is also

positive but less than . (Decay RATE is less than 100%)

PYTHAGOREAN THEORM

SIDES OF A RIGHT TRIANGLE

a2+b

2 = c

2

c is the HYPOTENUSE, a and b legs

TRIPLETS: 3,4,5 AND 5,12,13


STATISTICS

MODE = most frequent score

MEDIAN = middle number of an

ORDERED list

MEAN = average = Sum divided by

number of items

RANGE = high score – low score

OUTLIERS = values far away from rest of

data

NUMBER SUMMARY:

Min, Quart 1, Median, Quart #3, Max

QUARTILES divide data into 4 (25%)

equal parts.

PERCENTILES: Percentage of scores at or

below this percent=

#100

#

of scores below

total of scores

BOX AND WHISKER

Min and Max at ends of “WHISKERS”

Quartile 1, Median, Quartile 3 form the box

1 2

1 2

( ) ( )AverageRateof change

Linear Functions: averagerateof changeisa constant.

QuadraticFunctions: averagerateof changeisnot constant

GRAPHS

f x f x

x x


Unit 1 – Analyzing Graphs of Functions

Homework 1: Foundations - Domain and Range (A-REI.10,F-IF.1,F-IF.2)

1) Name the domain and the range of each relation and state whether it is a function and justify your

answer:

a) (3,5),(4,6),(5,7),(6,6){ } b) ( ,2),( ,4),( ,6){ }A B C c) (1,4),(1,5),(1,9){ }

Domain: Domain: Domain:

Range: Range: Range:

Function: Function: Function:

2) State the domain and range for each graph below and state whether it is a function and justify your

answer. Use interval notation.

a) b)

c) d)


3) State the domain and range for each graph below and state whether it is a function and justify your

answer.

a) b)

c) d)

e) f)



Homework 2: Piecewise Linear Functions (F-IF.4, F-IF.7.b, N-Q.2)

Review

1) State the domain and range for each of the following. State if they are a function.

a) {(1,2) (2,2) (3,2)} b) c)

2) The elevation versus time graph below represents a bike ride by Marie. Use the graph to answer the

following questions.

a) How many feet did Marie travel in 2 minutes ?

b) For how many minutes was Marie resting?

c) How long did it take Marie to return to her starting position?

d) State the intervals where Marie’s elevation is increasing.

e) State the interval where Marie’s elevation is decreasing.

f) State the interval where Marie’s elevation is constant.


Hw 2 continued

3) Create a story to match each graph below.

a) Story:

b) Story

c) Story

d) Draw up an elevation-versus-time graphing story of your own and then make up a story for it.

Story


Hw 2 continued

4) The graph below shows a runner’s velocity for 8 seconds.

a) What is the runner’s average acceleration

over the interval from 3 to 8 seconds.

b) What is the runner’s average acceleration


c) What is the runner’s average acceleration


5) The following graph shows the amount of milk left

in Kitty’s milk dish over a period of seconds.

a) How much time elapsed before Kitty had her first

drink?

b) How long did she wait before drinking a second time?

c) How long did it take her to finish all the milk?

d) How many times did she pause before finishing all the milk?

e) What is Kitty’s average rate of drinking from 30 seconds to 50 seconds?



Homework 3: Foundations: Graphs of Quadratic Functions (A-CED2)

1) Sketch the graph of each function.

a) 23y x b) 21

2y x

c) 2 8 18y x x d) 2 8 18y x x

e) Why are these graphs called a quadratic function and not a linear function?



Homework 4: Analyzing Graphs of Quadratics/Rate of Change (A-CED2, F-IF.7.a)

Review

1) State whether or not each graph represents a function. Justify your answer.

(a) (b)

2) Is the set of points, { ( 2, 3), ( 4, 5), ( 2, 6), ( 7, 0) } a function? Explain your answer.

3) Write in interval notation, the set of all numbers greater than 2 and less than or equal to 9.

4) a) Sketch a graph of 2( 2) 1y x

b) Is this a quadratic function or linear? Explain your answer.


Hw 4 continued

5) Use the table below to answer the following questions.

x 0 1 2 3 4 5 6

y 0 52

6 212

16 30

a) Plot the points (x,y) in this table on a graph (except when x = 5).

b) Find the y – value when x = 5

c) Find the average rate of change from x = 2 to x = 4

d) What kind of graph is this function?


Hw 4 continued

6) Use the table below to answer the following questions.

x 0 1 2 3 4 5 6

y 0 -0.5 -1 -1.5 -2 -3

a) Plot the points (x,y) in this table on a graph (except when x = 5).

b) Find the y – value when x = 5

c) Find the average rate of change from x = 1 to x = 3

d) Find the average rate of change from x = 2 to x = 4

e) Is the average rate of change a constant for this function? Justify your answer.


Hw 4 continued

7) Emma is 1 mile south of her school. While walking north at a constant speed, she passes her school

after 2 hours.

a) What is Emma’s' rate of speed?

b) Create a table showing Emma's distance from school for 2 hours , 3 hours and 4 hours

c) Draw a graph illustrating this story.

d) State the function rule.

e) State the domain and range

8) The elevator in Macys climbs 1 floor per minute. After 2 minute it is on the third floor.

a) What is the rate of speed of the elevator?

b) Create a table showing the floor the elevator is on for the following times in minutes.





Homework 5: Foundations: Graphs of Exponential Functions (A-CED.2)

1) Graph each of the following exponential functions. State the domain and range for each function.

) 2xa y 1

)2

( )b y x

) 4 2xc y 1

) 42

( )d y x



Homework 6: Analyzing Exponential Graphs (F-IF.2)

Review

1) A ramp is made in the shape of a right triangle using the dimensions described in the picture below.

The ramp length is 12 feet from the top of the ramp to the bottom, and the horizontal width of the

ramp is 11.5 feet.

A ball is released at the top of the ramp and takes 1.8 seconds to roll from the top of the ramp to the

bottom. Find each answer below to the nearest 0.1 feet/sec.

a. Find the average speed of the ball over the 1.8 seconds.

b. Find the average rate of horizontal change of the ball over the 1.8 seconds.

c. Find the average rate of vertical change of the ball over the 1.8 seconds.


Hw 6 continued

2) For the new school year, Your High School requires every student to own an iPad. The school hopes

to reduce paper usage by 20% each year. Last year, Your High School used 12,000 pounds of paper.

a) Complete the table and construct a graph to show how paper usage is expected to decrease over the

next 4 years. Be sure to label and mark your axes.

b) Write an equation that shows paper usage ( ) as a function of time in years ( ).

c) In how many years does Your High School expect paper usage to fall below 1000 pounds?



Homework 7: Two Graphing Stories (F-IF.2,.6,.7)

REVIEW

1) Antwan leaves a cup of hot chocolate on the counter in his kitchen. Which graph is the best

representation of the change in temperature of his hot chocolate over time?

(1) (2) (3) (4)

2) A project’s projected profit is represented by the equation y = - 3x2 + 18x where y is the profit in

millions of dollars and x is the number of months of operation. When will the project show the

maximum profit? When will the project start losing money?

3) Laura and Frank live at opposite ends of the hallway in their apartment

building. Their doors are 60 feet apart. They each start at their door

and walk at a steady pace towards each other and stop when they meet.

Suppose that:

Laura walks at a constant rate of 2 feet every second.

Frank walks at a constant rate of 3 feet every second.

a. Graph both people’s distance from Laura’s door versus time

in seconds.

b. According to your graphs, approximately how far will they

be from Laura’s door when they meet?


Hw 7 continued

4) Consider the story:

Kay, Jane, and Julie were running at the track. Kay started first and ran at a steady pace of 1 mile every

12 minutes. Jane started 4 minutes later than Kay and ran at a steady pace of 1 mile every 10 minutes.

Julie started 2 minutes after Jane and ran at a steady pace, running the first lap (quarter mile) in 1.75

minutes. She maintained this steady pace for 3 more laps and then slowed down to 1 lap every 3

minutes.

a. Sketch Kay, Jane, and Julie’s distance versus time graphs on a coordinate plane.

b. Create linear equations that represent each girl’s mileage in terms of time in minutes. You will need

two equations for Julie since her pace changes after 4 laps (1 mile).

c) Who is the first person to run 3 miles?

d. Did Jane and Julie pass Kay on the track if they did, when and at what mileage?

e. Did Julie pass Jane on the track if she did when and at what mileage?



Homework 8: Unit 1 Review

1) Which graph below represents a quadratic function?

2) Which graph does not represent a function?

3) What are the domain and the range of the function shown in the graph below?

1) 2) 3) 4)


Hw 8 continued

4) On January 1, a share of a certain stock cost $180. Each month thereafter, the cost of a share of this

stock decreased by one-third. If x represents the time, in months, and y represents the cost of the

stock, in dollars, which graph best represents the cost of a share over the following 5 months?

5) a) State the domain and range of the graph.

b) Does the graph represent a function? Explain.

6) Write the inequality 1 2x in integer notation.


Hw 8 continued

7) Create a graph to represent the following story

A car travelling at 26 mph accelerates to 42 mph in 5 seconds. It maintains that speed for

the next 5 seconds, and then slows to a stop during the next 5 seconds.

8) Which equation is represented by the graph below?

9) Given the relation { ( 8 , 2 ), ( 3 , 6 ), ( 7 , 5 ) and ( k , 4 )}, which value of k will result in the

relation NOT being a function?

1) 1 2) 2 3) 3 4) 4

1)

2)

3)

4)


Hw 8 continued

10) Which graph represents a relation that is not a function?

1) 2)

3) 4)

11) The Smith family kept a log of the distance they traveled during a trip, as represented by the graph

below.

During which interval was their average speed the greatest?

(1) the first hour to the second hour (2) the second hour to the fourth hour

(3) the sixth hour to the eight hour (4) the eighth hour to the tenth hour


Hw 8 continued

12) These graphs represent walking trips taken by two friends who leave for the trip at the same time.

The starting distance is how far they are from home. At distance = 0 is the location of their home.

a) Which friend is walking slower in

i) Graph A

ii) Graph B

iii) Graph C

b) In Graph B, what does the intersection point represent?

c) In Graph C, create a story to describe the two trips.

d) In graph D , describe their journey.


Unit 2 - Algebraic Expressions

Homework 1: Foundations - Signed Numbers (A.SEE.1B, A-SSE.2, A-APR.1)

1) Perform the following operations with signed numbers. (No calculator is suggested)

A) ( +7) + ( +3) B) ( +15) + ( - 12) C) ( - 25) + ( + 18) D) ( - 30) + ( - 12)

E) ( +7) – ( +3) F) ( +15) – ( - 12) G) ( - 25) – ( + 18) H) ( - 30) – ( - 12)

I) +8 + 6 J) 10 + 5 K) 14 – 8 L) - 15 + 8

M) - 20 – 5 N) - 30 – ( - 5) O) - 15 – ( +15) P) -12 + 12

2) Perform the following operations with signed numbers. (No calculator is suggested)

A) ( + 3) ( + 7) B) ( + 12 ) ( - 5) C) ( - 20 ) ( + 6 ) D) ( - 8 ) ( - 9 )

E) 5 12 F) 8 ( - 11) G) - 6 6 H) -12 ( - 10)

I) 72 J) ( - 9 )

2 K) ( + 2 )

3 L) ( - 3 )

3

M) 15

3

N)

28

7

O)

49

7

P)

36

3

Q) 72

12 R)

56

8 S)

39

3

T)

100

25


HW 1 continued

3) One morning, the temperature was 8° below zero. By noon, the temperature rose 18° Fahrenheit (F)

and then dropped 6° F by evening. What was the evening temperature?

4) Which number line below best represents the addition problem -10 + (-20) =?

1) 2)

3) 4)

5) Jason started his own lawn service. The table below shows the profit or loss each month for four

months. Jason represented profit as positive numbers and loss as negative numbers. How much profit

or loss did Jason have after being in business for four months?

Month June July August September

Profit/Loss - 380 600 - 800 330

1) loss of $250 2) profit of $250 3) loss of $2110 4) profit of $2110

6) Kim states that 6 + (- 4) is the same as 6 - 4.

Do you agree with Kim? Justify your answer.

7) James was observing the number of students entering and leaving the library at school. He observed

12 student leave the library and 9 students entered . Later he observed 4 more students enter the

library and 14 people left. What was the net increase or decrease in the number of students in the

library?



Homework 2: Foundations: Algebraic Expressions /Order of Operation (A-SSE.1B,A-SEE.2)

Review

1) One morning, the temperature was 6°(F) below zero. By noon, the temperature rose 14°

Fahrenheit (F) and then dropped 4° F by evening. What was the evening temperature?

2) Evaluate each of the following

(a) (-6) – (-8) (b) (-4) x (3) (c) 12

2

(d) (-3) + (-5)

3) Find the value of each.

a) 3+2 5 b) 20 30 5 5 c) (12 3)

12 2 2(2 1)

d) 224 6 2(9 6) 6 2 e) 26 3 4 5 f) 2(2 6) 4

8 2(5 3)

g) 212 (2 4) 3 h) 2 24 3 5 i) 3[14 (1 7)]

j) 2 2 2 2(8 6 )(1 5 ) k) 3[6 (5 3)] l) (17 13) (10 25)

m) 6 + 3 5 n) 32 – 4 6 - 3 o) 5 ( 7 – 3 )2 p) 18 3 2 + 4

q) 15 3

4 2

r) 20 – 8 + 5 3 s) 10 3 6 – 1 t) 4( 6 – 2)

2 – 34

v) 7 + 2 5 – 32 + 4 w) ( 10 – 15 )

2 + 18 3

2 – 30 x)

2

2

3(13 9) 2

(3 2)


HW 2 continued

4) Find the value of the following algebraic expressions if a = 6 , b = 2 and x = -4:

a) a+b+x b) 2a+3b-x c) 3a+5b+2x-1 d) 4ab+5b-x

e) a b

a b

f)

2 7

13

a b g) 3a+5ab-b+x h) 10a-2ab-3b

i) 2 22a ab b j) 1 (2 )2

abx ax x k) 2(a+b) – 3( a-x) l) 22 5 3

2 3

x x

x

5) If 4y , find the value of :

2 2) 2 ) (2 )a y b y

Are the two expressions the same?

Explain your reasoning.

6) If x = 3, find the value of :

2 2) ) ( )a x b x

Are the two expressions the same?

Explain your reasoning.

7) Find the value of 2 29 16x y when

1 1

3 4x and y



Homework 3: –Distributive, Commutative & Associative Properties (A-SEE.1B, A-SEE.2)

Review

1) Find the value of 4xy – y when x = 2 and y = -5

2) Evaluate 24 12 ( 3) 4

3) Match each property to an appropriate expression:

A) Commutative property of addition a) 7 + (-7) = 0

B) Commutative property of multiplication b) 3(2 + 5) = 3 * 2 + 3 * 5

C) Associative property of addition c) 4 * 1 = 4

D) Associative property of multiplication d) Add any 2 elements of the set,

the answer must be in the set.

E) Distributive property of multiplication e) 1

1aa

F) Additive Inverse f) a + b = b + a

G) Multiplicative Inverse g) 3*(2 * 5) = (3 * 2) * 5

H) Additive Identity h) a * 0 = 0

I) Multiplicative Identity i) b + 0 = b

J) Closure Property for Addition j) 3 * (-2) = (-2) * 3

K) Multiplication Property of zero k) (a + d) + x = a + (d + x)

4) Below is a flow diagram to show that (xy)z=(zy)x

State the property that was used for each arrow

#1) ______________________

#2 _______________________

#3 _______________________


3( 5) (5 4) 5 30

3 15 (5 4) 5 30 ) _________________

3 15 5 (4 5) 30 ) _________________

3 15 5 9 30

3 5 15 9 30 ) _________________

2 24 30

2 6

3

x x

x x a

x x b

x x

x x c

x

x

x

Hw 3 continued

In questions 5 - 10

a) Fill in the box with a value that makes the statement true.

b) Name the property illustrated in the new sentence.

5) 4+3 = 3+

6) 8 x 3 = 3 x

7) (2 x 3) x 4 = 2 x (3 x )

8) 4( a + 3) = 4a +3( )

9) 6 + 0 =

10) 4 x = 1

11) Henry solved the following equation below. Identify the property used to obtain each of the

following steps below.

12) When solving the equation 2 23(2 5) 7 5 4x x , James wrote 2 26 15 7 5 4x x as his first

step. Which property justifies James's first step?

a) addition property of equality b) commutative property of addition

c) multiplication property of equality d) distributive property of multiplication over addition


Hw 3 continued

13) Fill in each circle of the following flow diagram with one of the letters: C for Commutative

Property (for either addition or multiplication), A for Associative Property (for either addition or

multiplication), or D for Distributive Property

a)

b)



Homework 4: Expressions (A-SSE.1A, A-SSE.1B, A-SSE-2)

Review

1) Explain how 4x + 5x = 9x is an example of the distributive property

2) Below is a flow diagram to show that (a + b) + c = (c +b) + a

State the property that was used for each arrow

#1) ______________________

#2 _______________________

#3 ______________________

3) Identify whether or not each of the following are mathematical expressions. (YES or NO)

A) 4xy + 7 B) 3x2y

5 – 3x C) -6abc

2 + 7a - 3 D) 4x

2 + 5 = 9

E) 3x + 1 > 4 F) 3

5 2

x

y G) 6

12

x H) x

4) Write what the numerical coefficient is and what the variable(s) is(are) in each expression.

A) 5x B) -3y2 C) st

3 D) -xy

5) Write what the base is and what the exponent is in each expression.

A) 73 B) x

4 C) 3y

2 D) (st)

3

E) -42 F) (2y)

4 G) ( -8)

2 H) -5t

5

6) Write how many factors are in the expression and what the factors are in each expression.

A) 7x B) 3rst C) 1

3ab D) 5


4 6

8 3

6

7

x y

x y

. 3 4 3

. 5

. 7 10

I x y z

II x

III x

Hw 4 continued

7) How many terms are found in each of the following expressions?

A) 5abc B) 5 + x C) 3a – 4b + 5c D) 7x3y

2 + 4

8) Determine the degree and the leading coefficient of each.

A) 3x2 – 4 B) 2x + 1 C) 4x

3 – 5x

2 +2x + 9

D) 9 – 4y2 E) 4 F) 7x

5 + 3y

2 – 2xy + 12

9) is best described as a(n)

1) variable 2) coefficient 3) expression 4) constant

10) What is the coefficient of the squared term? 28 5 3x x

1) 2 2) 3 3) 8 4) 16

11) What is the degree of the following expression? 3 24 5 7 3x x x

1) 1 2) 2 3) 3 4) 6

12) How many terms are in the expression 6 4 25 3 4 7a a a

1) 1 term 2) 2 terms 3) 3 terms 4) 4 terms

13 )Which of the following is an example of a mathematical expression?

1) I only 2) II only 3) III only 4) I and III


Hw 4 continued

14) What is the degree of the following expression? 6 3 2 24 5 3x x y y

1) 1 2) 3 3) 4 4) 6

For questions 15 – 22 ,write each as an algebraic expression, represent the number with n:

15) eight less than a number

16) a number increased by 6

17) 5 more than a number

18) one-half a number increased by 7

19) 9 is subtracted from 4 times a number

20) The sum of 4 times a number and 6

21) the sum of the number and twice the number

22) three times the number decreased by one –third that number


3 3 5 2 5 21) 6 2) 90 3) 90 4) 6x y x y x y x y

Unit 2 –Foundations - Algebraic Expressions


1) Write each as an algebraic expression, represent the number with n:

A) Three times a number increased by 2

.

B) Twelve divided by x decreased by 2.

C) Six times the sum of 3 and a number.

D) The product of 5 and n squared.

E) The difference of 6 and the square root of n

2) Find the value of each of the following.

A) If x = - 3 and y = 3, find the value of x2y

3

B) If a = 3 and b = 4 and c = - 5, find the value of 3a – b2 + 2c

2

C) Find the value of 3( )x y

z

, if x = 2, y = 5 and z = -9.

D) Find the value of a + b( a – b)2 – a b, if a = 15 and b = 5.

3) What is the GCF of ?

3 2 518 30x y and x y


Hw 5 continued

4) If a + b = a, what is the numerical value of b? Justify your answer.

5) If xy = y, what is the numerical value of x? Justify your answer.

6) If ab=0 and a 0 , what is the numerical value of b? Justify your answer

7) Place parentheses to make each statement true.

a) ) 4 3 2 4 5a b) 4 4 4 4 4 4

) 2 2 2 2 2 0c d) 5 5 5 5 5 1

8) Using the digits 1,2,3 and 4, create an expression that evaluates to the following numbers . Only

addition and multiplication are used and each number appears only once. You may use grouping

symbols.

a) 18 b) 20 c) 25

9) Which of the following are examples of the distributive property?

a) 4( 2 + 3) = 4(2) + 4(3) b) 3(x+5) = 3x + 15 c) (a+b)+c=a+(b+c)

d) 5x+10=5(x+2) e) x + y = y + x f) ab +ac = a(b+c)


Unit 2 –Foundations - Algebraic Expressions

Homework 6: Cumulative Review Questions (Unit 2)

1) Which property is illustrated by the equation ?

(1) associative (3) distributive

(2) commutative (4) identity

2) Which verbal expression represents ?

(1) two times n minus six (3) two times the quantity n less than six

(2) two times six minus n (4) two times the quantity six less than n

3) The statement is an example of the use of which property of real numbers?

(1) associative (3) additive inverse

(2) additive identity (4) distributive

4) What is the additive inverse of the expression x – 3?

(1) x + 3 (2) - x + 3 (3) - x - 3 (4) - ( - x + 3)

5) Which of the following IS a mathematical expression?

(1) 3x – 2 = 9 (2) 2x + 4 > 7 (3) x2 – 3 = y (4) 2x – y + 2

6) In the expression 3xt + 4 (A) what does the t represent? (B)How many terms are in the

expression? (C)What does the x represent? (D) What is the 3 called?

A: B: C: D:

7) Write as a mathematical expression “ Six less than eight plus x”

(1) 6 – ( 8 + x) (2) ( 6 – 8 ) + x (3) ( 8 + x ) – 6 (4) 6 – 8 - x

8) Write the equation from the following word problem. “ Twenty minus a number, then divided by 2

equals seven”

(1) 7 - 2

y= 20 (2)

207

2

y (3) 20 -

2

y= 7 (4)

207

2

y


9) When solving the equation 2 25(2 5) 7 12 3,x x Jane wrote 2 25(2 5) 12 10x x

as her first step. Which property justifies Jane’s first step?

(1) addition property of equality (2) commutative property of addition

(3) multiplication property of equality (4) distributive property of multiplication over addition

10) An appliance repairman charges $65 per hour for the labor and a $45 service charge just to come

to the site. If c represents the total charges in dollars and h represents the number of hours worked,

which formula can be used to calculate the total charges for the repairman?

(1) c = 65 + 25h (2) c = 65h + 20 (3) c = 45 + 65h (4) c = ( 45 + 65)h

11) Jim found three times the amount of items on a scavenger list as Mary, who found 1

2as many as

Bob found. The three put all of the items together and evenly divided them into two piles. Which

expression shows the number of items (T) in one of these piles?

(1) 3T + T + 1

2T 2 (2) (3T + T +

1

2T) 2

(3)

1 13( )

2 2

2

T T T (4)

1 1

2 3

2

T T T

12) Solve the following expression using x = 2 and y = 7. 3x2 – 2y – 5

(1) 7 (2) – 7 (3) – 27 (4) 17

13) The function f has a domain of {3, 5, 7,9} and a range of {4, 6,8}.

Could f be represented by { (3,4), (5,6), (9,4)}?

Justify your answer.

14) Which statement is not always true?

1) The product of two irrational numbers is irrational.

2) The product of two rational numbers is rational.

3) The sum of two rational numbers is rational.

4) The sum of a rational number and an irrational number is irrational.

15) What is true about the sum of two negative integers? The sum is always

1) zero 2) positive 3) negative 4) zero, positive or negative


Unit 3 –Polynomials

Homework 1: Addition and Subtraction of Polynomials (A-SSE.2, A-APR.1)

1) Circle the like terms in each expression ( if there are none, write NONE.)

A) x + y + 3 + 4y B) -3a2 + 4b + 3a

2 C) 2 – 3t + x – 4 D) 5x

2 – 3x + 1 – 4x

E) 5abc – 2ab+ 3 abc2 – 5ab

2c F) 3x

2y

2 – 4x

2y + 6xy

2 + 9x

2y + x – 3x

2y

2) Combine like terms in each expression. (NO calculator is suggested)

A) 3x - 7 + 2x - 8 B) 4x2 – 3x + 2 – 6x

2 – 5 C) x

2 + x

3 + x + x

2

D) 5 + 8xy – 3 + 2y E) 3abc – abc + 5ab + 7abc F) x5 + x

5 + x

5 – x

15 + x

15

G) 6a+ 3a -5a H) – 8x – 5x + 12x I) p + 14p – 23p

J) 9x2 + 12x

2 – 7x

2 K) 12xy - 7xy + 15xy L) 32abc

2 – abc

2 -18abc

2

M) 6i – 15i + 3i N) 4 7 + 8 7 - 2 7 O) 8 5 - 5 5 - 10 5

P) 4

5 +

3

5 -

4

5 Q)

6

11 +

4

11

2

11 R)

15

17 -

2

17 -

7

17


HW 1 continued

3) Simplify the following expressions by combining like terms.

A) Add 3x2 + 4x

2 + 10x

2

B) Add 25a2 + 21a +15 and 30a

2 – 10a -12

C) What is the sum of 8m + 6n, -12m – 3p and 4n – 5p?

D) Combine 8x2 – 5 – 3x – 2x

2 + 8 - 4x – 3 - 5x + x

2

E) From (5x2 – 6x + 13) subtract ( 2x

2 - 8x – 15)

F) Subtract ( 3a2 -5a + 12) from (7a

2 – 6a + 8)

G) Combine ( 7a + 5b – 2c2) – ( 9a - 3b – 5c

2)

4) If 25 7 5A x x and 24 8 5,B x x then find the value of each of the following:

i) A – B ii) B – A iii) A + B iv) B + A

v) Is A + B the same as B + A ? Give a mathematical reason for your answer.

vi) Is A – B the same as B – A ? Give a mathematical reason for your answer.


Unit 3 –Polynomials Homework 2: Multiplication and Division of Polynomials (A-SSE.2, A-APR.1)

Review

1) Find the sum or difference by simplifying and combining like terms.

5 5 2 2 2 2 2) (4 6 ) 3( 2) ) (4 3 5 ) 2(4 3 ) ) (4 3 ) 4( 1) (4 5)a x x x b a a a a c y y y

d) How much greater than 2 23x xy y is 2 24 9 3x xy y

2) Find the product of each.

A) 4( x + 5) B) 3x( x2 – 2x + 5) C) 2a

2b

3( 5ab

2 – 7a)

D) ( x + 2)( x + 3) E) ( 2x – 5) ( x – 2) F) ( x+ 3) ( x - 3)

G) (3x – 2)( x2 + 4x – 5) H) ( 4x

2 + 3x -1) ( 2x

2 – 4x + 5)

3) State the difference in each question and answer both versions. Are the answers the same?

(i) ( 3x)2 and ( 3 + x)

2 (ii) 2 3(5 )x and ( 5x

3)2 (iii) ( x + 3)

3 and ( 3x)

3

4) If A = 2y + 3 and B = 2y – 5 ,

a) Find A B b) Find B A

c) Why does A B = B A ?


Hw 2 continued

5) Find the quotient of each.

A) 215 10 5

5

x x B)

5 4 3

3

12 8 4

4

x x x

x

C)

3 2 2 2 221 15 6

3

a b c a b c abc

abc

D) 3( 7)

( 7)

x

x

E)

6( 2)

( 2)

x

x

F)

8( 2)

4( 2)

y

y

6) If the cost of a notebook is represented by 3x-1, express the cost of four notebooks.

7) A plane travels at a rate represented by (x + 70) kilometers per hour. Represent the distance it can

travel in (3x + 1) hours.

8) The cost of a pizza is 30 cents less than 8 times the cost of a soda. If x represents the cost of the soda

in terms of cents,

a) Express the cost of the pizza in terms of x

b) Express in simplest form the cost of 3 pizzas and 5 sodas.



Homework 3: Exponents – Review of basic properties (N-RN.1)

Review

1) Use the distributive property to write each as the sum of monomials in simplest form.

2 2) 5 ( 3) ) (3 5) 3 ) ( 3)( 4) ) ( 4) ) ( 2)( 4 5)a x x b x x c x x d a e x x x

2) Simplify each:

a) x5 x2

b) y4 y y3

c) 35 37

d) (2x) 3 (2x)

2

e) 6

2

x

x f)

16

4

y

y g)

9

3

4

4 h)

( )

( )

8

2

3x

3x

i) (3x) 2 j) (2x

2y

3) 3 k)

2

3 42x y

5

l) (-2x5) 3

m) (3x4

y3) (-4x

5 y

3) n)

( )

( )

10 5 7

5 5 9

24a b c

6a b c

o) 2

a 2b p)

x

y

3

3

q)

23x

2

r)

324x y

3a

s) x

y

3a

3a



Homework 4: Zero, Negative and Fractional Exponents (N-RN.1)

REVIEW 1) Simplify: 2 4 4

3 2

2x y 6 x z

3z 4 y 2) Simplify

33

2

2x

3y

3) Simplify each: Express all answers with positive exponents where applicable:

a) 30 b) (2x)

0 c) 4x

0 d) 4

-2 e) –2

-3

f) 2x-2

g)

2327 h)

3281 i)

1327

j)

238

k) (3x-2

y3) (5x

5y

-5) l) (4a

3b

-2c

-3)2 m)

5 -2 3

3 4 -2

12r s t

18r s t n)

( ) ( )

( )

2 1 2 3

3 2

5x y 3x

15x y

o) Write 0.0000567 in scientific notation. q) Write 38,200,000 in scientific notation.

4) Rewrite each without negative or fractional exponents. (Simplify if necessary)

A) 1

2x B)

2

3y C) x0 D)

2y E) 1x F)

1

2x

5) Write each as an exponent.

3 5 ?3) ) ) ) 1 ?A x B y C a D if x then


22 52 3 2 2 3 2 3

2 7

12 1)(4 )(3 ) ) ) (5 ) ( ) d) 27

4 5

a ba x y xy b c x x

a b


Homework 5: Removing Parentheses (A-APR.1, A-SSE.2)

Review

1) Simplify each using the laws of exponents.

In questions 2 – 12, remove parentheses and if possible combine like terms.

2) 6x+(4x-3) 3) 5a+(-8a-4b)

4) 9c-5g+(3g-4c) 5) (x+6y)+(5x-4y)

6) 28 (2 7 3)x x 7) 4 (3 5) 4 (3 8)a a x

8) 2[4 (3 5) 4]x x 9) 2 2 23 [ 5 (3 4) 5] 6x x x x x

10) 3x-4y+[3x-(3y-4x)]-(5x-8y) 11) 2 3 2 ( 5) 4 ( 3) 5x x x x x x x

12) ( 5)( 4) (x 6)(x 3)x x



Homework 6: Modeling (A-SSE.2, A-APR.1)

Review

1) Remove parentheses and if possible combine like terms.

4 4 2) (4 5) 6( 3) ( 4) ) (12 8 ) 3(4 2) ) (3 2)( 5)a x x x b x x x c x x

2) What algebraic expression is represented by this set of algebraic tiles?




2( 3 2 )x y z

HW 6 continued

5) Write the sum represented by the algebraic tiles

6) Simplify 4 3[5 2(3 ) 6 ]x x x x

7) Expand and simplify:

8) Use the geometric picture to represent (x + y)2

Evaluate (x + y)2

9) Consider the expression: ( 1) ( 2)x y x

a. Draw a geometric picture to represent the expression.

b) Write an equivalent expression by applying the Distributive Property


25 4 2x x 23 2?x x

HW 6 continued

10) Consider the expression : ( 2) ( 1)x y y



11) What must be added to in order to get



Homework 7: Geometric Applications (A-SSE.2, A-APR.1)

1) Represent the perimeter of a square each of whose sides is represented by

a) 5x + 3 b) 3x – 5

c) 2 3 2x x d) 2 22x xy y

2) The length of a rectangle is 5 more than its width. If x represents the width of the rectangle represent

the perimeter of the rectangle in terms of x

3) The length of a rectangle is represented by 5x – 3 and the width by 4x, represent the area of the

rectangle as a polynomial in simplest form.

4) The measure of the base of a triangle is represented by 4x+3 and the height is 6x, represent the area of

the triangle as a polynomial in simplest form.

5) a) Express the area of the outer rectangle in terms of x.

b) Express the area of the inner rectangle in terms of x.

c) Express the area of the shaded region as a polynomial in simplest form.




1) Simplify: 2 2(4 5 8) (2 6)x x x

2) Simplify:

3) Simplify:

4) What must be added to in order to get 27 2 15x x ?

5) From the sum of 2 2 24 7 5 5 8, 4 7 9x x and x x subtract x x .

6)

7) Simplify: 2 22 ( 3w 5 1)w w

8) Simplify: (2 3)(4 1)x x

9) Multiply:

10) If 3 2 4 3 2(2 3 4)( 3) 2 9 14 19 12x x Ax x x x x x , then what is the value of A?

22 6 12x x

( 1)( 3)2 2

x x

3 2( 6 4) (2 5 1)x x x x

[ ( 3)]x x x

4 3Multiply: 3a (2 3 1)a a


Hw 8 continued

11) The simplest form of (3 7)(2 1) (5 1)( 3)x x x x is a trinomial with positive coefficients. Find

the trinomial and the sum of the coefficients of the trinomial.

12) If 5 224x y is divided by 2 23 ,x y what is the quotient?

13) Which monomial is equivalent to 3 2(4 ) ?x

14) The expression 6 3

4 5

12

3

x y

x y is equivalent to

15) Consider the expression : ( 1) ( 2)x y y






2 22 2 10 8

2 2

4 4) 4 ) ) 4 )

x ya x y b c x y d

y x

5 6 5 6) 8 ) 8 ) 16 ) 16a x b x c x d x




1) Simplify -10y7 – 4y

7 (1) 14y

7 (2) -14y

7 (3) 6 (4) -14

2 ) When 3g2 – 4g + 2 is subtracted from 7g

2 + 5g - 1 , the difference is

(1) -4g2- 9g +3 (2) 4g

2 + g + 1

(3) 4g2 + 9g – 3 (4) 10g

2 + g + 10

3) From the sum of 7x2 – 4x + 5 and 2x

2 – 8x - 7 subtract 5x

2 + 2x + 5.

(1) 4x2 - 10x – 7 (2) 4x

2 - 14x + 3

(3) 4x2 - 14x – 7 (4) 14x

2 - 10x + 3

4) Simplify 3p2( p +4) + 5(p

3 – 2p

2 + 3)

(1) 10p5 + 15 (2) 8p

3 + 2p

2 +15

(3) 25p5 (4) 8p

3 – 10p

2 + 27

5) Find the product of (3x – 1)( x + 2)

(1) 3x2 – 2 (2) 4x + 1

(3) 3x2 – 5x – 2 (4) 3x

2 + 5x – 2

6) The length of a rectangle is one more than twice the width. If w represents the width of the rectangle,

which expressions represent the perimeter and the area of the rectangle?

(1) P = 6w +2, A = 2w2 + w (2) P = 4w + 1, A = 2w

2

(3) P = 6w + 2, A = 2w2 (4) P = 4w + 1, A = 2w

2 + w

7) Simplify ( 4x + 5)2

(1) 16x2 + 25 (2) 81x

2

(3) 16x2 + 40x + 10 (4) 16x

2 + 40x + 25


Hw 9 continued

8) Simplify : 32 +4 18 9

(1) 4 (2) 14

(3) 17 (4) 26

9) Simplify: 4 9

2 3

16

4

x y

x y

(1) 4 x2 y

3 (2) 12 x

2 y

3

(3) 4x2 y

6 (4) 12 x

2 y

6

10) Simplify: 3x5 y

-2 z

-3

(1) 5

2 3

3x

y z (2)

2 3

5

3y z

x

(3) 3(xyz)10

(4) (3xyz)30

11) If 2 25 3 7 and B=-3x +7x+5, then findA x x B A

12) Find the quotient ( x + 2)2 7 10x x

(1) x + 8 (2) x + 5

(3) x2 + 8 (4) x

2 + 5

13) Simplify:

3 2

7 7(5) (5)

(1)

6

7(5) (2)

6

7(25)

(3)

5

7(5) (4)

5

7(25)

14) Simplify: 6 3 3

3

24 18 9

3

x x x

x

(1) 8x3 – 6 +

6

3

x (2) 8x

2 – 6x + 3 (3) 8x

3 – 6 + 3x

6 (4) 8x

3 – 6 + 3x


2

2

2

2

) 2 5 3 1 64

) 2 5 3 1 70

) 2 5 3 1 48

) 2 5 3 1 52

a

b

c

d

Hw 9 continued

15) Combine the following expression

16) ) Consider the expression : ( 1) ( 1)a b a



17) Insert parentheses to make each statement true.

18) Fill in the blanks of this proof showing that ( 3)( 2)x x is equivalent to 2 5 6x x .

Write either “Commutative Property,” “Associative Property,” or “Distributive Property” in each blank.

(x+3)(x+2) = (x+3)x+ (x+3) × 2

= x(x+3)+ (x+3) × 2

= x(x+3)+2(x+3)

= x2 +x×3+2(x+3)

= x2 +3x+2(x+3)

= x2 +3x+2x+6

= x2 + (3x+2x) +6

= x2+5x+6


Unit 4 –Foundations - Radicals

Homework 1: Add/Subtract Radicals (A-REL.4A, N-RN.2)

1) Identify the rational and irrational numbers.

A) 3.14 B) 25 C) D) 1.37 E) 26 F)3

7 G)

2

3

2) Find the value of each.

A) 81 B) - 121 C) 3 27 D) 3 8 E)9

25 F) 3

125

8

3) Simplify each.

A) 18 B) 75 C) 128 D) 5 28

E) 1

202

F) 4 90 G) 5 24 H) 8 9x

I) 28x J) 2 350x y K) 5 6 927x y L) 3 53 54x y

4) Combine like terms:

A) 6 2 2 5 3 2 5 B) 7 3 9 7 3 3 C) 3 32 9 5 9

D) 4 11 3 11 2 11 5 11x y E) 3 6 7 3 2 6xy xy xy


6 5

Hw 1 continued

5) Perform the indicated operation and express the result in simplest radical form.

A) 3 8 2 B) C) 3 50 5 18

D) 7 2 18 2 50 E) 24 3 6 4 54 F) 5 12 3 75 147

G)2 23 12a a H) 3 3 12x x I)

12 50 98 72

2

J) 12 3 4 2 25x x x K) 3 350 2 32x x L)

3 3 3 35 16 250x x

6) Express the perimeter of the triangle in simplest radical form.

7) Express the perimeter of the rectangle in simplest radical form.

27 75

8 5

10 5

32

8


Unit 4 – Foundations - Radicals

Homework 2: Multiplication / Division of Radicals (A-REL.4A, N-RN.3)

Review

1) Perform the indicated operation and express the result in simplest form.

2 1) 4 5 20 ) 18 8 ) 4 27 3 48

3 2a b c x x


A) (5 3 )(7 2 ) B) (5 8)(3 5) C) (6 12 )(2 6 )x x

D) ( 2 + 3)(5 2) E) (2 5 6)(3 5 4 6) F) ( 12 7)( 12 7)


A) 2(5 3) B) ( 23 5) C) 50

2 D)

3 48

2

E) 15 56

3 7 F)

12 20 32 45

4 5

G)

30 60 18 15

6 3

4) Find the area of a square whose side is 5 3 .


Unit 4 – Foundations - Radicals Homework 3: Cumulative Review Questions (Unit 4)

1) What is the quotient of 8.05 × 106 and 3.5 × 10

2 ?

(1) 2.3 × 103 (2) 2.3 × 10

4 (3) 2.3 × 10

8 (4) 2.3 × 10

12

2) Write a mathematical proof using the associative and commutative properties of the algebraic

equivalency of 2 2 2( )xy x y

3) What is 32

4 expressed in simplest radical form?

(1) 2 (2) 2 2 (3) 8 (4) 8

2

4) Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She

budgets $29.50 per month for total cell phone expenses without taxes. What is the maximum number of

minutes Tamara could use her phone each month in order to stay within her budget?

(1) 150 (2) 271 (3) 421 (4) 692

5) Which expression is equivalent to (5x)3

1) 5 2) 4 5 3) 4 5 4) 5 5 5x x x x x x x x x x

6) Which expression is equivalent to (3x2)3 ?

(1) 9x5 (2) 9x

6 (3) 27x

5 (4) 27x

6

7) What must be added to in order to get ?

(1) (2)

(3) (4)

8) Simplify: 5 8

3 2

27

(4 )(9 )

k m

k m


Hw 3 continued

9) In a game of ice hockey, the hockey puck took 0.8 second to travel 89 feet to the goal line.

Determine the average speed of the puck in feet per second.

10) Express the product of 3 20 (2 5 7) in simplest radical form.

11) The following is a proof of the algebraic equivalency of 3(4 )x and 364x . Fill in each of the blanks

with either the statement “Commutative Property” or “Associative Property.”

(4x)3

= 4x ∙ 4x ∙ 4x

= 4(x× 4)(x×4)x

= 4(4x)(4x)x

= 4 ∙ 4(x× 4)x ∙ x

= 4 ∙ 4(4x)x ∙ x

= (4 ∙ 4 ∙ 4)(x ∙ x ∙ x)

= 64x3

12) Solve the following using the algebraic tiles.


Unit 5 – Solving Equations and Inequalities

Homework 1: Solving Linear Equations (A-CED.1, A-REI.3)

1) Solve and check each equation. State the answer in set notation and graphically.

a) 6b – 20 = 2b b) 5x + 3 = 15 + 2x c) 6x – 4 = 20 – 2x

d) 3x + x – 2 = 7 – 2x e) 18 – x = 4x + 3 f) 4 + 4a = 11a – 6

g) 4( 2x + 6) = 40 h) 3x + 2( 50 – x ) = 110 i) 8 – 4( x – 1 ) = 2 + 3(4 – x)

j) 1

(4 2) 152

x k) 2 (3 1) 3 (2 1) 2x x x x l) ( 2)( 4) ( 10)x x x x

2) One number is 4 times a second number. The sum of the two numbers is 35. Find the smaller

number.

3) The first number is 8 more than a second number. Three times the second number plus twice the first

number is equal to 36. Find the first number.



Homework 2: Foundations: Fractional, Decimal and Literal Equations (A-CED.1, A-REI.1,.3)

Review

1) Solve each and check:

a) 4x – 3 = 17 b) -12 = 5a + 8 c) 3(x + 2) = 15 d) 5y + 2y – 8 = 20

e) 7x – 5 = 5x + 21 f) 5( 2x – 5) = 6x +7 g) 6(x + 2) + 3(2x – 3) = 51

2) Solve each and check.

a) 5 23

x b)

3 25

2 3

x x c)

2 3

5 4 2

x x

d) 1 42

25 10

x e) 3 3

5 2

x f)

4

2 5

x

x

(x ≠ 2)

g) 2 4 5

8 5

x x h)

5 15

3 27x (x ≠ 0) i)

214

3 5

x x

3) Solve each and check.

a) 0.4x+ 12 = 16 b) 0.5a – 3.5 = 5.5 c) 0.06y + 3 = 4.8 d) 0.25x – 2 = 5


Hw 2 continued

4) Solve for x:

a) 3xyz = 6yz b) 3x + b =13b c) bx = ab + bc

d) ax + bx = c e) 3(x-2a) = 24a f) 3(x – a ) = 4(x – 2a)

5) Solve for a in terms of b: 2a – 3b = 5b

6) Solve for x in terms of a,b and c: ax – c = b

7) Solve for h in terms of V, l and w: V = lwh

8) Solve for h in terms of A and b: 2

bhA



Homework 3: True and False Equations (A-CED.1, A-REI.1,.3)

Review

1) Solve for x :

a) 5x – 9 + 4x = 5 – 3x – 12 b) ( 4)( 5) ( 2)( 4)x x x x

2) Find the value of C if F = 12, using the formula 5

( 32)9

C F

3) Given the equation 3 3x x , where x represents a real number .

a) Is this statement a number sentence ?

b) If it is a sentence , is it true or false?

c) For what value(s) of x is the equation true?










2( 5) 3 12x x


Homework 4: Applications /Fractional Equations (A-CED.1, A-REI.1,2,.3)

1) Determine which of the following equations have the same solution set by recognizing properties,

rather than solving.

9) 3 2 9 4 ) 9 6 12 27 ) 9x 6 ) .5 0.75 2.25

4a x x b x x c x d x x

2) Solve the equation for 𝑥. For each step, describe the operation and/or properties used to convert the

equation.

3) Consider the equation 6 3 4x x

a. Show that adding 𝑥 + 3 to both sides of the equation does not change the solution set.

b. Show that multiplying both sides of the equation by 𝑥 + 3 adds a second solution of 𝑥 = −3 to the

solution set.


Hw #4 continued

4) Find the value(s) of x that make each of the following expressions undefined.

5) Rewrite each equation into a system of equations excluding the value(s) of 𝑥 that lead to a

denominator of zero; then, solve the equation for 𝑥.

6) Given the formula d

rt

,

a) find the value of d when r=36 and t =9

b) rearrange the formula to solve for d

1 3 1) ) )

4 2

2 1 1) ) )

5 2 1 ( 3)

xa b c

x x x

xd e f

x x x x

5 1) 4 ) 2

1 3

2 4 6 3) 3 )

2 3 1 4

x xa b

x x

xc d

x x


Hw #4 continued

7) The area of a rectangle is 36 in2. The formula for area of a rectangle is A =lw

a) If the width w is 8 inches, what is the length?

b) If the width w is 12 inches, what is the length?

c) Rearrange the area formula to solve for l

8) If

9) If the formula for the perimeter of a rectangle is 2 2P l w then w can be expressed as

10) If ,a ar b r the value of a in terms of b and r can be expressed as

11) If ,ey

k tn what is y in terms of e,n,k, and t

3 , then x equals

(1) 3 (2) 3

(3) (4)3 3

ax b c

c b a c b a

c b b c

a a

2 2(1) (2)

2 2

2(3) (4)

2 2

l P P lw w

P l P ww w

l

1(1) 1 (2)

1(3) (4)

1

b b

r r

b r b

r r b

(1) (2)

( ) ( )(3) (4)

tn k tn k

e e

n t k n t k

e e


) 150 ) 150 ) 85 50 150 ) 85 50 150a e c b e c c e c d e c


Homework 5: Foundation: Inequality Expressions (A-CED.1, A-REI.1,.3)

1) Frank’s mother said the cost of his lunch of a hamburger, h, French fries, f, and a soda, s, together

must be less than $7. Write an inequality to represent this relationship.

) 7 ) 7 ) 7 ) 7a h s b h f s c h s f d h f s

2) A certain rectangle has a perimeter of at least 60. Given l represents the length of the rectangle

and w represents the width, select the inequality which represents this situation.

) 2 2 60 ) 2 2 60 ) 60 ) 60a l w b l w c l w d l w

3) A company manufactures two types of shoes, one expensive and one cheap. The company decides

that to make a profit they must manufacture at least 150 pairs of shoes. The expensive shoes cost $85 a

pair and the cheap ones cost $50. If e represents the number of expensive shoes produced

and c represents the number of cheap shoes produced, then which inequality represents this situation?

4) If a + b is less than c + d, and d + e is less than a+ b, then e is

a) less than d b) less than c c) greater than d d) equal to c

5) Six more than twice a number y is at least four times the number. Which of the following inequalities

best represents this information?

) 6 2 4 ) 6 2 4 ) 2 6 4 ) 2( 6) 4a y b y y c y d y y

6) If a, b, c and d are real numbers, c d , e > b, b > a and e c , then which of the following has the

greatest value.

a) a b) b c) c d) d



Homework 6: Foundations: Inequality Word Problems (A-CED.1, A-REI.1,.3)

1) Students in a school measured their heights, h, in centimeters. The height of the shortest student was

145 cm and the height of the tallest was 175 cm. Which inequality represents the range of the heights?

(1) 145 ≤ h ≤ 175 (2) 145 < h < 175 (3) h > 145 or h < 175 (4) h ≥145 or h ≤ 175

2) Which inequality is a correct translation of “ Ten less than four times a number is greater than 19”.

(1) 10 – 4n > 19 (2) 10 – 4n < 19 (3) 4n – 10 > 19 (4) 4n – 10 < 19

3) Which ordered pair is in the solution set of the following system of inequalities?

y ≥ -2x + 4 (1) (0,0) (2) (1,1) (3) (2,2) (4) (-1,-1)

x – y < 1

4) The set { 5,6,7,8} is equivalent to

(1) {x | 5 < x < 8, where x is a whole number}

(2) {x | 4 < x < 8, where x is a whole number}

(3) {x | 4 < x ≤ 8, where x is a whole number}

(4) {x | 5 < x ≤ 8, where x is a whole number}

5) Which value of x is in the solution set of 3

6 182

x ?

(1) 6 (2) 8 (3) 10 (4) 12

6) Which quadrant would be completely shaded in the graph of y ≥ 2x?

(1) Quadrant I (2) Quadrant II (3) Quadrant III (4) Quadrant IV

7) Which interval notation represents the set of all numbers greater than or equal to 2 and less than 10?

(1) ( 2, 10) (2) ( 2, 10] (3) [2, 10) (4) [2,10]

8) Find the solution set for the following inequality. -2( x – 3) < 8



Homework 7: Solving Inequalities (A-CED.1, A-REI.1, A-REI.3)

Review:

1) Determine which of the following equations have the same solution set by recognizing properties,

rather than solving.

a) 3x + 5 = 12 – 7x b) 15 + 9x = -21x + 36

c) 7

4(3 5) 34

xx d) 0.6 1.0 2.4 1.4x x

2) Find the solution set of each. Express the solution in set notation and graphically on a number line.

a) 3x – 5 < 16 b) 4x – 3 > x + 21 c) 5( y – 2) ≤ 3y – 4

d) 5 – 3x ≥ 2x – 30 e) -3(x – 2) < 2(x -2) f) -4x + 1 > 9

g) If y is an integer, what is the solution set of -3 ≤ y < 1?

(1) { -3, -2, -1, 0, 1} (2) { -3, -2, -1, 0}

(3) { -2, -1, 0, 1} (4) { -2, -1, 0 ,1 }

3) Six more than 4 times a whole number is less than 60. Find the maximum value of the number.

4) Jane weighs 3 times as much as Barbara. The sum of their weights is less than 160 pounds. Find the

greatest possible weight for each girl if their weights are whole numbers.

5) Three times a number increases by 8 is at most 40 more than the number. Find the greatest value of

the number.



Homework 8: Inequalities Joined by “AND” or “OR” (A-CED.1, A-REI.1,.3)

Review:

1) Find the solution set of each. Express the solution in set notation and graphically on a number line.

a) 2 5 7x b) 4 2(5 3)x x c) 10 20 10(3 4)x x

2) Solve each compound inequality for 𝑥 and graph the solution on a number line.

b) 2 1 11 4 3 5 2x or x x

) 3 4 7d x

3) State whether the following statements is sometimes, always or never true and justify your answer.

a) If x < y, then x + a < y + a

b) If x < y, then x – a > y – a

c) if x < y then ax < ay

d) If x<y, thenx y

a a

) 4 2 12 8 4 16a x or x

) 3 2 5 11e x

) 4 2 4c x

1) 3 5

2

xf




1) Olivia solved the linear equation as follows:

She made an error between lines

a) 1 and 2 b) 2 and 3 c) 3 and 4 d) 4 and 5

2) Solve for x:

3) Solve for g:

4) Solve algebraically for x:

5) Which value of x is the solution of the equation ?

1) 1

2) 2

3) 6

4) 0

6) What is the value of x in the equation ?

1) 2) 2

3)

4)

4( 3) 2 15x [Line1] 4( 3) 2 15

[Line2] 4(x 3) 17

[Line3] 4 3 17

[Line4] 4 14

14 1[Line5] 3

4 2

x

x

x

x or


Hw # 9 continued

7) Which inequality is represented in the graph below?

1) 2) 3) 4)

8) Solve each compound inequality for 𝑥 and graph the solution on a number line.

9) A formula used for calculating velocity is 21.

2v at What is a expressed in terms of v and t?

10) Rewrite each equation into a system of equations excluding the value(s) of 𝑥 that lead to a

denominator of zero; then, solve the equation for 𝑥.

) 6 4 14 6 4 14a x or x ) 2 5 9b x

2

2

2 2(1) (2)

(3) (4)2

v va a

t t

v va a

t t

1 10) 5 ) 5

3

xa b

x x




1) If p = 2(l + w), which of the following is the solution for l in terms of p and w?

(1) 2

2

p wl

(2)

2

p wl

(3) l = p – w (4) l = 2p – w

2) Solve for x: 1 2 7

3 3x x (1) 1 (2) 2 (3) 3 (4) 4.5

3) Which value of x is in the solution set of the inequality -2x + 5 > 17?

(1) -8 (2) -6 (3) -4 (4) 12

4) Mark currently has collected 65 rare coins. If he buys c coins for w weeks, which expression

represents the total number of coins that he will have?

(1) 65cw (2) 65 + cw (3) 65c + w (4) 65 + c + w

5) What is the solution of 4 9

2 3

k k ?

(1) 1 (2) 5 (3) 6 (4) 14

6) If 3ax + b = c, then x equals

(1) c – b + 3a (2) c + b - 3a (3) 3

c b

a

(4)

3

b c

a

7) Solve for g: 3 + 4g = 5g – 9


22 3 9 1 1 2

3 3 6

4(5 8) 4 5 8

Hw 10 continued

8) Simplify: (25t2v + 20tv – 7t) – (14t

2v – 11t)

9) Write the algebraic equation or inequality that represents the following situations.

a) The distance d of an object is one half the product of the gravitational constant g and the square

of the time t.

b) The sum of a number n and its reciprocal is less than 16.

10) Solve for c in the following equation: ( )

2

a b cS

11) Identify which of the following are algebraic expressions. Are they also number sentences?

a) 4x-5=12 b) 2x2+5x c) d)

12) Determine whether the following number sentences are true or false.

40

) 12 8 )2

a b 2 2 23 4 5 c) 2

.6673 d)

13) In the following equations, let x = -4 and y = 34

. Determine whether the following equations

are true, false or neither true nor false.

a) xy = -3 b) x - 4y = -7 c) 8y = -2x d) x + z = 6

14) The function f has a domain of {2,4,6,8} and a range of {1,3,5}.

Could f be represented by {(2,1), (4,3), (6,5), (8,3)}?



Unit 6 – Solution Sets to Equations with Two Variables

Homework 1: Foundations: Verbal Problems (A-CED.1, A-CED.2, A.REI.3)

1) The ratio of 3 numbers is 2:3:5 and the sum of all three numbers are 180. Find the three numbers.

2) The larger of two integers is 4 times the smaller. If the sum of the two integers is 70, find both

integers.

3) The sum of three consecutive integers is 30. Find the largest integer.

4) One more than three times x is less than 22. Find the greatest integer for x.

5) Carlos has a total of 84 coins consisting of just nickels and dimes. The total value of the coins is

$7.15. How many dimes does he have?

6) Jack has $1.55 in nickels and dimes. He has 7 more nickels than dimes. Find the number of dimes.

7) Joy has 16 coins, some quarters and the rest nickels. The value of all her coins is $1.40. Find the

number of each kind of coin.

8) Karen and Mark left from the same place at the same time and drove in opposite directions along a

straight road. Mark traveled 15 miles per hour faster than Karen. After 3 hours they were 315 miles

apart. Find the rate at which each traveled.


Hw 1 continued

9) Two trains leave a station, one traveling north at a rate of 50 m.p.h. and the other south at the rate of

55 m.p.h.. In how many hours will they be 735 miles apart?

10) How fast did a car go to overtake a truck in 5 hours if the truck travels at 30 M.P.H. and left 3 hours

before the car?

11) Josh earns $8.00 an hour when he works on Monday. If he works any other day, he earns $12.00 an

hour. During the last week, Josh worked a total of 46 hours and made $528. How many hours did he

work on Monday?

12) There were 580 admission tickets sold. There were 3 times as many 50 cent tickets sold as 25 cent

tickets. Find the number of each.

13) Mr. George is 3 times as old as his son. In 12 years he will be twice as old. Find Mr. George’s age

now.

14) Ashley is 6 years older than Amy. In 2 years Ashley will be twice as old as Amy. Find their ages

now.

15) How many pounds of coffee worth $1.54 a pound should be blended with coffee worth $1.70 a

pound to make 40 pounds of blended coffee worth $1.60 a pound?


Hw 1 continued

16) Peter has a cell phone plan that charges a monthly fee of $15.00 per month for on-line usage plus a

$.05 per minute charge for any minutes over 300 minutes. What is the maximum number of minutes

Peter can use to stay within his budget of $24.00 for on-line usage?

17) The length of a rectangular room is 9 less than four times the width, w, of the room.

a) Represent the length of the room in terms of w.

b) Represent the area of the room in terms of w.

c) Represent the perimeter of the room in terms of w.

18) The ages of 3 sisters are consecutive odd integers. Four times the age of the youngest sister exceeds

the oldest sister by 23 years. What is the age of the youngest sister?

19) Marie ran a distance of 450 meters in 1

42

minutes. What was her speed in meters per hour?

20) Tom has 7 more books than John. Gary has twice as many books as Tom. If n represents the

number of books that John has, write an expression in terms of n, for the number of books that Gary

has.

21) Juan and Debbie each earn $9 per hour at their jobs. Debbie worked five hours more than Juan

during the week. If Juan and Debbie earned a total of $765 for the week, how many hours did

Debbie work?



Homework 2: Foundations: Graphing Linear Functions (F-IF.2)

1) Graph each of the following using the table method. Show at least 4 sets of points for each.

a) 3

42

y x b) 2 3 6x y

x y

c) 3( 1)y x d) 8.5 2y x

e) 2 4x y f) 2y



Homework 3: Graphs of Linear Equations (A-CED.1, A-CED.2, A.REI.3)

Review:

1) Graph 2 3 1y x 2) Graph 2 3 6x y

3) a) Find five members of the solution set of the sentence 3x + y = 8.

b) Create a graph that represents a solution set to the equation.

4) The difference of two numbers is 5. What are the possible numbers?

a) Create an equation using two variables to represent this situation. Be sure to explain the meaning of

each variable.

b) List at least 6 solutions to the equation you created in part (a).

c) Create a graph that represents the solution set to the equation.


Hw 3 continued

5) John has 25 coins, some are nickels and the rest are dimes. What are the possible number of nickels

and dimes.


each variable.

b) List at least 6 solutions to the equation you created in part (a).


6) The Math Club sells hot dogs at a school fundraiser. The club earns $120 and has a combination of

five-dollar and one-dollar bills in its cash box. Possible combinations of bills are listed in the table

below.

Number of five-dollar bills Number of one-dollar bills Total = $120

12 60 5(12) + 1(60) = 120

16 40

13 55

2 110

a. Find one more combination of ones and fives that

totals $120.

b. The equation 5𝑥 + 1𝑦 = 120 represents this situation.

Graph the line = −5𝑥 + 120 . Verify that each

ordered pair in the table lies on the line.

c. What is the meaning of the variables (𝑥 and 𝑦) and the

numbers (1, 5, and 120) in the equation 5𝑥 + 1𝑦 =120?



Homework 4: Foundations–Graphs of Simultaneous Equations (A-REI.6, A-REI.10, F-IF.1)

Review

1) If the point lies on the line represented by the equation , the value of k is

(1) 1 (2) 2 (3) -1 (4) -2

2) The sum of two numbers is 8. What are the possible numbers?


each variable.

b) List at least 6 solutions to the equation you created in part

(a).


3) On the given set of axes, solve the following system of equations graphically. State the coordinates

of the solution.

) 6

10

b y x

x y

) 4

2

a y x

x y


Hw 4 continued

4) On the given set of axes, solve the following system of equations graphically. State the coordinates of

the solution.

) 4 3 11

2 1 5

b x y

x y

) 5 3

3 2 8

a x y

y x

) 0

2

c x y

y x

) 5 2 7

3 5

d x y

x y

) 2 6 7

5 4 8

e x y

x y

) 2 5 3 0

6 2 0

f x y

x y



Homework 5: Simultaneous Equations Algebraically (A-REI.6,12)

Review:

1) On the grid, solve the system of equations graphically for x and y. y = -2x – 1

4x – 2y = 18

2) A system of equations is graphed on the set of axes below. The solution of this system is

(1) ( 0 , 4 )

(2) ( 2 , 4 )

(3) ( 4 , 2 )

(4) ( 8 , 0 )

3) Solve the following system of equations algebraically using the elimination method.

) 12

4

a x y

x y

) 3 10

4 11

b x y

x y

) 5 3 39

3

c x y

x y

) 12 9 21

10 6 10

d a b

a b

) 5 3 12

8 2 8

e x y

x y

) 3 2 10

4 5 18

f x y

x y


Hw 5 continued

4) Solve the following system of equations algebraically using the substitution method.

5a) Without graphing, construct a system of two linear equations where (0,1) is a solution to the first

equation but not to the second equation and where (2, 3) is a solution to the system.

5b) Graph the system and label the graph to show that the system you created in part (a) satisfies the

given conditions.

)

6

a y x

x y

) 6

4 3 27

b y x

y x

) 1

4 19

c y x

y x

) 2 3 7

3 2 4

d x y

x y

2)

3

5 34

e y x

y x

) 2

3 2 21

f y x

y x


Hw 5 continued

6) Consider two linear equations. The graph of the first equation is shown. And a table of values

satisfying the second equation is given. What is the solution to the system of the two equations?

7) For each question below, provide an explanation or an example to support your claim.

a) Is it possible to have a system of equations that has no solution?

b) Is it possible to have a system of equations that has more than one solution?

8) Solve the following system of equations first by graphing and then algebraically.

X value -2 -1 0 1 2

Y value 4 2 0 -2 -4

3 4 3

12 2 5

x y

x y



Homework 6: System of Inequalities (A-REI.6, A-REI.12)

Review:

1) Solve the following system of equations first by graphing and then algebraically.

2) Graph the solution set for the inequality 4x – 3y > 9 on the set of axes below. Determine if the point

(1, -3) is in the solution set. Justify your answer.

3) Which ordered pair is in the solution set of the system of linear inequalities graphed?

(1) ( 1, -4) (2) ( -5, 7) (3) (5 , 3) (4) ( -7 , -2)

2( 4) 3( 2)

4( 2) 5( 2)

x y

x y


Hw 6 continued

4) On the set of axes, graph the following system of inequalities and state the coordinates of a point in

the solution set.

) 1

1

a y

y x

) 2

3

b y x

y x

2) 2

3

4

c y x

x y

) 2 6

2

d x y

y x

) 3

3

0

e y x

y x

y

) 2

2

0

f y x

y x

x



Homework 7: Applications of Systems (N-Q.1, A-SSE.1A,A-CED1,2,3)

Review:

1) Explain a way to create a new system of equations with the same solution as the original

that eliminates variable 𝒚 from one equation, and then determine the solution.

ORIGINAL SYSTEM NEW SYSTEM SOLUTION

2) The sum of two numbers is 32 and their difference is 4. What are the numbers?

a) Create a system of two linear equations to represent this problem.

b) What is the solution to the system?

3) The difference between two numbers is 24 and their sum is 48. Find the two numbers



4) If 2 3 8 2 3x y and x y , then find the value of

) 3 ) 5a x y b x y

5 3 12

2 8

x y

x y


Hw 7 continued

5) Solve the system of equations: by graphing.

Then, create a new system of equations that has the same

solution. Show either algebraically or graphically that the

systems have the same solution.

6) Without solving the systems, explain why the following systems must have the same solution.

7) George and Tim together weigh 210 pounds. The difference between three times George’s weight

and twice Tim’s weight is 30 pounds. Find the weight of each.

8) There are 242 admissions tickets sold. Three times the number of 50 cent tickets is 12 more than four

times the number of 75 cent tickets. Find the number of 50 cent tickets sold.

22 3

3y x and y x

systemi 5 -3 system ii 15 3 -9

2 -3 -8 7 2 11

x y x y

x y x y


Hw 7 continued

9) A 20 acre orchard is planted with apple and peach trees. At most $10 000 can be spent on planting

costs. Planting cost for apple trees is $400/acre and for peach trees $1000/acre.

a) What are the variables?

b) Write inequalities for the constraints.

c) Graph and shade the solution set.

.

10) Ace Wheels Co. manufactures BMX and Mountain bikes. The plant equipment limits both kinds that

can be made in one day. The limits are as follows:

No more than 10 BMX bikes

No more than 15 mountain bikes

No more than 20 total

a) What are the variables?

b) Write inequalities for the constraints.

c) Graph and shade the solution set.



Homework 8 - Rates and Algebra Solutions (N-Q.1, A-SSE.1A, A-CED.1, .2, .3)

Review:

1) If 2 2

17 4,a b and a b find

a b

2) The difference between two numbers is 4. Twice the larger number is equal to three times

the smaller number increased by 2. Find the two numbers



3) Solve each of the following for x

4) Solve the following problem first using a tape diagram and then using an equation:

a) In the gymnasium at school, there are 300 students. The ratio of boys to girls is 3:2. Find the number

of boys and girls in the gymnasium.

b) In the computer class, the number of boys is 3 times greater than of girls. If there are 60 female

students, how many boys are in the class?.

c) Two numbers are in the ratio 3:7. The smaller number is 12 less than the larger number. Find the

numbers.

5 1) )

4 12 3 8

5 4 4 21) )

2 2

x xa b

x

xc d

x x x



Homework 9 - Unit 6 Review

1) A taxi ride costs 45 cents for the first mile and 25 cents for each succeeding mile. Write a formula for

the cost,  , in cents, of riding  miles where is an integer greater than 1.

2) A jogger observed children and dogs playing in a park. The jogger counted 12 heads and 30 legs. How

many children and how many dogs were playing in the park? Show how you arrived at your answer.

3) Frank has 28 coins. Some are nickels and some are dimes. The sum of the number of nickels and 3

times the number of dimes is 40. Find the number of nickels and dimes.

4) Robert bought 8 dollars’ worth of 6 cent stamps and 8 cent stamps. He has a total of 110 stamps.

Find how many of each stamp he has.

5) Olive is on vacation in New York City. One day she

decides to rent a bike. Power Cyclers charges $20

plus $3.50 per mile. Manhattan Cyclers charges $14

plus $5 per mile.

a) Write a cost equation for each bike rental in terms of

the number of miles.

b) Graph both cost equations.

c) For what trip distances should a customer use Power

Cyclers?

d) For what trip distances should a customer use

Manhattan Cyclers? Justify your answer algebraically and show the location of the solution

on the graph.




1) When solving the equation 2 24(2 5) 7 3 14x x , John wrote 2 24(2 5) 3 7x x as his first


a) addition property of equality b) subtraction property of equality


2) If 2ax - 3b = 5c, then x equals

(1) 5 3

2

c b

a

(2)

3 5

2

b c

a

(3) 5c + 3b – 2a (4)

5 3

2

c b

a

3) Which equation represents a line parallel to the x – axis?

(1) x = 5 (2) y = 10 (3) x = 1

3y (4) y = 5x + 17


(1) (2) (3) (4)

5) Which inequality is represented by this graph?

(1)

(2)

(3)

(4)


Hw 10 continued

6) What is the solution of 5 10

2 3

a a ? (1) 3 (2) 5 (3) 8 (4) 10

7) On a certain day in Toronto, Canada, the temperature was 15 Celsius (c). Using the formula

F = 9

325

C , Peter converts this temperature to degrees Fahrenheit (F). Which temperature represents

15C in degrees Fahrenheit?

(1) -9 (2) 35 (3) 59 (4) 85

8) Which value of x is in the solution set of the inequality -3(x + 2) < 6?

(1) -12 (2) -6 (3) -4 (4) -3

9) Maureen tracks the range of outdoor temperatures

over three days. She records the following information.

Express the intersection of the three sets as an

inequality in terms of temperature, t


the solution set.

2x – y ≥ 6

x > 2


Hw 10 continued

11) Victor takes 2 pages of notes during each hour of class. Write an equation that shows the

relationship between the time in class h and the number of pages p.

12) During a 45-minute lunch period, Albert (A) went

running and Bill (B) walked for exercise. Their

times and distances are shown in the

accompanying graph. How much faster was

Albert running than Bill was walking, in miles per

hour?

13) If the value of dependent variable y increases as the value of independent variable x increases, the

graph of this relationship could be a

a) horizontal line b) line with a negative slope

c) vertical line d) line with a positive slope

14) Draw a distance–time graph to show the following story.

Mary walked from home up the steep hill opposite her house. She stopped at the top to put her

skates on, then skated quickly down the hill, back home again.


Unit 7 – Statistics

Homework 1: Foundations: Relationships (S.ID.2,S-IC.1)

1) Determine whether each sample is biased or unbiased.

a) To determine whether a school should add a weight room, the first 5 football players that entered

the gym that day were surveyed.

b) To determine the preferred candidate for mayor, a newspaper asks readers to send in their opinion.

c) To determine which 3 members of a class will address the school board, all their names were

written on individual index cards, the cards all placed in a box that was shaken and 3 cards were

picked from the box.

2) Determine whether the given data sets can be classified as qualitative or quantitative.

a) The heights of the members of the basketball team.

b) The ages of the teachers in the school

c) The opinions of the parent council regarding school vacations.

d) The ratings of a professor as excellent, good or poor.

3) Determine if the situation should be analyzed using univariate or bivariate statistics.

a) John keeps track of his math grades for the marking period.

b) Melissa records her times for running the mile every week.

c) A farmer wishes to see the relationship between amount of rainfall and the height of his corn.

d) A student wishes to see the relationship between the amount of time spent on video games the

night before a test and the grade on the test.

4) Which of the following demonstrate a casual relationship and which do not.

a) The faster the race car, the sooner the car finishes the race.

b) If the number of packages to ship increases, the space needed in the van increases.

c) A song about the rain on the radio is heard and dark clouds appear.

d) Cutting a roll into two pieces and not finding butter in the refrigerator.

5) Find the mean, median and mode of each of the following data sets.

a) 1, 3, 6, 7, 9, 9, 10

b) 10, 14, 14, 16, 20, 21, 23, 26



Homework 2: Foundations: Histograms, Box & Whisker, Stem & Leaf (S-ID.1, S-ID.2)

1) Ms. Hopkins recorded her students' final exam scores in the frequency table below.

a) On the grid below, construct a frequency histogram based on the table.

b) Would you describe your graph as symmetrical or skewed? Explain your choice.

2) The Fahrenheit temperature readings on 30 April mornings in Stormcity, New York, are shown below.

a) Using the data, complete the frequency table below.

b) On the grid below, construct and label a

frequency histogram based on the table.

3) The following set of data represents the scores on

a mathematics quiz:

Complete the frequency table below and, on the accompanying grid,

draw and label a frequency histogram of these scores.

41 , 58 , 61 , 54 , 49 , 46 , 52 , 58 , 67 , 43 ,

47 , 60 , 52 , 58 , 48 , 44 , 59 , 66 , 62 , 55 ,

44 , 49 , 62 , 61 , 59 , 54 , 57 , 58 , 63 , 60

58, 79, 81, 99, 68, 92, 76, 84, 53, 57,

81, 91, 77, 50, 65, 57, 51, 72, 84, 89


Hw 2 continued

4) The test scores from Mrs. Gray’s math class are shown below.

Construct a box-and-whisker plot to display these data.

5) Using the line provided, construct a box-and-whisker plot for the 12 scores below.

6) Make a stem and leaf display for the weights of carry-on luggage in pounds. Also provide a key.

30 27 12 42 35 47 38 36 27 35

22 17 29 3 21 0 38 32 41 33

26 45 18 43 18 32 31 32 19 21

33 31 28 29 51 12 32 18 21 26

7) Law Enforcement: Speeding is a serious offense. The following data give the ages of a random

sample of 50 drivers ticketed for speeding in a 40 MPH zone.

46 16 41 26 22 33 30 22 36 34 63 21 26 18 27 24 31 38

26 55 31 47 27 43 35 22 64 40 58 20 49 37 53 25 29 32

23 49 39 40 24 56 30 51 21 45 27 34 47 35

(a) Make a stem-and-leaf display of the age distribution.

72, 73, 66, 71, 82, 85, 95, 85, 86, 89, 91, 92

26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10



Homework 3: Distributions and Their Shapes (S-ID.1, S-ID.2, S-ID.3)

1) James asked members of his class which kind of movie they liked the best. The results are in the

table below.

a) Create a Dot Plot for the data above.

b) What do you think this graph is telling us about the classes favorite movies?

c) Can you think of a reason why the data presented by this graph provides important information? Who

might be interested in this data distribution?

d) Would you describe this dot plot as representing a symmetric or a skewed data distribution?

2) A sample of 20 colleges and universities with the following class sizes are shown below.

a) Create a Dot Plot for the data above.

b) What do you think this graph is telling us about the class size in most colleges?

c) Can you think of a reason why the data presented by this graph provides important information? Who

might be interested in this data distribution?

d) Would you describe this dot plot as representing a symmetric or a skewed data distribution?

14 20 20 20 20 23 25 30 30 30

35 35 35 40 40 42 50 50 80 80


Hw 3 continued

3) The data set 5, 6, 7, 8, 9, 9, 9, 10, 12, 14, 17, 17, 18, 19, 19 represents the number of hours spent on the

Internet in a week by students in a mathematics class. Which box-and-whisker plot represents the

data?

4) What is the value of the third quartile shown on the box-and-whisker plot below?

5) The box-and-whisker plot below represents 20 students' scores on a recent English test.

a) What is the value of the upper quartile?

b) What do you think the box plot tells us about the students’ 20 scores on the English test?

c) Why might understanding the data behind this graph be important?

6) The box-and-whisker plot below represents the math test scores of the same 20 students.

a) What percentage of the test scores are less than 72?

b) What do you think the box plot tells us about the students’ 20 scores on the Math test?

c) Why might understanding the data behind this graph be important?

d) What can you say about the math test versus the English test results?


Hw 3 continued

7) The accompanying histogram shows the heights of the students in Kyra’s health class.

a) What is the total number of students in the class?

b) What do you think this graph is telling us about the

heights of the students in Kyra’s health class?

c) Why might we want to study the data represented

by this graph?

d) Based on your previous work with histograms, would you describe this histogram as representing a

symmetrical or a skewed distribution? Explain your answer.

8) The accompanying histogram shows the scores of students on a Math regent.

a) How many students have scores of 96 to 100?

b) What do you think this graph is telling us about the

difficulty of this math test?

c) Why might we want to study the data represented by this graph?

d) Based on your previous work with histograms, would you describe this histogram as representing a

symmetrical or a skewed distribution? Explain your answer.



Homework 4: Describing the Center of a Distribution (S-ID.2)

Review:

1) The following cumulative frequency histogram shows the distances swimmers completed in a recent

swim test.

a) Based on the cumulative frequency histogram, determine the

number of swimmers who swam between 200 and 249 yards.

b) Determine the number of swimmers who swam between 150

and 199 yards.

c) Determine the number of swimmers who took the swim test.

d) Why might we want to study the data represented by this

graph?

e) Based on your previous work with histograms, would you

describe this histogram as representing a symmetrical or a

skewed distribution? Explain your answer.

2) Find the mode of the following data: 87, 98, 85, 90, 98, 78, 93, 87, 76, 98

3) Find the median of the following set of data: 23, 25, 12, 25, 15, 20, 18

4) Find the mean of the following set of data: 90, 88, 94, 95, 81

5) Find the mode, median and mean of the following set of data: 25, 28, 15, 32, 27, 23, 28, 22, 30, 21,

28, 15, 20, 30, 24

6) a) Find the mean, median and mode of the data presented in the given frequency table.

b) Construct a dot plot of the data

.


Hw 4 continued

7) If the mean of a set of data is 32 and the data includes 30, 35, 28, 25, 32, and x. Find the value of x.

8) If the median of a set of data is 50 and the data includes 25, 67, 75, 48, and x. Find the value of x.

9) Which of the following statements is true about the data 25, 37, 45, 40, 37, 39?

(1) median = mode (2) mean > median (3) mean < median (4) mode > mean

10) Using the data in the given frequency table, which of the following statements is true about the data?

(1) median = mode (2) mean > median (3) mean < median (4) mode > mean

xi fi

65 8

75 4

85 5

95 3

11) The table below provides the average retail price (cents per kilowatt-hour) to residential customers

of the New England states in October of 2009. Find the mean, median and mode of this data.

a) Compute the mean and the median.

b) If you wanted to describe a typical price for

electricity, would you use the mean or the median?

Justify your choice.

12) Using the scores 47, 45, 33, 67, 47, 55, 42 and x. What is the value of x if it is the median of the

data? What is the value of x if it is the mean of the data?


13) A sample of 20 colleges and universities reported the following class sizes.

a) Compute the mean, median and mode.

b) If you wanted to describe the typical class size at college, would you use the mean or the median?


14) The Humanities Division recorded the number of students signed up for the Student Abroad

Program each quarter. The results are

a) Compute the mean, median and mode.

b) If you wanted to describe the typical number of students who sign up for Student Abroad

Program, would you use the mean or the median?


14 20 20 20 20 23 25 30 30 30

35 35 35 40 40 42 50 50 80 80

58 26 21 26 33 47 42 36 44 56

52 64 68 59 63 36 34 45 51 50



Homework 5: Interpreting the Mean as a Balance Point (S-ID.1,2,3)

Review:

1) The data below are the calories in an ice cream bar. Find the quartiles and draw a box and whisker

plot. Label all aspects.

2) Make a stem and leaf display for the weights of carry-on luggage in pounds. Also provide a key.

Find the mean and the median. If you wanted to describe the typical weight of carry-on luggage

would you use the mean or the median?

Justify your choice

3) Estimate the balance point in each dot plot below by placing an arrow on the number line.

a)

b)

c)

342 377 319 353 295 234 294 286 377 1 82 310 439 1 11

201 1 82 1 97 209 1 47 1 90 1 51 1 31 1 51

30 27 1 2 42 35 47 38 36 27 35

22 1 7 29 3 21 0 38 32 41 33

26 45 1 8 43 1 8 32 31 32 1 9 21

33 31 28 29 51 1 2 32 1 8 21 26


Hw 5 continued

4) Compute the mean for each part of question 3. How does the calculated mean score compare

with your estimated balance point?

5) Draw a dot plot of a data distribution representing the weight of twenty people for which the median

and the mean would be approximately the same.

6) Draw a dot plot of a data distribution representing the weights of twenty people for which the median

is noticeably less than the mean.


Hw 5 continued

7) The following data represents the size of the diameter of sample roses from two florist

RoseA Florist:

RoseB Florist:

a) Draw a dot plot for RoseA and a dot plot for RoseB

b) Estimate the balance point for RoseA

c) Compute the mean and median for RoseA

d) Estimate the mean and median for RoseB

e) Is the mean diameter for RoseA less than, approximately equal to, or greater than the

median size? If they are different, explain why. If they are approximately the same, explain

why.

f) Is the mean diameter for RoseB less than, approximately equal to, or greater than the median

size? If they are different, explain why. If they are approximately the same, explain why.

2,3,5,5,7,7,8,8,9

1,2,3,4,6,7,7,10,14


Unit 7– Statistics

Homework 6: Summarizing Deviations from the Mean (S-ID.2)

(Unless otherwise directed, round to the nearest tenth, when appropriate.)

Review:

1) Find the mean, median and mode of the following set of data. Draw the dot plot.

15, 27, 16, 18, 23, 18, 20, 24, 18, 22, 16, 24, 18, 14, 25

2) For each set of scores, find the range

a) 26, 67, 45, 62, 46, 15, 49, 55, 32 b) 15, 23, 7, 34, 12, 16, 35, 27, 19

3) The following is a list of ages of participants entered in a 5K race.

a) Compute the mean

b) Calculate the deviations from the mean for these ages, and write your answers in the

appropriate places in the table below.

4) What percentage of Canada goose nests are successful (at least one gosling survives)? Studies in

regions of Montana, Illinois, Wyoming, Utah, and California gave the following percentage of

successful nests:

23.9 52.5 60.0 68.5 78.6 71.0 17.8 57.5 59.0 52.0

a) Compute the mean.



24 31 8 29 36 55 42 40 24 1 9

43 38 1 8 32 50 1 0 24 35 25 28



Homework 7: Measuring Variability for Symmetrical Distributions (S-ID.2)

Review:

1) The average snowfall in January for some cities is shown in the table.


b) Calculate the deviations from the mean for

these ages, and write your answers in the


2) What are the standard deviations of the following set of data?

158, 180, 123, 153, 176, 135, 192, 156, 144 (answer to the nearest tenth)




c) Find the sum of the squared deviation

d) What is the value of 𝒏 for this data set? Divide the sum of the squared deviations by n-1

e) State the standard deviation.


Hw 7 continued

3) The table shows the average daily high temperature

in July for various vacation cities. Calculate, to the

nearest tenth, the mean temperature, the standard

deviation of these temperatures.


b) Calculate the deviations from the mean for these

ages, and write your answers in the appropriate

places in the table below.


d) State the standard deviation.

4) A random sample of 7 Northern Pike from Taltson Lake (Canada) gave the following lengths rounded

to the nearest inch.

21 27 46 35 41 36 25








Homework 8: Interpreting the Standard Deviation (S-ID.2, S-ID.5, S-ID.9)

Perform the following questions using a calculator

Review:

1) If all of the scores on a test were 85, what is the mean? What is the standard deviation?

2) If the variance of a set of data is 64, what is the standard deviation?

3) The given table shows the ages of children who attended a recent “children’s movie” at a local

theater. (a) What is the mean age of the children attending to the nearest hundredth? (b) What are

the mode and the median of the data?

4) Both of the following sets of data have the same mean. Without actually calculating the mean or the

standard deviation, which set would appear to have the smaller standard deviation?

A) 40, 50, 55, 60, 45 B) 20, 85, 55, 50, 40

5) Check your answers by finding each mean and standard deviation.

Can you explain what causes the difference in standard deviations?

6) a) If all students were given a 5-point bonus on a particular test, what change (if any) would occur to

the mean of that test?

(b) What change (if any) would occur to the median?

(c) What change (if any) would occur to the standard deviation.


Hw 8 continued

7) a) If all workers salary were to be doubled, what change (if any) would occur to the mean of those

salaries?

(b) What change (if any) would occur to the median?

(c) What change (if any) would occur to the standard deviation.

8) The following data represents the annual snowfalls (in inches) for a city in northern Wisconsin.

24 37 28 13 38 29 112 21 40 36

46 81 15 47 22 20 119 41 62 18

a) Find the mean b) Find the standard deviation

9) A random sample of 6 people, each 20 pounds overweight, volunteered to go on the same diet. After

3 months, their weight loss (in pounds) were

12 5 14 19 15 8

a. Find the range. _________ c. Find the variance ___________

b. Find the mean _________ d. Find the standard deviation __________

10) What percentage of Canada goose nests are successful (at least one gosling survives)? Studies in

regions of Montana, Illinois, Wyoming, Utah, and California gave the following percentage of

successful nests:

23.9 52.5 60.0 68.5 78.6 71.0 17.8 57.5 59.0 52.0

(a) Compute the range

(b) State the mean.

(c) State the standard deviation.



Homework 9: Skewed Distributions (Interquartile Range) (S-ID.1, S-ID.2, S-ID.3, S-ID.4)

Review:

1) For the following data

5 3 7 2 4 4 2 4 8 3 4 3 4






2) The data below are the calories in an ice cream bar.

a) Find Q1, median and Q3

b) Draw the box and whisker plot.

c) What is the interquartile range (IQR) for this distribution? What percent of the ice cream bars fall

within this interval?

d) Do you think the data distribution represented by the box plot is a skewed distribution? Why or why

not?

e) Estimate the typical number of calories in an ice cream bar. Explain why you chose this value.

342 377 319 353 295 234 294 286 377 1 82 310

439 1 11 201 1 82 1 97 209 1 47 1 90 1 51 1 31 1 51


3) Law Enforcement: Speeding is a serious offense. The following data give the ages of a random

sample of 50 drivers ticketed for speeding in a 40 MPH zone

46 16 41 26 22 33 30 22 36 34 63 21 26 18 27 24 31 38

26 55 31 47 27 43 35 22 64 40 58 20 49 37 53 25 29 32

23 49 39 40 24 56 30 51 21 45 27 34 47 35

a) Draw a dot plot of the data above

b) How many drivers where older than 45?

c) Is this data distribution considered skewed? Explain your answer.

d) Is the tail of this data distribution to the right or to the left? How would you describe several

of the ages in the tail?

e) Draw a box plot over the dot plot.



Homework 10: Comparing Distributions (S-ID.1, S-ID.2, S-ID.3)

1) Using the histograms of the number of hours spent at the gym, approximately how many of the

members of gym A spend between 2 to 6 hours at their gym? Approximately how many of the

members of gym B spend between 2 to 6 hours at their gym.

2) What 2 - hour interval of members represented in the histogram of the Gym B distribution has the

most people?

3) Why are the mean hours greater than the median hours for members in Gym A?

4) Using the two histograms, can you determine which gym is more successful? Explain your answer.

5) Based on your previous work with histograms, would you describe the histogram for Gym B as

representing a symmetrical or a skewed distribution? Explain your answer.


Hw 10 continued

6) The first dot plot is a dot plot of the ages of sixty eight people from a random sample of people who

attended a basketball game and the second dot plot is a dot plot of sixty eight ages from a random sample

of people who attended a football game.

Draw a box plot over this dot plot.

a) Based on your box plots, what is the median age for people attending the basketball game and those

attending the football game?

b) What does the box plots of the two games indicate about the possible differences in the age

distributions of people who attend the basketball games and football games?

7) The following box plot summarizes ages for a random sample from a made up county named C

County.

Make up your own sample of sixty ages that could be represented by the box plot for C County. Use a

dot plot to represent the ages of the sixty people in C County.

Is the sample of sixty ages represented in your dot plot of C County the only sample that could be

represented by the box plot? Explain your answer.



Homework 11: Bivariate Categorical Data & Relative Frequencies (S-ID.5, S-ID.9)

Review

1) Tanner and Robbie discovered that the means of their grades for the first semester in Mrs. Merrell’s

mathematics class are identical. They also noticed that the standard deviation of Tanner's scores is

20.7, while the standard deviation of Robbie's scores is 2.7. Which statement must be true?

a) In general, Robbie's grades are lower than Tanner's grades

b) Robbie's grades are more consistent than Tanner's grades.

c) Robbie had more failing grades during the semester than Tanner had.

d) The median for Robbie's grades is lower than the median for Tanner's grades.

2) A random sample of 284 students was asked to evaluate teacher performance. The students were also

asked to supply their midterm grade.

Teacher evaluation

A B C Row total

Positive 35 33 28 96

Neutral 25 46 35 106

Negative 20 22 40 82

Column Total 80 101 103 284

a) Calculate the relative frequencies for each of the cells to the nearest thousandth. Place the relative

frequencies in the cells of the following table.

b) Based on your relative frequency table, what is the relative frequency of students who had an

A?

c) Based on your table, what is the relative frequency of a student who received a B and gave a

negative rating?

d) If a student were randomly selected from the 284 students, do you think the student selected

would have received a C grade?

e) If a student were selected at random from the 284 students, do you think this student would

give a neutral rating? Explain your answer.

f) Based on the relative frequencies how would you rate this professor? Explain your answer.


Hw 11continued

3) Several students at Common High School were debating whether males or females were more

involved in afterschool activities. There are three organized activities in the afterschool program –

intramural volleyball, computer club, and jazz band. Due to budget constraints, a student can only

select one of these activities. The students were not able to ask every student in the school whether

they participated in the afterschool program or what activity they selected if they were involved.

a) Complete the above table for the 120 students who were surveyed.

b) Write questions that could be included in the survey to investigate the question the students

are debating.

c) Common High School has approximately 1800 students. Jim suggested that the first 120

students entering the cafeteria for lunch would provide a random sample to analyze. Janet

suggested that they pick 120 students based on a school identification number. Who has a

better strategy for selecting a random sample? How do you think 120 students could be

randomly selected to complete the survey?

d) Complete the calculations of the row conditional relative frequencies. Round your answers

to the nearest thousandth. Place your answer in the table above.

e) Are the row conditional relative frequencies for males and females similar, or are they very

different?

f) Do you think there is a possible association between gender and after high school

activities? Explain your answer.

g) If Jack, a male student at Common High School, completed the after-school survey, what

would you predict was his response? Explain your answer.

h) If Joan, a female student at Common High School, completed the after-school survey, what

would you predict was her response? Explain your answer.

i) Do you think there is an association between gender and choice of after-school program?

Explain.



Homework 12: Relationships between Two Numerical Variables (S-ID.5, S-ID.6)

1) Construct a scatter plot that displays the data for 𝒙 = elevation above sea level (in feet)

and 𝒘 = mean number of partly cloudy days per year.

2) Based on the scatter plot you constructed in Question 1, is there a relationship between elevation and

the mean number of partly cloudy days per year? If so, how would you describe the relationship?

Explain your reasoning


Hw 12 continued

3) The speeds ( in miles per hour) and stopping distances ( in feet) for an automobile braking system are

represented in the table below

a) Draw a scatter plot.

b) Is there a relationship between speed and stopping distance, or are the data points scattered?

4) What type of model (linear, quadratic or exponential) would best describe the relationship in each

scatter plot? Explain your reasoning.

a) b) c)

d) e) f)


Hw 12 continued

5) According to basic economics, if the demand for a product increases, then the price will decrease.

The following chart shows the number of items requested and the corresponding price.

a) Draw the scatter plot

b) What type of model (linear, quadratic, or exponential) would you use to describe the

relationship between demand and the price of the items?

c) One model that could describe the relationship between and price is:

Graph this exponential curve on the same graph with the scatter plot.

d) Does this model do a good job of describing the relationship between demand and price?

Explain why or why not.

e) Based on this exponential model, what price would you predict for 30 items?

Demand Price

1 $105

4 $92

7 $80

12 $60

16 $50

20 $40

114(0.95)xy


6) Biologists conducted a study of the nesting behavior of a type of bird called a flycatcher.

They examined a large number of nests and recorded the latitude for the location of the nest

and the number of chicks in the nest.

Data Source: Ibis, 1997

a) What type of model (linear, quadratic or exponential) would best describe the relationship

between latitude and mean number of chicks?

b) One model that could be used to describe the relationship between mean number of chicks

and latitude is: 𝒚 = 𝟎. 𝟏𝟕𝟓 + 𝟎. 𝟐𝟏𝒙 − 𝟎. 𝟎𝟎𝟐𝒙𝟐, where 𝒙 represents the latitude of the

location of the nest and 𝒚 represents the number of chicks in the nest. Use the quadratic

model to complete the following table. Then sketch a graph of the quadratic curve on the

scatter plot above.

𝒙

(degrees) 𝒚

30

40

50

60

70

c) Based on this quadratic model, what is the best latitude for hatching the most flycatcher

chicks? Justify your choice.



Homework 13: Modeling Relationships with a Line (S-ID.6, S-ID.7, S-ID.8, S-ID.9)

Review

1. Find, to the nearest hundredth, the mean, and the standard deviation of the following set of data.

Interval Frequency

110 - 129 12

90 - 109 30

70 - 89 24

50 - 69 14

2. (a) Which of the scatter diagrams on the right represent a

strong positive correlation?

(b) Which of the scatter diagrams represents no

correlation?

c) Which of the scatter diagrams on the right represent a

strong negative correlation?

3. (a) Find the linear correlation coefficient for the relationship between height and shoe size as

expressed in the given table. Round all answers to the nearest hundredth.

(b) Create a scatter diagram for the data on the axis provided.

(c) Find the mean of the heights.

(d) Find the mean of the shoe sizes.

(e) Find the equation of the line of best fit.

Height 60 61 62 63 64 65 66 67 68

Shoe Size 7 7 8 8 8.5 9 9 9.5 10


Hw 13 continued

4. (a) Find the linear correlation coefficient for the relationship between age and the number of absences

as expressed in the given table. Round all answers to the nearest hundredth.

(b) Create a scatter diagram for the data on the axis provided.

(c) Find the mean of the ages.

(d) Find the mean of the number of absences.

(e) Find the equation of the line of best fit.

5. (a) Find the linear correlation coefficient for the relationship between the height and the weight of the

following data given in the table. Round all answers to the nearest tenth.

(b) Find the equation of the line of best fit for this data.

(c) Based on the line of best-fit model, what would the expected weight

be if the height were 70 inches?

Height

(inches)

Weight

(lbs)

45 168

55 175

55 172

63 180

65 186

80 192

50 165

48 168

51 171

60 174



Homework 14: Interpreting Residuals from a Line (S-ID.6, S-ID.7, S-ID.8, S-ID.9)

(Unless otherwise directed, round to the nearest tenth, when appropriate.)

Review

1) (a) Find the linear correlation coefficient for the relationship between the weight of a box and the

number of walnuts inside the box..

(b) Find the equation of the line of best fit for this data.

(c) Based on the line of best-fit model, what would the expected # of

walnuts in a box that weighs 42.4 grams.

2. The table below lists the total estimated numbers of a certain type of disease cases, by year of

diagnosis from 2004 to 2009 in the United States.

(a) Plot the data, letting x = 0 correspond to the year 2004

(b) Determine the quadratic regression model equation that represents the data.

(c) Plot the quadratic graph with the data to determine how well the model fits the actual data.

(d) Use the model to predict the number of cases of the disease in the year 2011.

Weight

(grams)

# of

walnuts

42.3 87

42.7 91

42.8 93

42.4 87

42.6 89

41.9 80

42.2 82

42.5 88

42.9 94

41.8 87

YEAR # of

CASES

2004 21350

2005 21150

2006 20700

2007 21180

2008 23050

2009 24010


Hw 14 continued

Review

3) The data shows the cooling temperature of a liquid left at room temperature over time. Use the

rounded equation from part a to answer all other parts.

(a) Determine an exponential regression model equation to represent this data.

(b) Graph the new equation.

(c) When is the liquid at a temperature of 106 degrees?

(d) What is the predicted temperature of the liquid after 1 hour?

(e) How long should it take before the liquid is not hotter than 155º

TIME

(mins)

TEMP

(°F)

0 179.5

5 168.7

8 158.1

11 149.2

15 141.7

18 134.6

22 125.4

25 123.5

30 116.3

34 113.2

38 109.1

42 105.7

45 102.2

50 100.5


Hw 14 continued

4) Complete each table below using the given linear regression model above it. Express all calculations

to the nearest tenth.

a) Linear regression model: 0.5 0.3y x

b) ) Linear regression model : 0.4 6.4y x

5) If you see a clear curve in the residual plot, what does this say about the original data set?

6) If you see a random scatter of points in the residual plot, what does this say about the original data

set?


Hw 14 continued

7) Complete each table below using the given nonlinear regression model above it. Express all

calculations to the nearest tenth. Construct the residual plot.

a) Exponential regression model : (203.4)(1.03)xy

b) Quadratic regression model: 270.4 3.3 0.2y x x



Homework 15: Analyzing Residuals & Correlations (S-ID.6, S-ID.7, S-ID.8, S-ID.9)

Review

1) Complete the table below using the given nonlinear regression model above it. Express all

calculations to the nearest tenth. Construct the residual plot.

Quadratic regression model: 244.6 1213.8 10855.8y x x

2) In each graph below ,

a) Draw the least-squares line on each graph.

b) State whether each line has a positive slope or negative slope and a possible linear correlation

c) Which graph do you think has a stronger correlation? Explain your answer.


Hw 15 continued

3) a) Is the relationship displayed in Scatter Plot 1, a positive or negative linear relationship?

b) Is the relationship displayed in Scatter Plot 2, a positive or negative linear relationship?

c) In Scatter plot 1, does the value of the 𝒚 variable tend to increase or decrease as the value of

𝒙 increases? If you were to describe this relationship using a line, would the line have a

positive or negative slope?

d) In Scatter Plot 2, as the value of one of the variables increases, what happens to the value of

the other variable? If you were to describe this relationship using a line, would the line have

a positive or negative slope?

e) What does it mean to say that there is a positive linear relationship between two variables?

f) What does it mean to say that there is a negative linear relationship between two variables?

4. What do you think a scatter plot that shows the strongest possible positive linear relationship would

look like? Draw a scatter plot with 5 points that illustrates this.

5. How would a scatter plot that shows the strongest possible negative linear relationship look different

from the scatter plot that you drew in the previous question?


Hw 15 continued

6) For each of the following residual plots, what conclusion would you reach about the

relationship between the variables in the original data set? Indicate whether the values

would be better represented by a linear or a non-linear relationship. Justify you answer.

7) Using a graphing calculator, construct the scatter plot of the data set and the residual plot.

Include the least-squares line on your graph. Make a sketch of the scatter plot including the

least-squares line on the axes below.

Do you see a clear curve in the residual plot? Is the original data set linear or nonlinear?

Explain your answer.


Hw 15 continued

8) Do heavier cars really use more gasoline? Let x be the weight of the car (in hundreds of pounds and

let y be the miles per gallon in the chart below.

a) Using a graphing calculator, construct the scatter plot of the data set and the residual plot.

Include the least-squares line on your graph. Make a sketch of the scatter plot including

the least-squares line on the axes below. State the equation of the least-squares line.

b) Complete the table below using the equation from part a. Express all calculations to the

nearest tenth. Construct the residual plot.

c) What would be the miles per gallon for a car that weighs 38 (hundred pounds).

d) Using the information from the residual value, how confident are you about your answer? Explain.




1) Which set of data can be classified as quantitative?

1) first names of students in a chess club

2) ages of students in a government class

3) hair colors of students in a debate club

4) favorite sports of students in a gym class

2) Which situation should be analyzed using bivariate data?

1) Ms. Saleem keeps a list of the amount of

time her daughter spends on her social

studies homework.

2) Mr. Benjamin tries to see if his students’

shoe sizes are directly related to their

heights.

3) Mr. DeStefan records his customers’ best

video game scores during the summer.

4) Mr. Chan keeps track of his daughter’s

algebra grades for the quarter.

3) A survey is being conducted to determine which school board candidate would best serve the Yonkers

community. Which group, when randomly surveyed, would likely produce the most bias?

1) 15 employees of the Yonkers school district

2) 25 people driving past Yonkers High School

3) 75 people who enter a Yonkers grocery store

4) 100 people who visit the local Yonkers

shopping mall

4) The scatter plot below shows the profit, by month, for a

new company for the first year of operation. Kate drew a

line of best fit, as shown in the diagram.

Using this line, what is the best estimate for profit in the 18th

month?

1) $35,000

2) $37,750

3) $42,500

4) $45,000


Hw 16 continued

5) The number of hours spent on math homework each week and the

final exam grades for twelve students in Mr. Dylan's algebra class

are plotted below.

Based on a line of best fit, which exam grade is the best prediction for

a student who spends about 4 hours on math homework each week?

1) 62

2) 72

3) 82

4) 92

6) The graph below illustrates the number of acres used for

farming in Smalltown, New York, over several years.

Using a line of best fit, approximately how many acres will

be used for farming in the 5th year?

1) 0

2) 200

3) 300

4) 400

7) Megan and Bryce opened a new store called the Donut Pit. Their goal is to reach a profit of $20,000

in their 18th month of business. The table and scatter plot below represent the profit, P, in thousands

of dollars that they made during the first 12 months. Draw a reasonable line of best fit. Using the line

of best fit, predict whether Megan and Bryce will reach their goal in the 18th month of their business.



Hw 16 - continued

8) The hours that John worked over the past 12 weeks are recorded in the table. For these hours find (to

the nearest tenth) (a) the mean (b) the median (c) the mode (d) the

standard deviation (e) the variance

9) Luggage weights (per passenger) for a particular flight are reported in

the following table. Find the mean and the standard deviation of these

weights to the nearest hundredth.

10) The residuals for a set of data represent the

(1) differences between consecutive x-values

(2) vertical differences between data points and the line of best fit

(3) data points that lie above the line of best fit

(4) data points that lie below the line of best fit

11) The following table compares the wing length (in cms) of a particular

species of bird, with the age (in days) of the bird. ( nearest tenth)

(a) Find the correlation coefficient. Is this considered a high or low

correlation?

(b) Find the equation of the line of best fit.

(c) Use this equation to estimate (nearest ten thousandth) how old a bird

with a wing length of 2.8 might be.

Hours Frequency

30 1

35 2

37 5

40 3

42 1

WEIGHTS

(lbs)

# of

PASSENGERS

0 - 8 12

9 - 17 25

18 – 26 38

27 – 35 22

36 - 44 15

WING

LENGTH

(cms)

AGE

(days)

1.5 4.0

2.2 5.0

3.1 8.0

3.2 9.0

3.2 10.0

3.9 11.0

4.1 12.0

4.7 14.0


Hw 16 continued

12) The data below represents the length and diameter of a particular bone of a certain animal.

(Express answers to the nearest thousandth.)

(a) Create the scatter plot of the data.

(b) Determine a exponential regression model equation to represent this data.

(c) Graph the new equation.

(d) What length will correspond to a diameter of 84 mm?

13) The graph shows the residuals for a set of data with respect to a line of best fit. How could the line be

adjusted to improve the fit?

(1) increase the slope of the line

(2) decrease the slope of the line

(3) increase the y-intercept of the line

(4) do not adjust the line it is the best fit line

DIAMETER

(mm)

LENGTH

(mm)

17.6 159.4

26.0 206.2

31.9 236.4

38.9 269.7

45.8 300.5

51.4 324.1

58.5 352.2

64.3 376.9


Hw 16 continued

14) The table below represents a projection of future sales in the thousands of dollars by months in

business. (nearest hundredths)

a) Draw a scatter plot below.

b) What type of model (linear, quadratic or exponential) would best

describe the relationship between months in business and sales?

c) Determine a quadratic regression model equation to represent this

data.

d) Use the quadratic model equation to complete the following table.

Then sketch a graph of the quadratic curve on the scatter plot below.

e) Based on this quadratic model, what would you predict sales will be after 10 months?




Homework 17: Cumulative Review Unit 7

1) Mrs. Smith wrote “Eight less than three times a number is greater than fifteen” on the board. If x

represents the number, which inequality is the correct translation of this statement?

(1) 3x- 8 > 15 (2) 3x – 8 < 15 (3) 8 – 3x > 15 (4) 8 – 3x < 15

2) If 2ax - 3b = 5c, then x equals

(1) 5 3

2

c b

a

(2)

3 5

2

b c

a

(3) 5c + 3b – 2a (4)

5 3

2

c b

a


(1) (2) (3) (4)

4) Which inequality is represented by this graph?

(1)

(2)

(3)

(4)

5) On a certain day in Toronto, Canada, the temperature was 15 Celsius (c). Using the formula

F = 9

325

C , Peter converts this temperature to degrees Fahrenheit (F). Which temperature represents

15C in degrees Fahrenheit?

(1) -9 (2) 35 (3) 59 (4) 85

6) Which value of x is in the solution set of the inequality -3(x + 2) < 6?

(1) -12 (2) -6 (3) -4 (4) -3


Hw 17

7) Maureen tracks the range of outdoor temperatures

over three days. She records the following

information.

Express the intersection of the three sets as an

inequality in terms of temperature, t


the solution set.

2x – y ≥ 6

x > 2

9) Given:

Which expression results in a rational number?

1) L x M 2) M x N 3) N x P 4) P x L

10) During a 45-minute lunch period, Albert (A) went

running and Bill (B) walked for exercise. Their

times and distances are shown in the

accompanying graph. How much faster was

Albert running than Bill was walking, in miles per

hour?

3

2 3

15

26

L

M

N

P


Hw 17 continued

11) Draw a distance–time graph to show the following story.

Mary walked from home up the steep hill opposite her house. She stopped at the top to put her

skates on, then skated quickly down the hill, back home again.

12) Samantha constructs the scatter plot below from a set of data.

Based on her scatter plot, which regression model would be most

appropriate?

1) exponential 3) quadratic

2) linear 4) cubic

13) John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be

used to determine the number of dimes, x, in his pocket?

1)

2)

3)

4)


Hw 17 continued

14) The following data represents approximate heights for a ball thrown by a shot-putter as it travels x

meters horizontally. (nearest hundredth)

a) Draw a scatter plot below.

b) What type of model (linear, quadratic or exponential) would best

describe the relationship between distance and the height?

c) Determine a quadratic regression model equation to represent this data.

d) Use the quadratic model to complete the following table.

Then sketch a graph of the quadratic curve on the scatter

plot below.

e) Based on this quadratic model, what would you predict the height of the shot put will reach

for a distance of 20 feet? Justify your choice.

15) If 2 23 4 6 and B=-3x +6x+5, then findA x x A B , A – B.

16) John has eight more nickels than dimes in his pocket, for a total of $1.35. Which equation could be


1) 0.10( 8) 0.05( ) 1.35 2) 0.05( 8) 0.10( ) 1.35

3) 0.10(8 ) 0.05( ) 1.35 4) 0.05(8 ) 0.10( ) 1.35

x x x x

x x x x


Unit 8 – Sequences

Homework 1: Integer Sequences ( F-IF.2,F-IF.3,F-BF.1A,F-BF.2,F-LE.2)

1) Consider a sequence that follows a “plus 4” pattern: 5,9,13,17,...

a) Write a formula for the nth term of the

sequence. Be sure to specify what value of 𝑛

your formula starts with.

b) Using the formula, find the 25th term of the

sequence.

c) Graph the terms of the sequence as ordered

pairs (𝑛, 𝑓(𝑛)) on a coordinate plane.

2) Given the following pattern

a) Express the above pattern in table form

b) How many squares would you draw if n = 4

c) Write a formula for the nth term of the sequence. Be sure

to specify what value of 𝒏 your formula starts with.

d) Using the formula, find the 𝟓𝟎th term of the sequence.

e) Graph the terms of the sequence as ordered pairs (𝒏, 𝒇(𝒏)) on a coordinate plane.


Hw 1 continued

3) Given the following pattern

a) Express the above pattern in table form

b) How many circles would you draw if n = 4, n = 10

c) Write a formula for the nth term of the sequence. Be

sure to specify what value of 𝒏 your formula starts with.

d) Using the formula, find the 𝟓𝟎th term of the sequence.

e) Graph the terms of the sequence as ordered pairs (𝒏, 𝒇(𝒏)) on a coordinate plane.


Hw 1 continued

4) Consider a sequence that follows a “minus 3

pattern: 20,17,14,11,...

a) Write a formula for the nth term of the

sequence. Be sure to specify what value of 𝑛

your formula starts with.

b) Using the formula, find the 20th term of the

sequence.

c) Graph the terms of the sequence as ordered

pairs (𝑛, 𝑓(𝑛)) on a coordinate plane.

5) Consider a sequence generated by the formula 𝑓(𝑛) = 3𝑛 − 1 starting with 𝑛 = 1. Generate the

terms 𝑓(1), 𝑓(2), 𝑓(3), 𝑓(4), and 𝑓(5).

6) Consider a sequence given by the formula

starting with 𝑛 = 1. Generate the first 5 terms of the sequence.

7) Consider a sequence given by the formula starting with𝑛 = 1. Generate the first 5

terms of the sequence

1( )

2nf n

( ) ( 2) 5nf n



Homework 2: Recursive Formulas for Sequences (F-IF.3)

Review

1) Consider a sequence generated by the formula 𝑓(𝑛) = −2𝑛 + 3 starting with 𝑛 = 1. Generate the

terms 𝑓(1), 𝑓(2), 𝑓(3), 𝑓(4), and 𝑓(5).

2) Consider a sequence that follows a “minus 2” pattern: 4,2,0, 2

Write a formula for the nth term of the sequence.

3) Consider the sequence given by the formula where

a) Explain what the formula means.

b) List the first 5 terms of the sequence.

c) Write an explicit formula.









6) Consider the sequence given by the formula

a) List the first 4 terms of the sequence.

b) Write an explicit formula.

1 15, 2n na a a

1 14, 3 2n na a a

1 1

132,

2n na a a

1 11, 2n na a a

1n

1n

1n

1n


Hw 2 continued

7) Consider the sequence following a “minus 4” pattern: 𝟏𝟎, 𝟔, 𝟐, −𝟐, ….

a) Write an explicit formula for the sequence.

b) Write a recursive formula for the sequence.

c) Find the 𝟑𝟖th term of the sequence.

8) Consider the sequence given by the formula 𝒂(𝒏 + 𝟏) = 𝟒𝒂(𝒏) and 𝒂(𝟏) = 𝟑 for 𝒏 ≥ 𝟏.


b) List the first 𝟓 terms of the sequence.



Homework 3: Arithmetic Sequences (F-IF3, F-BF.1, F-BF.2)

Review

1) Consider a sequence generated by the formula 𝑓(𝑛) = −4𝑛 + 3 starting with𝑛 = 1. Generate the

terms 𝑓(1), 𝑓(2), 𝑓(3), 𝑓(4), and 𝑓(5).

2) How many circles would you draw if n = 4, n = 10

Write a formula for the nth term of the sequence.

In exercises 3 – 6, find the common difference for each arithmetic sequence

3. 5, 10, 15, 20, 25 4. -4, 0, 4, 8, 12 5. 4, 1, -2, -5, -8 6. 1.5, 3, 4.5, 6

7. Find the next 3 terms in each of the sequences

5, 7, 9, ______, ______, ______

1, 1.5, 2, ______, ______, ______

c, c-3, c-6, ______, ______, ______

–n, 0, n, _____, ______, ______

8. Find the 21th

term of the arithmetic sequence with 1 3a and 1

4d .

9. Find the 50th

term in the sequence 19, 25, 31, …..

Find an explicit form for the sequence in terms of 𝒏.


Hw 2 continued

10. Find the 30th

term in the sequence 1.5, 3, 4.5, …


11. Find the 58th

term of the arithmetic sequence 10, 4, -2, ….


12. Find the 28th

term of the sequence: 2, 2.4, 2.8, 3.2, 3.6, …

13. Find the 68th

term in the sequence 16, 7, -2, …….

14. Find the first term in the sequence for which 12

197a and d = 10.

15. Find the first term in the sequence for which 15

52a and d = -3

16. A sequence is formed by adding the constant c to each preceding term. The 6th

term of the sequence

is 25 and the 26th

term is 105. What is the 8th

term of the sequence?



Homework 4: Geometric Sequences (A-SSE.4, F-BF.1, F-LE.2)

Review

1. Find the 21th term in the sequence 5, 11, 17, …… Find an explicit form for the sequence in

terms of 𝒏.

2. What is the tenth term of the arithmetic sequence: 13

22

5

2, , , …

3. List the first three terms of the sequence an

n 3 1( ) .

4. A free-falling body that starts from rest drops about 16 feet the first second, 48 feet the second second,

80 feet the third and so on. How many feet does the object fall in 10 seconds?

5. Find the common ratio and the next 3 terms in each of the geometric sequences:

a) 4, 12, 36, ______, ______, ______ b) 1 1 1, ,2 4 8

,_____, _____, _____

c) 2, -6, 18, ______, _______, ______ d) 1 1 1, , ,32 16 8

_____, _____, _____

6. The first term of a geometric sequence is –3 and the common ratio is 23

. Find, in fractional form,

the next 3 terms.

7. Find the 5th

term of the geometric sequence whose first term is 6 and whose common ratio is 2.

8. Find the 5th

term in the sequence 2, 6, 18, ….

9. Find the 6th

term in the sequence 1, 1 1,3 9

, ….

10. Find the 4th

term of the geometric sequence 10, .1, .001, ….

11. Find the first 3 terms of the geometric sequence for which a4 25 . and r = 2.



Homework 5: Investment Applications (F-LE.5)

Review

1) Determine a2and a4

so that the following sequence 5 452 4, , , ,...,a a an is

a. an arithmetic sequence

b. a geometric sequence

2) Find the 5th

term in the sequence 1 1 1

, , ,...2 4 8

3) Carl invested $2000 at a bank that pays 𝟔% simple interest. Calculate the amount of money

in the account after 𝟏 year, 𝟒 years, 𝟔 years, and 𝟏𝟎 years.

4) The amount of money A, in a bank account is determined by the formula A = t

P 1 r , where P is

the initial amount invested, r is the yearly rate of interest and t is the number of years invested. Find

the following answers to the nearest hundredth.

a) If $2000 is invested at 5% compounded annually, what is the value of the investment after 8

years? What was the total interest earned over the eight years?

b) How long must $5000 be left in an account that pays 4% interest compounded annually in order

to grow to an amount over $7500?

5) Mary invested $2000 at a bank that pays 𝟓% interest compounded annually. Calculate the

amount of money in the account after 𝟏 year, 𝟒 years, 𝟔 years, and 𝟏𝟎 years.


Hw 5 continued

6) Based on the information in questions 3 and 5, who made the better investment choice for

the 4 year investment?

7) A friend invests a sum of money at 8.5% interest compounded annually. How much must she invest

to have a total of $10,000 in ten years?

8) What amount is reached by investing $425 for 6 months at 10% interest compounded annually?

9 The table below shows the average yearly balance in a savings account where interest is compounded

annually. No money is deposited or withdrawn after the initial amount is deposited.

Which type of function best models the given data?

a) linear function with a negative rate of change

b) linear function with a positive rate of change

c) exponential decay function

d) exponential growth function

10) What amount should have been deposited 5 years ago at 8% interest compounded annually in order

to have $1000 today?



Homework 6: Exponential Growth & Exponential Decay (F-LE.1C, F-LE.2, F-LE.5, F-BF.1)

Review: 1) What is a formula for the nth term of sequence B shown below?

1)

2)

3)

4)

2) What is the fifteenth term of the sequence 5, -10, 20, -40,80,…?

(1) -163,840 (2) -81,920 (3) 81,920 (4) 327,680

3) A population of 100 rabbits increases at an annual rate of 22%. How many rabbits will there be in 5

years? ( )

4) The population of Masonville was 3,620 in 2009, and is declining at an annual rate of 3.5%. If this

rate continues, what will be the approximate population in 2020? ( )

5) A type of bacteria has a very high exponential growth rate at 80% every hour. If there are 10 bacteria

to start, determine how many there will be in 5 hours. Write the explicit formula for the sequence

that models this growth.

How many hours would it take before the number of bacteria will exceed 10000?

6) If the number of electronic devices increase in a particular region by the formula

E(x) = 3.25(1.08)x, where x is the number of new residents in the region , how many electronic

devices are expected when 24 new residents arrive?

0( ) (1 )xR x R r

0( ) (1 )tP t P r


Hw 6 continued

7) In 2002, New Land had a population of 3,962,000 with a population growth rate of 1.7% per year.

Assuming the population continues to increase at the same rate,

a) Complete the table and construct a graph to show how the population is expected to increase over the

next 4 years. Be sure to label and mark your axes. Write the explicit formula for the sequence that

models this growth.

b) How many years (from 2002) will it take for New Land’s population to reach 5,000,000? Round to

the nearest whole year.

8) The population of a certain Midwest City is modeled by the function

where t is the number of years from 2010.

a) What is the population in the year 2010?

b) What is the rate at which the population is decreasing per year?

c) In what year will the population of this city drop below 25,000?

( ) 68,990(0.925)tP t



Homework 7: Review for Unit 8 Test

1. Write the first five terms of the sequence whose nth term is 2

1

2

n

n

.

2. Find the 7th

term of the arithmetic sequence with 1 3a and 1

2d .

3. Find the 7th

term of the geometric series 1

2

1

4

1

8 ...

4. The first term of a geometric series is 1

10. The second term is

1

5. What is the common ratio?

5. Which of the following is an expression for the nth term of the sequence 13, 17, 21,..?

A. 12n +1 B. 13

2

n

n C. 4n + 1 D. 4n + 9

6. Write the first three terms of the geometric sequence with 1 3a and 2

5r . Give your answers in

fraction form.

7. Find the third term in the recursive sequence ,

1 12 1, 3.k ka a where a


Hw 7 continued

8. If a certain bacteria doubles every hour, starting with 2.25 thousand bacteria.

a) Write the explicit formula for the sequence that models this growth.

b) How many bacteria are present after 3 hours?

9. On a golf course in 2010, it was estimated that there were 500 Canadian Geese and that the number of

geese were growing at a rate of 5% a year. If the estimates are correct and the geese population continues

to grow at the estimated rate,

a) Write the explicit formula for the sequence that models this growth.

b) How many geese will be present after 4 years?

10. On January 1, a share of a certain stock cost $180. Each month thereafter, the cost of a share of this

stock decreased by one-third. If x represents the time, in months, and y represents the cost of the stock,

in dollars, which graph best represents the cost of a share over the following 5 months?

(1) (2)

(3) (4)


Unit 9 – Functions and Interval Notation

Homework 1: Patterns in Linear Equations (F-IF.2, F-IF.4, F-IF.7)

1. Complete each table and find a rule for each pattern.

a)

Rule

b) Rule

c) Rule

d) Rule

e) Rule



Homework 2: Modeling Linear Equations (F-IF.2, F-IF.4, F-IF.7)

Review:

1) Complete each table and find a rule for each pattern.

Rule

2) Which of the following could be modeled by y = 2x + 3? Answer YES or NO for each one.

If you answer no, give the correct equation.

a) Nicholas earns $2.00 for each magazine he sells. Each time he sells a magazine he also gets a

three-dollar tip. How much money will he earn after selling x magazines?

b) Olivia charges $2.00 an hour for babysitting. Parents are charged $3.00 if they arrive home

later than scheduled. Assuming the parents arrived late, how much money does she earn for x

hours?

c) Christopher creates a sequence of integers. The first term of the sequence is 5 and the

difference between any consecutive terms is always equal to 2.

d) Thomas wants to become a member of a video rental store. There is a $2.00 initiation fee and

a $3.00 per video rental fee.

How much would Thomas owe on his first visit if he becomes a member and rents x videos?

3) A computer salesperson earns a base salary of $30,000 plus a commission of $400 for every

computer she sells. Write an equation that shows the total amount of income the salesperson earns, if

she sells x machines in a year.

a) Write a linear equation to represent the situation above.

b) How many machines would she need to sell to earn $80,000 a year?


Hw 2 continued

4) Mr. Jackson is tracking the progress of his plant’s growth. Today the plant is 7 cm high. The plant

grows 2.3 cm per day.

a) Write a linear equation that represents the height of the plant after d days.

b) What will the height of the plant be after 12 days?

5) Thomas is 2 miles south of his school. While walking north at a constant speed , he passes his school

after 2 hours.

a) What is Thomas' rate of speed?

b) Create a table showing Thomas' distance from school for 2 hours , 3 hours and 4 hours




Hw 2 continued

6) The elevator in Macys climbs 2 floors per minute. After 1 minute it is on the first floor.

a) What is the rate of speed of the elevator?

b) Create a table showing the floor the elevator is on for the following times in minutes.





Homework 3: Evaluating Functions (F-IF.1, F-IF.2)

Review

1) For the following graphs, describe the features, include: what intervals does it increase/decrease, what

quadrants does it reside in, what are its min/max, what are the intercepts, and what are the domain and

range?

a) b)

c) d)


Hw 3 continued

2) If a function f(x) is defined as ( ) 3 1f x x , find the value of each function for the given input.

a) f(1) b) f(-2) c) f(0) d) 2

( )3

f

e) f(0.02) f) f(10.2) g) f( -0.4) h) 5

( )3

f

i) ( 5)f j) ( 2)f k) ( 2)f l) 5

( )3

f

m) f(2)+f(4) n) f(3) – f(2) o) ( 5) ( 3)f f p) 5 2

( ) ( )3 3

f f

3) If a function f(x) is defined as ( ) 0.3(4)xg x , find the value of each function for the given input.

a) g(0) b) g(1) c) g(2) d) g(-1)

e) 1

( )2

g f) 3

( )2

g g) g(2) +g(1) h) g(3 1

( ) ( ))2 2

g g


Hw 3 continued

4) Let ( ) 5 2f x x and let ( ) 0.3(2)xg x , and suppose 𝑎, 𝑏, 𝑐, and ℎ are real numbers. Find the value

of each function for the given input.

a) f(b) b) f(a) c) g(a) d) g(b)

e) f(2b) f) f(2a) g) g(4a) h) g(2h)

i) f( c + a) j) f( a + h) k) g(a – 3) l) g( a+c)

m) f( b + 1) n) f( a – 2) o) g( a + 1) p) g ( b – 3)

q) f( b + 1 ) – f (b) r) g( b – 3) – g(b) s) f ( a + h) – f( h)


Hw 3 continued

5) What is the range of each function given below?

a) ( ) 7 3f x x b) 1

( ) 22

f x x c) ( )f x x

d) ( ) 2xg x e) ( ) 5xg x f) 3( ) 5 xg x

g) 2( )h x x h) 2( ) 1h x x i) 2( ) 2h x x

j) ( )f x x k) ( ) 2f x x l) ( ) 2f x x

m) f(x) = 2x +1 such that x is a negative integer

n) ( ) 3 0 3xg x for x

6) Give A domain and range to complete the definition of each function.

a) let f(x) = 3x +2 b) let ( ) 3xf x

c) Let A(x) = x + 273, where A(x) is the Absolute temperature reading when the temperature is x

degrees Centigrade.

d) Let ( ) 250(3 )xb x where 𝐵(𝑥) is the number of bacteria at time 𝑥 hours over the course of one

day.


Hw 3 continued

7) Let 𝑓: 𝑋 → 𝑌, where 𝑋 and 𝑌 are the set of all real numbers and 𝑥 and ℎ are real numbers.

a) Find a function 𝑓 such that the equation 𝑓(𝑥 − ℎ) = 𝑓(𝑥) − 𝑓(ℎ) is not true for all values of 𝑥 and ℎ.

Justify your reasoning.

b) Find a function 𝑓 such that equation 𝑓(𝑥 − ℎ) = 𝑓(𝑥) − 𝑓(ℎ) is true for all values of 𝑥 and ℎ. Justify

your reasoning.

c) Let ( ) 3xf x . Find a value for 𝑥 and a value for ℎ that makes 𝑓(𝑥 + ℎ) = 𝑓(𝑥) + 𝑓(ℎ) a true

number sentence.

8) Given the function 𝑓 whose domain is the set of real numbers, let 𝑓(𝑥) = 0 if 𝑥 is a rational number

and let 𝑓(𝑥) = 2 if 𝑥 is an irrational number.

a) Explain why 𝑓 is a function.

b) What is the range of 𝑓?

c) Evaluate 𝑓 for each domain value shown below.

𝑥 2/5 1 −3 √3 𝜋

𝑓(𝑥)

d) List four possible solutions to the equation 𝑓(𝑥) = 0.



Homework 4: Foundations - Functions (F-IF.1, F-IF.2)

1) Which set of ordered pairs represents a function?

(1) { (1,6), (3,6), (3,8)} (3) { (5,3), (6,3), (7,3)}

(2) { (2,1), (6,5), (6,7), (5,0)} (4) {(3,5), (4,5), (3,7), (4,7)}

2) Match the type of function with the graphs shown.

1) Linear (A) (B)

2) Absolute value

3) Quadratic (C) (D)

4) Exponential

3) Which of the following graphs are functions? (Answer YES of NO)

a) b) c)

4) Determine if each relation is a function. (Answer YES or NO)

a) {(3,2), (4,3) (5,4)} c) d)

b) {(0,1), (0,2), (1,3),(1,4)}

e) { ( 1,2), (2,2), (3,2), (4,2) }

X Y

2 3

5 1

7 3

9 1

X Y

3 3

4 -3

4 3

5 -3


Hw 4 continued

5) Determine whether the following relations are functions and state the domain and range of each.

a) (1,5),(1,10),(1,15){ } b) y = x2 c)

6) Which of the following graphs would describe 7) Which of the following 2 graphs

a bike trip if the biker rode slowly at first and represent the cost of a taxi trip if the

then increased speed? first ¼ mile costs $2 and every additional

¼ of a mile costs $2 more?

8) If a function f is defined by f(x) = 2x2 – 3, find

a) f(2) b) f(-3) c) f(a) d) f( a + b) e) f( 5 )

9) If a function g is defined by g(t) = 1

2

t

t

, find

a) g( 5) b) g( 1) c) g( -1) d) g( b)

10) Find the value of x such that if f(x) = 2x – 1 then f(x) = 7.


Hw 4 continued

11) Which interval notation represents the set of all real numbers greater than 5 and less than or equal

to 15?

(1) (5,15) (2) (5,15]

(3) [5,15) (4) [5,15]

12) Which interval notation represents the set of all numbers greater than or equal to 8 and less than

16?

(1) [8,16) (2) (8,16]

(3) (8,16) (4) [8,16]

13) Which interval notation represents the set of all numbers from 4 through 9 inclusive?

(1) (4,9] (2) (4,9)

(3) [4,9) (4) [4,9]

14) Which graph is the best representation of the cooling of a very hot room once the air conditioner

is turned on?

(1) (3)

(2) (4)



Homework 5: Unit 9 Review Questions

1) If a function f(x) is defined as ( ) 6 11f x x , find the value of each function for the given input.

a) f(1) b) f(-2) c) f(0) d) 2

( )3

f

e) f(0.02) f) f(10.2) g) f( -0.4) h) 5

( )3

f

i) ( 5)f j) ( 2)f k) ( 2)f l) 5

( )3

f

m) f(2)+f(4) n) f(3) – f(2) o) ( 5) ( 3)f f p) 5 2

( ) ( )3 3

f f

2) If a function f(x) is defined as ( ) 0.4(2)xg x , find the value of each function for the given input.

a) g(0) b) g(1) c) g(2) d) g(-1)

e) 1

( )2

g f) 3

( )2

g g) g(2) +g(1) h) g(3 1

( ) ( ))2 2

g g


Hw 5 continued

3) Provide a suitable domain and range to complete the definition of each function.

a) let f(x) = 7x - 2

b) let ( ) 2xf x

c) Let ( ) 550(3 )xb x where 𝐵(𝑥) is the number of bacteria at time 𝑥 hours over the course of one

day.

4) Officials in a town use a function, C, to analyze the number of cars that pass a certain intersection.

represents the rate of traffic through an intersection where n is the number of observed vehicles in a

specified time interval. What would be the most appropriate domain for the function? Explain your

choice.

1 2 4 7) {..., 2, 1,0,1,2,3,...} ) { 2, 1,0,1,2,3} ) {0, , ,1, , ,2} ) {0,1,2,3,...}

3 3 3 3a b c d


x

y y y y



1) Which graph represents a function?

(1) (2) (3) (4)

2) Rhonda has $1.35 in nickels and dimes in her pocket. If she has six more dimes than nickels, which

equation can be used to determine x, the number of nickels she has?

(1) 0.05(x + 6) + 0.10x = 1.35 (3) 0.05 + 0.10(6x) = 1.35

(2) 0.05x + 0.10(x + 6) = 1.35 (4) 0.15(x + 6) = 1.35

3) If the formula for the perimeter of a rectangle is p = 2l + 2w, then w can be expressed as

(1) 2

2

l pw

(2)

2

2

p lw

(3)

2

p lw

(4)

2

2

p ww

4) Which value of x is the solution of 2 1 7 2

5 3 15

x x ?

(1) 3

5 (2)

31

26 (3) 3 (4) 7

5) Which value of x is in the solution set of the inequality -4x + 2 > 10 ?

(1) -2 (2) 2 (3) 3 (4) -4

6) Which interval notation represents the set of all numbers from 2 through 7, inclusive?

(1) (2,7] (2) (2,7) (3) [2,7) (4) [2,7]

x x x


y 7) Which type of graph is shown in the accompanying diagram?

(1) absolute value (3) linear

(2) exponential (4) quadratic

8) The statement 4 + (-4) = 0 is an example of the use of which property of real numbers?

(1) associative (2) additive identity (3) additive inverse (4) distributive

9) Nicole’s aerobics class exercises to fast paced music. If the rate of the music is 120 beats per

minute, how many beats would there be in a class that is 0.75 hour long?

(1) 90 (2) 160 (3) 5400 (4) 7200

10) Which relation represents a function?

(1) { (1,4), (2,5), (1,6)} (3) { (3,0), (5,4), (5, -2)}

(2) { -4,5), (-4,7), (-11,9), (-13,6)} (4) {(-5,6), (-7,5), (-3, 6), (-8,5)}

11) Which of the following homework problems are equations? Justify your answer.

(1) 2x3 – 4x

2 (2) 6 – 3x = 6x (3) 3(2x – 7) (4) 5x

2 + 3x - 2x

2 +3 (5)

3 1

4 8

x

12) Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words

every day.

Write an inequality that can be used to determine how many days, d, it takes Peter to be able to

spell at least 75 words.

Use this inequality to determine the minimum number of whole days it will take for him to be able to

spell at least 75 words.

13) Which expression is equivalent to 4 3( )a

7 12 64(1) (2) (3) (4)a a a a


14) Given the graph of f(x), sketch the following graphs:

a. f(x) + 2

b. f(x) – 3

c. 2f(x)

15) The graph of g(x) is given for the values -5 x 5.

Find the following

a) The domain of g(x).

b) The range of g(x).

c) Is g(x) a function?

d) g( 0) = ?

e) g( 3) = ?

f) if g(x) = 3, find x.

g) How many values of x satisfy g(x) = 1?

h) What is the maximum value of g(x)?

i) How many roots does g(x) have?

16) Administrators at a school use a function, I, to assign each student a unique identification number.

I(n) represents the id number assigned to the student and n is the students in your school. What

would be the most appropriate domain for the function? What would be the most appropriate range

for the function?

17) Express the product of 2x2 + 7x - 10 and x + 5 in standard form.


Unit 10 – The Graph of Functions

Homework 1: Interpreting the Graph of a Function (F-IF.1, F-IF.2, F-IF.4, F-IF.6)

1) Identify the rate of change in each of the following and state how you arrived at that answer.

a) b)

Draw the diagram when n = 4

2) Identify the rate of change and the domain and range for each graph below.

a) b)

3) John left his home and walked 3 blocks to his

school, as shown in the accompanying graph.

a) What is one possible interpretation of the section

of the graph from point B to point C?

b) Between which two points was he walking the fastest?

Explain how you arrived at that decision.

x f(x)

-20 -37

-15 -27

-10 -17

-5 -7

0 3


4) An electronic store has 20 CD players in stock. The manufacturer ships these in boxes of 12 Cd

players per box. Write a linear function that relates the number of boxes to the total number of CD

players in the store. Graph the function. State the domain of the function.

a) Identify the dependent variable

b) Identify the independent variable

c) Graph the function

d) State the domain of the function

5) Tom walks away from his house at a speed of 2 meters per second. He walks for 50 seconds.

At 100 meters from home Tom starts to walk towards home. He walks for 60 meters at a speed of 3

meters per second. Tom now changes direction and is now walking away from home at a fast pace.

His speed is 4 meters per second. He walks at this speed for 30 seconds. After Tom has walked for

160 meters in 100 seconds, he stops and rests for 20 seconds.

a) Identify the dependent variable

b) Identity the independent variable

c) Create a table of values

d) Graph the results showing his walk


Unit 10 – Graph Linear Functions

Homework 2 –Graphing Functions/ Programming Code ( F-IF.1,F-IF.2, F-IF.7,F-LE.2)

Review

1) The cost of a taxi ride for three companies is listed below:

Company A charges $6.30 plus 35¢ per ⅛ of a mile.

Company B charges $3.50 plus 55¢ per ⅛ of a mile.

Company C charges a flat fee of $30 for any ride less than 6  miles.

a) Create an equation for each company where C is the cost of going x miles.

b) Graph your equations on the same coordinate system. Label and mark your axes.

c) Give a mileage where Company A is cheaper, where Company B is cheaper, and where C is cheaper.

d) For what mileage is Company A the same cost as Company B?


Hw 2 continued

2) a) Perform the instructions for the following programming code as if you were a computer and your

paper was the computer screen.

Declare x integer

Let f(x)= 3x - 1

Initialize G as {}

For all x from -1to 2

Append( x , f(x) ) to G

Next x

Plot G

b) Write three or four sentences describing in words how the

thought code works.

3) Perform the instructions for the following programming code as if you were a computer and your



Hw 2 continued



a)


Hw 2 continued

5) Answer the following questions about the thought code:

a) What is the domain of the function f?

b) Plot the graph of f according to the instructions in the thought code.

c) Look at your graph of f. What is the range of f?

d) Write three or four sentences describing in words how the thought code works.



Homework 3 – Piecewise Functions (F-IF.6, F-IF.7, F-BF.3)

1) The graph of a piecewise function f is shown to the right. The domain of 𝑓 is 2 5x

a. Create an algebraic representation for 𝑓. Assume that the graph of 𝑓 is composed of straight line

segments.

b) Sketch the graph of 𝑦 = (𝑥-2) and state

the domain and range.

c) Sketch the graph of 𝑦 = 2(𝑥) and state the domain and range.

d) Sketch the graph of 𝑦 = (2𝑥) and state the domain and range.

e) How does the domain of 𝑦 = (𝑥) compare to the domain of 𝑦 = (𝑘𝑥), where 𝑘 > 1?


2 1 2

5 4 2

x xf x

x x

Hw 3 continued

2) Sketch the graph of


4) Mary went online to find the cost of mailing a package to her friend Jessica. She found the following

chart of cost for mailing a package using regular mail from her location to Jessica’s home

Write the equation that represents this data.

Graph the data.



Homework 4 – Transformations of Functions with Parent Graphs (F-IF.4, F-BF.3)

Review

1) Graph each of the function below WITHOUT using your graphing calculator.

a) 2y x b) | |y x

c) y x d) 1

yx

e) 3y x f) y x (greatest integer function)


Hw 4 continued

2) Graph 2xy and graph the following and explain what transformation takes place.

a. 12 xy

b. 12 xy

Observation (Conclusion)

______________________________________________

______________________________________________


a. 2)1( xy

b. 2)1( xy


_______________________________________________

_______________________________________________


a. 2xy


________________________________________________

________________________________________________


Hw 4 continued


a. 22xy

b. 2

2

1xy


________________________________________________

________________________________________________

6) Graph y x and graph the following and explain what transformation takes place.

a. xy

b. y x


_________________________________________________

_________________________________________________

7) Graph y x and graph the following and explain what transformation takes place.

a) 2y x

b) 1

2y x


_________________________________________________

_________________________________________________



Homework 5: Transformations of Functions – Sketching Graphs (F-IF.4, F-BF.3, F-LE.2, F-IF.7)

Review

Explain what transformation happens to f(x) for each of the followings where c is a constant

1) a. y = f(x) + c ___________________________________________________

b. y = f(x) – c ___________________________________________________

c. y = f(x + c) ___________________________________________________

d. y = f(x – c) ___________________________________________________

e. y = 2f(x) ____________________________________________________

f. y = ½ f(x) ____________________________________________________

g. y = - f(x) _____________________________________________________

h y = f(-x) _____________________________________________________

2) Graph each of the following without your calculator.

a) 1y x b) 1 2y x


Hw 5 continued

3) Graph each of the following without your calculator.

a) | 2 |y x b) | 1 | 2y x

c) | | 1y x d) 2 | |y x

e) 2y x f) 1y x


Hw 5 continued

4) Write a new equation according to the transformations given on the parent equation.

a. y x Shift right 4, shift down 2

New equation ___________________________________________________

b. 3y x reflect over x-axis, shift up 1

New equation ___________________________________________________

c. Use 3y x and sketch the graph of 3( 2) 4y x

d) Use y = y x and sketch the graph of 2 1y x



Homework 6 - Concept Connectors (F-IF.4, F-BF.3, F-LE.2)

1. Given the graph of f(x) as shown below over the domain 3 6x

a. )()(1 xfxf b. )()(2 xfxf c. 1)()(3 xfxf

d. )1()(4 xfxf e. )2()(5 xfxf f. 6 ( ) ( ) 1f x f x

g. )2()(7 xfxf h.

22

1)(8

xfxf



Homework 7: Foundations – Slopes of Linear Equations (F-IF.4, F-IF.6)

1) Find the slope of each line through the given points.

a) (3,7) and (6,10) b) ( -2, 1) and (7, 1) c) ( 2, -4) and ( 4, -12)

d) (6, 8) and (6, -2) e) f)

2) What is the slope of each of the following lines?

a) y = -2x + 4 b) y – x = 2 c) 3y – 4x = 9 d) 2x – 5y = 6

3) For each of the following write the equation of the line in slope-intercept form.

a) Write the equation of a line parallel to the x-axis through the point (3 , 6).

b) Write the equation of the line parallel to y = 2x – 3 with a y-intercept of 5.

c) Write the equation of the line parallel to the y-axis through the point ( -2, -6).

d) Write the equation of the line having a slope of 3 and passing through the point (-2, 4).

4) Which point lies on the line whose equation is 3x – 4y = 5?

(1) ( 0 , 2) (2) (2 , 1) (3) (3 , 1) (4) (1 , -1)


Hw 7 continued

5) Which linear equation represents a line containing the point (2,-2)?

(1) x + y = 4 (2) x – y = 4 (3) 2x + 2y = 4 (4) 2x – y = 2

6) What is the equation of the line that has a slope of -4 and passes through the point (3 , -2)

(1) y = -4x + 10 (2) y = -4x – 10 (3) y = -4x + 5 (4) y = -4x - 14

7) If point is on the line whose equation is , what is the value of b?

8) A line having a slope of passes through the point . Write the equation of this line in slope-

intercept form.

9) What is an equation of the line that passes through the point and has a slope of 2?

10) Which linear equation represents a line containing the point (1, 3)?

11) Write the equation that represents the line that passes through the point (3, 4) and is parallel to

the x-axis?

12) Write the equation of a line that is perpendicular to the equation 2 3 6x y and passes through the

point (4,1).




1a) Perform the instructions for the following programming code as if you were a computer and your


Declare x integer

Let f(x)= 4x +3

Initialize G as {}

For all x from -1to 2

Append( x , f(x) ) to G

Next x

Plot G

b) Write three or four sentences describing in words how the thought code

works.



Declare x integer

For all x from -2 to 3

Print 3x2

Next x

3) The graph of a piecewise function f is shown to the right.

The domain of 𝑓 is 6 7x

a. Create an algebraic representation for 𝑓. Assume that

the graph of 𝑓 is composed of straight line segments.

b) Sketch the graph of 𝑦 = (𝑥-2) and state

the domain and range.

c) Sketch the graph of 𝑦 = 2(𝑥) and state the domain and

range.

d) How does the domain of 𝑦 = (𝑥) compare to the

domain of 𝑦 = k(𝑥), where 𝑘 > 1?


Hw 8 continued


5) Eva and James live at opposite ends of the hallway in their apartment

building. Their doors are 40 feet apart. They each start at their door

and walk at a steady pace towards each other and stop when they meet.

Suppose that:

Eva walks at a constant rate of 2 feet every second.

James walks at a constant rate of 3 feet every second.

a. Graph both people’s distance from Eva’s door versus time

in seconds.

b. According to your graphs, approximately how far will they

be from Eva’s door when they meet?

3 1 2

2 3 2

x xf x

x x




1) What is the equation of the line that passes through the points (3,-3) and (-3,-3)?

(1) y = 3 (2) x = -3 (3) y = -3 (4) x = y

2) What is the value of x in the equation 2 26

3x x ?

(1) -8 (2) 1

8 (3)

1

8 (4) 8

3) What is the speed, in meters per second, of a paper airplane that flies 24 meters in 6 seconds?

(1) 144 (2) 30 (3) 18 (4) 4

4) What is the slope of the line that passes through the points (2,5) and (7,3)?

(1) 5

2 (2)

2

5 (3)

8

9 (4)

9

8

5) Which value of p is the solution of 5p – 1 = 2p + 20?

(1) 19

7 (2)

19

3 (3) 3 (4) 7

6) Which graph represents a linear function?

(1) (2) (3) (4)

7) Which property is illustrated by the equation b(x – y) = bx – by?

(1) associative (2) inverse (3) commutative (4) distributive


Practice 10 continued

8) The accompanying table represents the number of hours a student worked and the amount of money a

student earned. Write an equation that represents the number of dollars, d, earned in terms of the number

of hours, h, worked.

Using this equation, determine the number of dollars the

student would earn for working 40 hours.

9) On the grid, solve the system of equations graphically for x and y 2x – y = 6

2y = -x + 8

and check your answers.

10) The line graph shows temperatures in

Celsius over the year in Jamaica.

a) Which month had the highest

temperature?

b) Which month had the lowest

temperature?

c) What is the difference in temperature

between March and May?

d) How many months have a temperature

higher than 32 degrees Celsius?

11) The function f has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}.



Number of hours (h) Dollars earned (d)

8 $50.00

15 $93.75

19 $118.75

30 $187.50


Unit 11 – Foundations – Rational Expressions

Homework 1: Rational Expressions ( & ) (A-APR.1, A-APR.2, A-APR.6, A-APR.7)

REVIEW

1) Factor completely

a) 5y2 – 125 b) 3ax

2 – 12ax –15a c) 2x

2 + 3x – 2

2) For what value(s) of x is the rational expression undefined?

a) 3

2x b)

3

5

x

x

c)

4

x d)

2

4

9x e)

2

2

1

6

x

x x

3) Express each expression in simplest form with positive exponents only.

a) 3 5

4 3

10

15

x y

x y b)

2 3

2 2 3

9

3

x y z

x y z c)

2

2

16

4

x

x x

d)

2

2

2 8

2 8

y y

y

4) Perform the indicated operation and reduce to lowest terms.

a) 2 4 2 2

3 3 3

5 9

3 20

x y y z

y z xy b)

2 9 4

2 6 3

x x

x x

c) 2 23 2 1

5 10 10 10

x x x

x x

d)

2

2

6 3 6

4 5

x x x

x x


HW 1 – continued

e. 2 23 2 1

6 4 6 6

y y y

y y

f.

2 2

2

16 5 6

10 40 6 8 2

x x x

x x x

Express each in simplest form.

5) 3 9 2 2

5 3 2

15 10

3 6

x y x y

y z z 6)

2

3

5 7 10

25 2

x x x

x x x

7) Find the area of a rectangle whose length is 2 9

3

x

x

and whose width is

2

4 16

7 12

x

x x

.


Unit 11 – Foundations – – Rational Expressions

Homework 2: Rational Expressions (Addition & Subtraction) (A-APR.1, A-APR.7)

REVIEW

1) For what value(s) of x is the rational expression undefined? 2

1

4

x

x

2) Express in simplest form: 3 23 2x x x

x

3) Perform the indicated operation and reduce to lowest terms: 2

2 2

12 6 2

20 3 75

x x x

x x x

4) Express in simplest terms.

a) 6 2

5 5x x b)

7 14

2 2

x

x x

c)

2 3 3 5

2 10 2 10

y y y

y y

d) 4 2

3 5

x x e)

3 2

4x x f.)

2

3 2

y y

g) 3 3

2x x

h)

5 2

3y y

i)

2

5

25 5

y

y y


HW 2– continued

j) 2

2 1

2 3 3

x

x x x

k)

2 2

6 3

4 3 7 12y y y y

l) 2

3 3 2

1 1 1

x

x x x

m)

2 2

2

8 12 2

y

y y y y

Express in simplest terms.

5) 7 14

2 2

x

x x

6)

2

22

1x

7) Find the perimeter of the rectangle whose length is 1x

x

and whose width is

2

2

x ?


Unit 11 – Foundations – – Rational Expressions

Homework 3: Solving Fractional Equations (A-ARP.1, A-ARP.7, A-REI.2)

REVIEW:

Express each of the following in simplest terms:

1)2 2

2

6 16 5 5

5 109 8

x x x x

xx x

2)

2 2

7 6

49 2 35y y y

3) Solve each equation and check.

a) 5 2

2 3

x

x

b)

8 6

2 4x x

c)

3 2 1

3 2 2

x

x

d) 1 3 28

3 5 x e)

3 1 1

2 2y y f)

7 1 5

9 6x

g) 2

4 3

x x

x x

h)

2 1 1

2 5 3

y y

y y

i)

2 3 4

2 4 2

y

y y


HW 3 continued

4) Find the solution set of each of the following.

a) 1 1 1

5 10x x b)

2 1 2

3 6 x c)

1 4

6 3 6

x

x x

5) Solve each equation and check.

a) 2

4 1 1

2 4 2x x x

b)

2 86

3 3x x


Unit 12 – Quadratic Functions

Homework 1: Factoring Polynomial Expressions (A.SSE.2)


A) 4( x + 5) B) 3x( x2 – 2x + 5) C) 2a

2b

3( 5ab

2 – 7a)

D) ( x + 2)( x + 3) E) ( 2x – 5) ( x – 2) F) ( x+ 3) ( x - 3)

G) (3x – 2)( x2 + 4x – 5) H) ( 4x

2 + 3x -1) ( 2x

2 – 4x + 5)

I) 2(3 )x J) 2(2 3) 3)x x

2) Factor each. a) 4x + 8 b) 12a + 15 c) 2ax - 7a

d) 5ax + 15 e) 6x2 - 9x f) 4x

3 – 8x + 4 g) 25x

4y

2 – 10x

2y

h) 2 2x y xy i) 3 25 10 15y y j) ( ) ( )a x y b x y k) ( ) y(x y)x x y

3) Factor each:

a) x2 – 25 b) 2 36a c) 4x

2 – 49 d) 16x

2 – 9y

2

e) 2 2425

9x y f) 9 – x

2 g) x

2 – y

2 h) 225 a

i) 2 2

9 4

x y j) 2 2a b k) 20.25 0.64x l) 21

19

x


Hw 1 continued

4) Factor each.

a) x2 + 7x + 10 b) y

2 – 9y + 18 c) x

2 - 2x –15

d) y2 + 7y – 18 e) x

2 - x – 42 f) y

2 + 25y + 150

g) 24 4 1x x h) 4 2 2 42a a b b i) 2 2 42r rs s

5) Factor completely a) 3x2 – 12 b) ay

2 – 64a

c) 2x2 – 2x – 12 d) 3x

2 – 9x – 30 e) x

4 – y

4

f) 5y3 – 10y

2 – 75y g) 3 21

9x xy h) ax

2 – 5ax + 4a



Homework 2: Geometric Applications using Polynomials (A-APR.1, A-APR.7, F-BF.1A, F-IF.8A)

Review:

1) Factor completely:

2 2 2 4 4 24) 9 48 64 ) ) 36 24 5

25a x xy y b x x y c x x


A) 4( x + 5) B) 3x( x2 – 2x + 5) C) 2a

2b

3( 5ab

2 – 7a)

D) ( x + 2)( x + 3) E) ( 2x – 5) ( x – 2) F) ( x+ 3) ( x - 3)

G) (3x – 2)( x2 + 4x – 5) H) ( 4x

2 + 3x -1) ( 2x

2 – 4x + 5)

3) Use algebra to explain how you know that a rectangle with side lengths three less and three

more than a square will always be 9 square unit smaller than the square. What is the

difference if the sides are 4 more and 4 less?

4) The length of a rectangle is 7 more than its width. If x represents the width of the rectangle represent

the perimeter of the rectangle in terms of x.

5) The length of a rectangle is represented by 3x – 1 and the width by 3x, represent the area of the

rectangle as a polynomial in simplest form.


Hw 2 continued

6) The measure of the base of a triangle is represented by 6x+1 and the height is 3x, represent the area of

the triangle as a polynomial in simplest form.







9) A playground in a local community consists of a rectangle and two semicircles, as shown in the

diagram below.

Write an expression that represents the amount of fencing, in yards, that would be needed to

completely enclose the playground?



Homework 3: Factoring Strategies (A-APR.1, A-APR.7, F-BF.1A, F-IF.8A, A-SEE.3)

Review

1) Find the product and simplify each. a) 23 (2 5 )x x x b) 2 3 35 (3 4 )a b ab a b

c) 2 3 2(4 )m n d) (3x – 4y)(3x + 4y) e) ( 3x – 2)(x + 5) f) (5x – 3)2

2) Factor each completely: a) 6ax2 – 9ax b) x

2 – 81 c) x

2 + 4x – 12

d) 2 24121

25x y e) 2x

2 + 6x – 36 f) x

2 – x – 20

g) x2 +8x + 7 h) x

2 – 17x + 72 i) x

2 - 11x +30

3) Factor a) 2x2 + 7x –15 b) 3x

2 – 7x + 2 c) 5x

2 + 13x – 6

d) 6x2 + 7x – 5 e) 10x

2 +17x +3 f) 6x

2 + 11x –10

g) 12x2 + 8x – 15 h) 6x

2 – 26x – 20 i) 22 6

5 5 5

xx


Hw 3continued

4) Use the structure of these expressions to factor completely.

2 2 4 2) 4 12 7 ) 9 12 4 ) 4 5a x x b x x c x x

5) Use algebra to explain how you know that a rectangle with side lengths five less and five

more than a square will always be 25square unit smaller than the square. What is the

difference if the sides are 2 more and 2 less?

6) A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the walkway is 15

feet more than the width. Write an equation that could be used to determine the dimensions of the walkway.

Solve this equation to find the length and width, in feet, of the walkway.

7) The area of the rectangle below is represented by the expression12𝑥2 + 12𝑥 + 3 square units.

Write two expressions to represent the dimensions, if the length is known to be three times the width.

8) Jack is building a rectangular dog pen that he wishes to enclose. The width of the pen is 2 yards less

than the length. If the area of the dog pen is 15 square yards, how many yards of fencing would he

need to completely enclose the pen?



Homework 4: Solving Quadratic Equations (A-SSE.3, A-APR.3, A-REI.4B, F-IF.8)

Review:


2 2 2 4 4 29) 9 48 64 ) ) 36 24 5

16a x xy y b x x y c x x

2) The accompanying diagram shows a square with side y inside a square with side x.

Express the area of the shaded region as a polynomial in terms of x and y

3) Solve each equation and check:

a) x2 – 5x –14 = 0 b) x

2 + 21 = 10x c) x

2 – 49 = 0

d) x2 –5x = 0 e) 3x

2 +13x –10 = 0 f) 2x

2 – 10x – 12 = 0

g) 3x2 + 2x – 1 = 0 h) 15x

2 – 10x = 0 i) x(x – 5) + 4 = 0

j) x2 – 7x + 6 = 0 k) x

2 + 8x + 15 = 0 l) x

2 – 3x - 10 = 0

m) 2x2 + 7x + 6 =0 n) x

2 – 4x = 0 o) 25x

2 – 9 = 0



Homework 5: Solving Quadratic Equations (A-SSE.3, A-APR.3, A-REI.4B, F-IF.8)

Review:

1) Solve each equation for x:

a) 3x2 +10x + 3=0 b) 2y

2 + 11y + 5=0 c) 5x

2 – 3x =8 d) 6x

2 + 5x = 4

2) Solve :

3) Amy tossed a ball in the air in such a way that the path of the ball was modeled by the

equation . In the equation, y represents the height of the ball in feet and x is the

time in seconds. At what values of x does the ball hit the ground?

4) An arch is built so that its shape can be represented by a parabola with the equation ,

where y is the height of the arch. Find the width of the arch at its base.

2 2 2) 9 1 5 ) 8 4 ) 5 125 0a x b x c x

2 2 22) 4 5 11 ) 12 0 ) 6 3 15

3d x e x f x

2 2 2) 2( 3) 12 ) 5( 6) 1 19 ) 10 ( 2) 6g x h x i x



Homework 6: Creating Quadratic Equations (A-APR.3, A-REI.4B, F-IF.8, F-BF.1, F-LE.3)

Review:

1) Solve:

2) Find three consecutive positive integers such that the square of the first is 45 more than the sum of the

second and the third.

3) One positive number is 5 more than another. Their product is 36. What are the numbers?

4) Find three consecutive positive integers such that the square of the first is 12 more than the sum of the

second and the third.

5) The area of the rectangular playground enclosure at South School is 500 square meters. The length of the

playground is 5 meters longer than the width. Find the dimensions of the playground, in meters. [Only an

algebraic solution will be accepted.]

6) A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the

walkway is 15 feet more than the width. Write an equation that could be used to determine the

dimensions of the walkway. Solve this equation to find the length and width, in feet, of the walkway

2 2 225) 1 ) ( 3) 1 8 ) 4 ( 2) 2

4a x b x c x


Unit 12 – QUADRATICS

Homework 7: Graphs of Quadratic Functions (A-APR.3, A-REI.4B, F-IF.8A, F-IF.7C)

Review:

1) Find the roots of the following equations:

a) x2 – 7x + 6 = 0 b) x

2 + 8x + 15 = 0 c) x

2 – 3x - 10 = 0

d) 2x2 + 7x + 6 =0 e) x

2 – 4x = 0 f) 25x

2 – 9 = 0

2) Answer the following questions based on the graph below:

Graph A Graph B Graph C

a) State the x-intercepts:

b) State the y-intercept:

c) Vertex:

d) Sign of the leading coefficient:

e) Does the vertex represent a minimum or maximum?

f) Find two x values that have symmetry with the axis of symmetry

g) State the equation of the axis of symmetry.

h) Describe the end behavior.

Graph A Graph B Graph C


Hw 7 continued

3) Answer the following questions based on the graph below:

a) Interval where the function is increasing.

b) Interval where the function is decreasing.

c) Average Rate of Change on an Interval [1,3]

d) Average Rate of Change on an Interval [3,4]

4) Compare the two graphs below

a) Explain the differences between their key features.

b) Explain the similarities between their key features.






Homework 8: Graphing Functions from Factored Form (A-APR.3, A-REI.4B, F-IF.8A, F-IF.7C)

Review:

1) Solve the following equations: 2 2 2 2) 16 9 ) 5 6 ) 2 12 5 ) 3 17 10a x b x x c x x d x x




3) Find the x intercepts for each of the following using algebraic techniques.

2 2 2) ( ) 21 10 ) ( ) 25 ) ( ) ( 5) 4 ) ( ) 3 16 5a f x x x b g x x c h x x x d k x x x

4) Find the y intercept for each of the following using algebraic techniques.

5) Given the equation ( ) ( 2)( 3)f x x x



c) State the equation of the axis of symmetry

d) State the vertex

e) Is the vertex a maximum or a minimum?

f) Graph the equation

2 23 2) ( ) 5 1 ) ( ) ( 3) 2 ) ( ) 3

4 3a f x x x b g x x x c h x x x


Hw 8 continued

6) Given the equation 2( ) 2 6 36g x x x




d) State the vertex


f) Graph the equation.

7) Given the equation ( ) 2( 3)( 1)h x x x




d) State the vertex



8) Given the equation 2( ) 9h x x




d) State the vertex




Hw 8 continued

9) A rocket shot into the air attains a height that can be described by the equation y = -16x2 + 240x

where y is the height of the rocket in feet and x is the time in seconds after launch. What is the

maximum height of the rocket and when will it hit the ground?

10) A coin is thrown upward from the top of a platform and the height of the coin is represented by the

equation y = -4.9x2 + 19.6x + 300 where y represents the height in meters and x represents the time

in seconds. What is the coin’s maximum height to the nearest tenth of a meter? How long, to the

nearest tenth of a second, will the coin stay in the air?

11) A diver’s position above the water is represented by the equation y = -16t2 +32t + 48 where t

represents the time in seconds and y represents the height in feet above the water. Find the greatest

height the diver attains and how many seconds will elapse before the diver enters the water?

12) Future projection for sales of a company are modeled by the equation s = 2x2 – 24x +100 where s is

in thousands of dollars and x is the number of months in the future. (0 ≤ x ≤ 24). What is the

minimum amount of sales expected according to the model? In how many months will this

minimum amount occur?



Homework 9: Interpreting Quadratic Functions (F-LE.3 A-REI.4B, F-IF.8A, F-IF.7C)

Review

1) Given the equation ) 3( 4)( 2)fx x x




d) State the vertex



2) A Projects projected profit is represented in the

graph below where y is the profit in millions of

dollars and x is the number of months of operation.

a) How many months will it take for the company

to achieve its maximum profit?

b) When is the first time the company showed a

profit? Explain your answer.

c) Estimate the value of 𝑃(0) and explain what

the value means in the problem and how this

may be possible.

d) How long will it take the company to make a profit of 8 million dollars?

e) Find the domain that will only result in a profit for the company and find its corresponding range of

profit.

f) Choose the interval where the profit is increasing the fastest:

[3,4.5] [4.5,6] [7.5,9]


Hw 9 continued

3) Jim and Kevin each threw a baseball into the air.

The vertical height of Jim’s baseball is represented by the graph 𝑷(𝒕) below. 𝑷 represents the

vertical distance of the baseball from the ground in feet and 𝒕 represents time in seconds.

The vertical height of Kevin’s baseball is represented by the table values k(t) above.

𝑲(𝒕) represents the vertical distance of the baseball from the ground in feet and 𝒕 represents

time in seconds.

Use the above functions to answer the following questions.

a) Whose baseball reached the highest? Explain your answer.

b) Whose ball reached the ground fastest? Explain your answer.

c) Jim claims that his ball reached its maximum faster than Kevin’s? Is his claim correct or

incorrect? Explain your answer.

d) Find 𝑷(𝟎) and 𝑹(𝟎) values and explain what it means in the problem. What conclusion can

you make based on these values? Did they throw the ball from the same place? Explain

your answer.

e) Kevin claims that he can throw the ball higher than Jim. Is his claim correct or incorrect?

Explain your answer.



Homework 10: Completing the Square (A-SSE.3B, A-REI.4a, b, F-IF8)

Review

1) Factor each completely: a) 64x2 – 121 b) 15x

3 + 5x

2 c) x

2 + 8x + 12

d) 2x2 + 3x – 5 e) 4x

2 – 8x – 60 f) 6x

2 – 13x + 5 g) x

3 – 81x + x

2 - 81

2) Solve for x: a) x2 – 14x + 33 = 0 b) 3x

2 - 16x + 5 =0 c) x

2 +3x = 28

3) Rewrite each expression by completing the square. Express each answer such that it

includes a perfect square binomial.

2 2 2 2

2 2 2 2

2 2 2 2

2 2 2

) 6 3 ) 8 5 ) 4 2 ) 10 10

1 3 2 3) 5 1 ) 7 5 ) )

2 16 5 25

) 2 8 3 ) 3 12 14 ) 3 2 5 ) 9 4 1

1 1) 2 5 ) 2 5 ) 2.4 3.6 8.25

2 3

a x x b x x c x x d x x

e x x f x x g x x h x x

i x x j x x k x x l x x

m y y n a a o k k


2 2 2

2 2 2

2 2 2

) 6 5 0 ) 2 6 0 ) 4 32 0

) 2 5 8 0 ) 4 4 99 0 ) 4 4 39 0

1) 5 9 ) 1.2 4.8 2.4 ) 4 24 11

2

a x x b x x c x x

d x x e x x f x x

g x x h x x i x x


Homework 11: Solving by Completing the Square (A-SSE.3B, A-REI.4a, b, F-IF8)

Review:

1) Rewrite each expression by completing the square.

2) Solve each equation by completing the square.

2 2 2 21) 4 2 ) 6 12 5 ) 1.2 4.8 12 ) 2 5

3a x x b x x c x x d x x



Homework 12: Solving Equations by Formula (A-REI.4B, A-SSE.3, A-APR.3, F-IF.8)

Review:


2

2

3 4) 2 7 ) ( 4) 1 ) 2a x x b x x c

x x

2) Solve each of the following by the quadratic formula. Express all answer in simplest radical form.

2 2 2

2 2

2 2

) 12 29 ) 2 7 ) 5 3

10 1) 2 3 2 ) 5 ) 2 3

2

) 3 2 0 ) 4 ( 1) 8 10 ) 2 5 0

a x x b x x c x x

d x x e x f x xx

g x x h x x x i x



Homework 13: Applying the Discriminant (A-REI.4B, A-SSE.3, A-APR.3, F-IF.8)

REVIEW:

1) Solve for x:

a) x2 – x + 4 = 3x + 49 b) x

2 – 10x – 5 = 0

2) Without solving, determine the number of real solutions for each quadratic equation.

a) 2x2 – 4x + 5 = 0 b) 3x

2 – 5x = 4 c) x

2 – 6x + 9 = 0

d) 3x2 + 5x –2 = 0 e) 4x

2 + 20x + 25 =0 f) x

2 = 25

3) Which of the following equations has real, rational and equal roots?

(1) 2x2 + 7x – 9 = 0 (2) 9x

2 + 6x + 1 = 0 (3) 9x

2 – 16 = 0 (4) x

2 – 2x –15 = 0

4) Which of the following equations has no real solutions?

(1) 2x2 + 5x + 9 = 0 (2) x

2 + 6x + 9 = 0 (3) x

2 – 49 = 0 (4) x

2 + 2x –15 = 0

5) Which of the following could be the value of the discriminant of a parabola that intersects the x axis

at 2 distinct points? (1) 0 (2) 25 (3) -15 (4) -4

6) Find the value(s) of b, which would produce two real, rational and equal roots. x2 + bx + 9 =0


Hw 13 continued

7) Find the largest integral value of c for which the roots of 3x2 + 5x + c = 0 are real.

(1) 1 (2) 2 (3) 3 (4) - 1

8) For what value of b will the roots of 2x2 – bx + 9 = 0 produce two real, rational and unequal roots?

(1) - 1 (2) 0 (3) 5 (4) 9

9) Which of the following describes the graph of 2x2 – 3x – 2 =0?

(1) The parabola would lie entirely above the x axis.

(2) The parabola would lie entirely below the x axis.

(3) The parabola would be tangent to the x axis.

(4) The parabola would intersect the x axis at two distinct points.

10) The graph shown below is an example of a quadratic equation whose discriminant is

(1) A negative number

(2) 0

(3) A positive number that is a perfect square.

(4) A positive number that is not a perfect square



Homework 14: Vertex Form /Standard Form (F-IF.8a, A-REI.4B, A-SSE.3)

Review:

1) Without solving, determine the number of real solutions for each quadratic equation.

a) 3x2 – 5x + 5 = 0 b) 2x

2 – 5x - 3 = 4 c) x

2 – 8x + 7 = 0

d) 2x2 - 5x –2 = 0 e) x

2 - 8x + 16 =0 f) x

2 = 16

2) Find the vertex of the graphs of the following quadratic equations.

2 2 2 21) ( 3) 2 ) ( 2) 3 ) 2( 1) 4 ) ( 4.5) 2.5

2a y x b y x c y x d y x

3) Write a quadratic equation to represent a function with the following vertex.

Use a leading coefficient of 1.

) : (3,2) ) : 100, 50 ) : ( 10,30)a vertex b vertex c vertex

4) Write a quadratic equation to represent a function with the following vertex.

Use a leading coefficient other than 1.

5) Write two different quadratic equations whose graphs have vertices at

a) (3 , 2) b) ( - 4, 20) c) (-5,-1) d) (0,4)

) : (20,25) ) : 200, 150 ) : ( 100,30)a vertex b vertex c vertex


Hw 14 continued

6) Graph each of the following on the same coordinate plane and answer the following questions:

2

2

2

) ( 1) 2

) 2( 1) 2

) 2( 1) 2

a y x

b y x

c y x

i) State the vertex of the graph in part a.

ii) What can you say about the vertices in part b and c?

iii) State the graph(s) that open up

iv) State the graph(s) that open down

v) How do graphs b and c relate to graph a?

vi) Is it a shrink or a stretch?

7) Use vocabulary stretch, shrink, opens up, opens down, etc. to compare and contrast the graphs of the

quadratic equations 𝒚 = 𝒙𝟐 + 𝟑 and 𝒚 = −𝟐𝒙𝟐 + 𝟑.



Homework 15: Graphing Root Functions ((F-IF.4, F-BF.3, F-LE.2, F-IF.7))

Review:


2) Create the graphs of 𝒚 = 𝒙𝟐 and 𝒚 = √𝒙.

a) How are the two graphs related?

b) How are they the same?

c) How are they different?

3) Create the graphs of the functions 2( ) 3 ( ) 3f x x and g x x




2 2 2 21) ( 1) 3 ) ( 4) 1 ) 2( 5) 4 ) ( 1.5) 2.5



Hw 15 continued

4) Create the graphs of 𝒚 = 𝒙𝟑 and 𝒚 = √𝒙𝟑

.




5) Create the graphs of the functions y = 3 31 1y x and y x




6) What transformation would you perform on 3 3toproduce 1y x y x

7) What transformation would you perform on 3 3 1y x to produce y x

8) What transformation would you perform on 3 3toproduce ( 2)y x y x



Homework 16: Translating Functions (F-IF.4, F-BF.3, F-LE.2, F-IF.7)

1) Study the graphs below. Identify the parent function and the transformations of that function depicted

by the second graph. Then write the formula for the transformed function.




Hw 15 continued






Hw 15 continued

5) Graph each set of functions in the same coordinate plane. Do not use a calculator.

e) Explain how g(x) is related to h(x).

6) Graph each set of functions in the same coordinate plane. Do not use a calculator.

e) Explain how g(x) is related to k(x)

) ( )

) ( ) 2

) ( ) 2

) ( ) 2

a f x x

b g x x

c h x x

d k x x

3

3

3

3

) ( )

) ( ) 2

) ( ) 2

) ( ) 2

a f x x

b g x x

c h x x

d k x x


Hw 15 continued

7) Graph each set of functions in the same coordinate plane. Do not use a calculator. State the

transformation of f(x) = x2.

8) Write the formula for the function whose graph is the graph of 𝒇(𝒙) = 𝒙𝟐 translated 𝟒. 𝟐𝟓

units to the left, vertically stretched by a factor of 𝟓, and translated 𝟏. 𝟓 units down.

9) Write the function 𝒈(𝒙) = −𝟐𝒙𝟐 + 𝟒𝒙 + 𝟏 in completed square form. Describe the

transformations of the graph of the parent function, 𝒇(𝒙) = 𝒙𝟐, that result in the graph of 𝒈.

2

2

2

2

2

) ( )

) ( ) ( 1) 3

) ( ) ( 3) 2

) ( ) 2 8 9 ,Express in vertex form

) ( ) 2 8 5 ,Express in vertex form

a f x x

b g x x

c h x x

d k x x x

e p x x x



Homework 16: Review for Unit 12 Test

1) Solve each for x:

a) x2 – 6x + 8 =0 b) 3x

2 + x = 10

c) x4 – 29x

2 + 100 = 0 d)

4 16 3

3 3

x x

x x

2) Graph each set of functions in the same coordinate plane. Describe the transformations of the graph

of the parent function. Do not use a calculator.

f) Explain how g(x) is related to h(x).

) ( )

) ( ) 2

) ( ) 2

) ( )

) ( ) 1 2

a f x x

b g x x

c h x x

d k x x

e p x x


Hw 16 continued

3) Graph each set of functions in the same coordinate plane. Describe the transformations of the graph

of the parent function. Do not use a calculator.


5) Write the formula for the function whose graph is the graph of 𝒇(𝒙) = 𝒙𝟐 translated 2 units

to the left, vertically stretched by a factor of 3, and translated 3 units up.

6) Write the formula for the function whose graph is the graph of translated 3 units

to the right, vertically stretched by a factor of 2, and translated 4 units down.

7) Write the function 2( ) 2 12 18g x x x in completed square form. Describe the

transformations of the graph of the parent function, 𝒇(𝒙) = 𝒙𝟐, that result in the graph of 𝒈.

2

2

2

2

) ( )

) ( ) ( 3)

) ( ) 2( 1)

) ( ) 2( 1) 2

a f x x

b g x x

c h x x

d k x x

2 2 2 21) ( 1) 3 ) ( 4) 1 ) 2( 3) 1 ) ( 2.5) 3.5


3( )f x x


215

4y x

Hw 16 continued

8) The height of a projectile can be modeled by the equation y = -16x2 + 96x + 256, where y is the

height in feet and x is the time in seconds that the projectile is in the air. Find the greatest height of this

projectile. Find how many seconds it takes to attain this height. Find the total time that

the projectile is in the air.

9) Which of the following is the graph of ?

(1) (2) (3) (4)


a) x2 + 6x – 16 = 0 b) x

2 - 4x –7 = 0

11) Jane is given the graph of the function

She wants to find the zeroes of the function but is unable to read them exactly from the graph. Find the zeroes in simplest radical form.

12) Solve each equation and express roots in simplest radical form:

a) 2x2 – 3x – 2 = 0 b) x

2 – 10x + 13 = 0




1) When solving the equation 2 24(2 5) 7 3 14x x , John wrote 2 24(2 5) 3 7x x as his first


a) addition property of equality b) subtraction property of addition


2) Solve for x and express your answer in simplest radical form: 4 3

71x x

3) A baseball player throws a ball from the outfield toward home plate. The ball’s height above the

ground is modeled by the equation y = -16x2 + 48x + 6, where y represents height, in feet, and x

represents time, in seconds. The ball is initially thrown from a height of 6 feet. How many seconds after

the ball is thrown will it again be 6 feet above the ground? What is the maximum height, in feet, that the

ball reaches? ( The use of a grid is optional.)

4) A landscape architect’s designs for a town park call for two parabolic-shaped walkways. When

the park is mapped on a Cartesian coordinate plane, the pathways intersect at two points. If the

equations of the two curves of the walkways are y = 11x2 + 23x + 210 and y = -19x

2 – 7x + 390,

determine the coordinates of the two points of intersection.


Hw 17 continued

5) The graph of ( )f x is shown here:

What are the zeroes of the function?

If 2( )f x ax bx c what is ( )f x in factored form?

6) The graph of ( )f x is shown here:



7) What is the product of 2 1

1

x

x

and

3

3 3

x

x

expressed in simplest form?

(1) x (2) 3

x (3) x + 3 (4)

3

3

x

8) Which situation should be analyzed using bivariate data?

(1) Ms. Saleeem keeps a list of the amount of time her daughter spends on her social studies

homework.

(2) Mr. Benjamin tries to see if his student’s shoe sizes are directly related to their heights.

(3) Mr. DeStefan records his customers’ best video game scores during the summer.

(4) Mr. Chan keeps track of his daughter’s algebra grades for the quarter.

9) Kathy plans to purchase a car that depreciates (loses value) at a rate of 14% per year. The initial cost

of the car is $21,000. Which equation represents the value, v of the car after 3 years?

(1) v = 21,000(0.14)3 (2) v = 21,000(0.86)

3 (3) v = 21,000(1.14)

3 (4) v = 21,000(1.86)

3


Hw 17 continued

10) Which equation most closely represents the line of best fit for the

accompanying scatter plot?

(1) y = x (2) 2

13

y x (3) 3

22

y x (4) 3

2y x

11) What is the value of the third quartile shown in the box

and whisker plot?

(1) 6 (2) 8.5 (3) 10 (4) 12

12) A school wants to add a coed soccer program. To determine student interest in the program, a survey

was taken. In order to get an unbiased sample, which group should the school survey?

(1) every third student entering the building (2) every member of the varsity football team

(3) every member in Mr. Zimmer’s drama classes (4) every student having a French class

13) The prices of seven race cars sold last week are listed in the table below.

What is the mean value of these race cars, in dollars?

What is the median value of these race cars, in dollars?

State which of these measures of central tendency best represents the value

of the seven race cars. Justify your answer

14) Solve the following system of equations algebraically: 3x + 2y = 4

4x + 3y = 7

(Only an algebraic solution can receive full credit)


Hw 17 continued

15) Twenty students were surveyed about the number of days they

played outside in one week. The results of this survey are shown

below. {6,5,4,5,0,7,1,5,4,4,3,2,2,3,2,4,3,4,0,7}

Complete the frequency table below for these data.

Complete the cumulative frequency table below using these data.

On the grid , create a cumulative frequency

histogram based on the table you made.

16) There is a negative correlation between the number of hours a student watches television and his or

her social studies test score. Which scatter plot below displays this correlation?

(1) (3)

(2) (4)

(4)

17) Express the product of 2x2 + 7x - 10 and x + 5 in standard form.


Hw 17 continued

18) The accompanying table represents the number of hours each student studied for a particular test

and the grade that each student achieved.

a) Is the data univariate or bivariate?

b) Is the data quantitative or qualitative?

c) Does the data indicate a positive correlation, negative correlation or no

correlation?

d) What is the equation of the line of best fit?(nearest hundredth)

e) Use the line of best fit to predict a grade if a student studied for exactly 4

hours

19) A company that manufactures cycles first pays a start-up cost, and then spends a certain amount

of money to manufacture each cycle. If the cost of manufacturing c cycles is given by the function

, then the value 35 best represents

a) the start-up cost b) the profit earned from the sale of one radio

c) the amount spent to manufacture each radio d) the average number of radios manufactured

What would it cost to produce 100 cycles?

What does the 25.50 represent?

Study

Time

(hrs)

Grade

3 84

1 68

5 98

4.5 92

2 66

( ) 25.50 35p c c


Full Year Practice Test 1

Part I ( 2 points each)

1) It takes Tammy 45 minutes to ride her bike 5 miles. At this rate, how long will it take her to ride 8

miles?

(1) 0.89 hour (2) 1.125 hours (3) 48 minutes (4) 72 minutes

2) What are the roots of the equation x2 – 7x + 6 = 0?

(1) 1 and 7 (2) and 7 (3) and (4) 1 and 6

3) Which expression represents 18 5

6

27

9

x y

x y in simplest form?

(1) 3x12

y4 (2) 3x

3y

5 (3) 18x

12y

4 (4) 18x

3y

5

4) Marie currently has a collection of 58 stamps. If she buys s stamps each week for w weeks,

which expression represents the total number of stamps she will have?

(1) 58sw (2) 58 + sw (3) 58s + w (4) 58 + s + w

5) Which ordered pair is not in the solution set of 1

4 3 12

y x and y x

(1) (4,2) (2) (3,3) (3) (5,3) (4) (6,2)

6) The sign shown below is posted in front of a roller coaster ride at the Wadsworth County

Fairgrounds.

If h represents the height of a rider in inches, what is a correct translation of

the statement on this sign?

(1) h < 48 (2) h > 48 (3) h ≤48 (4) h≥ 48

7) Which value of x is the solution of the equation 2

53 6

x x ?

(1) 6 (2) 10 (3) 15 (4) 30


8) What is 6 2

4 3a a expressed in simplest form?

(1) 4

a (2)

5

6a (3)

8

7a (4)

10

12a

9) Given real numbers a, b, c, d and e such that c<d, e<c, e>b, and b>a, which of these numbers is

the greatest?

(1) a (2) b (3) c (4) d

10) What is 32 expressed in simplest radical form?

(1) 16 2 (2) 4 2 (3) 4 8 (4) 2 8

11) If the speed of sound is 344 meters per second, what is the approximate speed of sound, in meters

per hour?

(1) 20,640 (2) 41,280 (3) 123,840 (4) 1,238,400

12) The sum of two numbers is 47, and their difference is 15. What is the larger number?

(1) 16 (2) 31 (3) 32 (4) 36

13) If a + ar = b + r , the value of a in terms of b and r can be expressed as

(1) 1b

r (2)

1 b

r

(3)

1

b r

r

(4)

1 b

r b

14) Which value of x is in the solution set of 4

5 173

x ?

(1) 8 (2) 9 (3) 12 (4) 16

15) The box-and-whisker plot below represents students' scores on a recent English test.

What is the value of the upper quartile?

(1) 68 (2) 76 (3) 84 (4) 94


16) Which value of n makes the expression 5

2 1

n

n undefined?

(1) 1 (2) 0 (3) 1

2 (4)

1

2

17) At Genesee High School, the sophomore class has 60 more students than the freshman class. The

junior class has 50 fewer students than twice the students in the freshman class. The senior class is

three times as large as the freshman class. If there are a total of 1,424 students at Genesee High

School, how many students are in the freshman class?

(1) 202 (2) 205 (3) 235 (4) 236

18) What is the value of the y-coordinate of the solution to the system of equations x + 2y = 9

and x – y = 3?

(1) 6 (2) 2 (3) 3 (4) 5

19) Which statement is true about the relation shown on the graph

below?

(1) It is a function because there

exists one x-coordinate for

each y-coordinate.

(3) It is not a function because

there are multiple y-values

for a given x-value.

(2) It is a function because there

exists one y-coordinate for

each x-coordinate.

(4) It is not a function because

there are multiple x-values

for a given y-value.

20) Which graph represents the solution of 3y – 9 ≤ 6x ?

1) 2) 3) 4)


21) Which expression represents 2

2

2 15

3

x x

x x

in simplest form?

(1) -5 (2) 5x

x

(3)

2 5x

x

(4)

2 15

3

x

x

22) What is an equation of the line that passes through the point (4,-6) and has a slope of -3?

(1) y = -3x + 6 (2) y = -3x – 6 (3) y = -3x + 10 (4) y = - 3x + 14

23) When 4x2 + 7x - 5 is subtracted from 9x

2 – 2x + 3, the result is

(1) 5x2 + 5x – 2 (2) 5x

2 – 9x + 8 (3) -5x

2 + 5x – 2 (4) -5x

2 + 9x – 8

24) The equation y = x2 + 3x – 18 is graphed on the set of axes below.

Based on this graph, what are the roots of the equation x2 + 3x – 18 = 0 ?

(1) – 3 and 6 (2) 0 and 18 (3) 3 and – 6 (4) 3 and -18

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 points. Clearly indicate the

necessary steps, including appropriate formulas substitutions, diagrams, graphs, charts, etc. For

all questions, in this part, a correct numerical answer with no work shown will receive only 1

credit.


26) Jane wants to make trail mix made up of almonds, walnuts and raisins. She wants to mix one part

almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost

$10.50 per pound, and raisins cost $4 per pound. Jane has $15 to spend on the trail mix. Determine

how many pounds of trail mix she can make.


216

2y x

27 For English class, Gary must read Grapes of Wraft in 10 days. He reads 112

of the book each of

the first 4 days. For the remaining 6 days, what fraction of the book must Gary read per day?

28 Mr James is 4 times as old as his son. In 16 years he will be only twice as old. What is the age of

the son now.

29 A rectangle’s length is 14 cm more than its width. The perimeter is 264 cm. Find the dimensions

of the rectangle.

30 Solve for x : 2 3 2

4 3

x

x

31 Jane is given the graph of the function

She wants to find the zeroes of the function but is unable to read them exactly from the graph. Find the zeroes in simplest radical form.

32 Express in simplest form: 4 3 3

2

45 90

15

a b a b

a b


Part III




credit.

33 A bank is advertising that new customers can open a savings account with a 3

3 %4

interest rate

compounded annually. Robert invests $5,000 in an account at this rate. If he makes no additional

deposits or withdrawals on his account, find the amount of money he will have, to the nearest cent,

after three years.

34 The table below shows the number of prom tickets

sold over a ten-day period.

Plot these data points on the coordinate grid below. Use a

consistent and appropriate scale. Draw a reasonable line of

best fit and write its equation.

35 Find the roots of the equation x2 = 30 – 13x algebraically.

36 The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund.

Each year the fund will decrease by 5%. Determine the amount of money, to the nearest cent, that

will be left in the sports fund after 4 years.


Part IV




credit.

37 A man is climbing down a ladder that is 10 feet high. At time 0 seconds, his shoes are 10 feet

above the floor, and at time 6 seconds, his shoes are at 3 feet. From time 6 seconds to the 8.5

second mark, he drinks some water on the step 3 feet off the ground. When he completes drinking

the water, he takes 1.5 seconds to reach the ground and then he walks into the living room.

a) Draw a graph representing this story

b) What does the horizontal line segment represent in your graph?

c) If you measured from the top of the man’s head instead of his shoes, how would your graph

change if he is 6 feet tall.


Full Year Practice Test 2

Part I ( 2 points each)

1) If h represents a number, which equation is a correct translation of "Sixty more than 9 times a

number is 375"?

(1) 9h = 375 (2) 9h + 60 = 375 (3) 9h – 60 = 375 (4) 60h + 9 = 375

2) Which expression is equivalent to 9x2 – 16??

(1) (3x + 4)(3x – 4) (2) (3x – 4)(3x – 4) (3) (3x + 8)( 3x – 8) (4) (3x – 8)(3x – 8)

3) Which expression represents (3x2y

4)(4xy

2) in simplest form?

(1) 12x2y

8 (2) 12x

2y

6 (3) 12x

3y

8 (4) 12x

3y

6

4) An online music club has a one-time registration fee of $13.95 and charges $0.49 to buy each

song. If Emma has $50.00 to join the club and buy songs, what is the maximum number of songs

she can buy?

(1) 73 (2) 74 (3) 130 (4) 131

5) Which ordered pair is not in the solution set of 2 1 3 2y x and y x

(1) (1,3) (2) (-1,1) (3) (-2,-2) (4) (-4,-2)

6) Nancy’s rectangular garden is represented in the diagram below.

If a diagonal walkway crosses her garden, what is its length,

in feet?

(1) 17 (2) 22 (3) 161 4) 529


7 Which statistic would indicate that a linear function would not be a good fit to model a data set?

(1) r = -0.96 (2) r = 1 (3) 4)

8 For which function defined by a polynomial are the zeros of the polynomial –3 and –2? 2 2 2 2(1) 5 6 (2) 5 6 (3) 5 6 (4) 5 6x x x x x x x x

9) Solve for x: 3

( 2) 45

x x

(1) 8 (2) 13 (3) 15 (4) 23

10) If the quadratic formula is used to find the roots of the equation , the correct roots are

3 3 5 3 3 5 3 3 5 3 3 5(1) (2) (3) (4)

2 2 4 4

11) Which equation represents a line parallel to the x-axis?

(1) y = -5 (2) y = -5x (3) x = 3 (4) x = 3y

12) Mr. Smith’s algebra class is inquiring about slopes of lines. The class was asked to graph the

total cost , C , of buying h hotdog that cost 75 cent each. The class was asked to describe the slope

between any two points on the graph. Which statement below is always a correct answer about the

slope between any two points on this graph.

(1) the same positive value (2) the same negative value

(3) zero (4) a positive value, but the values varies


13) Which value of x is in the solution set of the inequality

(1) 0 (2) 2 (3) 3 (4) 5

14) The first 3 terms of a geometric sequence are 4 , 6 , 9. What is the next term in the sequence?

(1) 12 (2) 13.5 (3) 32.5 (4) 62.5

15) When solving the equation 2 23(2 5) 7 5 4x x , John wrote 2 26 15 7 5 4x x as his

first step. Which property justifies James's first step?

1) distributive property of multiplication over addition 2) commutative property of addition

3) multiplication property of equality 4) addition property of equality

16) The equation y = - x2 – 2x + 8 is graphed on the set of axes below.

Based on this graph, what are the roots of the equation ?

(1) 8 and 0 (2) 2 and (3) 9 and (4) 4 and

17) What is the sum of 3

2x and

4

3x expressed in simplest form?

(1) 2

12

6x (2)

17

6x (3)

7

5x (4)

17

12x

18) Which value of x makes the expression 2

2

9

7 10

x

x x

undefined?

(1) -5 (2) 2 (3) 3 (4) - 3

19) Which relation is not a function?

(1) {(1,5), (2,6), (3,6), (4,7)} (2) { (4,7), (2,1), (-3,6), ( 3,4)}

(3) { (-1,6), (1,3), (2,5), (1,7)} (4) {(-1,2), (0,5), ( 5,0), (2,-1)}


20) What is the value of the y-coordinate of the solution to the system of equations

x – 2y = 1 and x + 4y = 7?

(1) 1 (2) -1 (3) 3 (4) 4

21) The solution to the equation x2 – 6x = 0 is

(1) 0, only (2) 6, only (3) 0 and 6 (4) 6

22) When5 20 is written in simplest radical form, the result is 5k . What is the value of k?

(1) 20 (2) 10 (3) 7 (4) 4

23) What is the value of the expression | - 5x + 12 | when x = 5?

(1) (2) -13 (3) 13 (4) 37

24) Which equation is represented by the graph below?

(1) y = x2 – 3 (2) y = (x – 3)

2 (3) y = |x| - 3 (4) y = | x – 3|

Part II




credit.

25) Chad complained to his friend that he had five equations

to solve for homework. Are all of the homework problems

equations? Justify your answer.


212

4y x

26) If Mary takes 20 minutes to sort the customer requests and Pat takes 30 minutes to do the same

job, how many minutes will both Mary and Pat, working together, take to sort the customer list.

27) The ages of three brothers are consecutive even integers. Three times the age of the youngest

brother exceeds the oldest brother's age by 48 years. What is the age of the youngest brother?

28) Jim is given the graph of the function He wants to find the zeroes of the function

but is unable to read them exactly from the graph. Find the zeroes in simplest radical form.

29) The chart below compares two runners.

Based on the information in this chart, state which runner

has the faster rate. Justify your answer.

30 On the set of axes below, graph the function represented by 3 1y x for the domain 7 9x


31 What is the sum of the first 19 terms of the sequence 3, 10, 17, 24, 31,…?

32 A high school drama club is putting on their annual theater production. There is a maximum of

800 tickets for the show. The costs of the tickets are $6 before the day of the show and $9 on the

day of the show. To meet the expenses of the show, the club must sell at least $5,000 worth of

tickets.

Write a system of inequalities that represent this situation.

Part III




credit.

33) Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the

parabola whose equation is y = -2x2 – 8x + 3.

34) At the end of week one, a stock had increased in value from $5.75 a share to $7.50 a share. Find

the percent of increase at the end of week one to the nearest tenth of a percent. At the end of week two,

the same stock had decreased in value from $7.50 to $5.75. Is the percent of decrease at the end of

week two the same as the percent of increase at the end of week one? Justify your answer.


35) The test scores from Mrs. Gray’s math class are shown below.

72, 73, 66, 71, 82, 85, 95, 85, 86, 89, 91, 92

Construct a box-and-whisker plot to display these data.

36 Express in simplest form: 2 2

2 2

2 8 42 9

6 3

x x x

x x x

Part IV




credit.

37) On the grid below, solve the system of equations graphically for x and y.

4x – 2y = 10

y = - 2x - 1


7 49 491 2 3 4 49

2 4 2) ) ) )

Practice Test 3

Multiple Choice Questions

1 Brian correctly used a method of completing the square to solve the equation . Brian’s

first step was to rewrite the equation as . He then added a number to both sides of the

equation. Which number did he add?

2 The number of minutes students took to complete a quiz is summarized in the table below.

If the mean number of minutes was 17, which equation could be used to calculate the value of x?

3 Samantha constructs the scatter plot below from a set of data.

Based on her scatter plot, which regression model would be most appropriate?

1) exponential 2) linear 3) quadratic 4) cubic

4 What is the sum of the first 19 terms of the sequence 3, 9, 15,,…?

(1) 1083 (2) 1197 (3) 1254 (4) 1292

1)

2)

3)

4)


5 5 5 51 2 3 4

2 42 58 18) ) ) )

5 Which graph represents a relation that is not a function?

1) 2)

3) 4)

6 What is the range of ?

1)

2)

3)

4)

7 If , what is the value of ?

8 A population of rabbits doubles every 60 days according to the formula

t60P 10( 2 ) , where P is the

population of rabbits on day t. What is the value of t when the population is 320?

(1) 240 (2) 300 (3) 660 (4) 960


9 A sequence has the following terms 1 2 3 4a 4,a 10,a 25,a 62.5.

Which formula represents the n th term in this sequence?

(1) an = 4 + 2.5n (2) an = 4 + 2.5(n-1) (3) an = 4(2.5)n (4) an = 4(2.5)

n-1

10 What is the range of f(x) = |x – 3| + 2 ?

(1) { x | x 3} ( 2 ) { y | y 2} ( 3 ) { x| x real numbers } ( 4 ) { y | y real numbers }

11 On the axes below, for 2 x 2, graph .x 1y 2 3

12 What is the domain of the function shown below?

1) 2)

3) 4)

13 Which graph represents the solution set of ?

1)

2)

3)

4)


14 What is the equation of the graph shown below?

1) y = 2x 2) y = 2

-x 3) x = 2

y 4) x = 2

-y

15 Given the relation { ( 8 , 2 ), ( 3 , 6 ), ( 7 , 5 ) and ( k , 4 )}, which value of k will result in the

relation NOT being a function?

1) 1 2) 2 3) 3 4) 4

16 Which expression is equivalent to

1

2 6 2(9 )x y

?

1) 3

1

3xy 2) 3xy

3 3)

3

3

xy 4)

3

3

xy

17 If f(x) = 29 x , what are its domain and range?

1) domain { x | -3 ≤ x ≤ 3 }; range { y | 0 ≤ y ≤ 3} 2) domain { x | x ≠ ± 3 }; range { y | 0 ≤ y ≤ 3}

3) domain { x | x≤ -3 or x ≥ 3 }; range { y | y ≠ 0 } 4) domain { x | x ≠ 3}; range { y | y ≥ 0 }

18 When x2 + 3x – 4 is subtracted from x

3 + 3x

2 – 2x, the difference is

1) x3 + 2x

2 – 5x + 4 2) x

3 + 2x

2 + x – 4 3) –x

3 + 4x

2 + x – 4 4) –x

3 – 2x

2 + 5x + 4

19 What is the graph of the solution set of ?

1)

2)

3)

4)

20 What is the range of the function shown below?

1) 2) 3) 4)


2 2

2 2

1 1(1) (2) 3 (3) (4) 9

3 9x x

x x

(1 ) ,ntrA P

n

21) A company that manufactures radios first pays a start-up cost, and then spends a certain amount

of money to manufacture each radio. If the cost of manufacturing r radios is given by the function

, then the value 6.50 best represents

1) the start-up cost 2) the profit earned from the sale of one radio

3) the amount spent to manufacture each radio 4) the average number of radios manufactured

22 If n is a negative integer, then which statement is always true?

1) 2) 3) 4)

23 What is the common difference in the sequence 2a + 1, 4a + 4, 6a + 7, 8a + 10, ...?

(1) 2a + 3 (2) -2a – 3 (3) 2a + 5 (4) -2a + 5

24 Which expression is equivalent to 2 1(3 )x ?

25 If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment

in 5 years (Use the formula where A is the amount accrued,

P is the principal, r is the interest rate, n is the number of times per year the money is

compounded, and t is the length of time, in years.)

(1) $5190.33 (2) $5796.37 (3) $5805.92 (4) $5808.08

26 The graph of is shown below.

What is the product of the roots of the equation ?

1) 2) 3) 6

4) 4

( ) 6.50 110c r r


27) What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth?

1) 1.00 2) 0.93 3) -0.93 4) -1.00

28) Given:

Which expression results in a rational number?

1) L + M 2) M + N 3) N + P 4) P + L

29) John has five more nickels than dimes in his pocket, for a total of $1.35. Which equation could be


30) The Jamison family kept a log of the distance they traveled during a trip, as represented by the graph

below.

During which interval was their average speed the greatest?

1) the first hour to the second hour

2) the second hour to the fourth hour

3) the sixth hour to the eighth hour

4) the eighth hour to the tenth hour

5

2 3

25

16

L

M

N

P

1) 0.10( 5) 0.05( ) 1.35 2) 0.05( 5) 0.10( ) 1.35

3) 0.10(5 ) 0.05( ) 1.35 4) 0.05(5 ) 0.10( ) 1.35

x x x x

x x x x


31) Christopher looked at his quiz scores shown below for the first and second semester of his Algebra

class.

Semester 1: 78, 91, 88, 83, 94

Semester 2: 91, 96, 80, 77, 88, 85, 92

Which statement about Christopher's performance is correct?

1) The interquartile range for semester 1 is

greater than the interquartile range for

semester 2.

2) The median score for semester 1 is greater

than the median score for semester 2.

3) The mean score for semester 2 is greater

than the mean score for semester 1.

4) The third quartile for semester 2 is greater

than the third quartile for semester 1.

32) The diagrams below represent the first three terms of a sequence.

Assuming the pattern continues, which formula determines , the number of shaded squares in the nth

term?

33) When solving the equation , Emily wrote

as her first step.

Which property justifies Emily's first step?

(1) addition property of equality (2) commutative property of addition

(3) multiplication property of equality ( 4) distributive property of multiplication over addition

34) Officials in a town use a function, C, to analyze traffic patterns. represents the rate of traffic

through an intersection where n is the number of observed vehicles in a specified time interval.

What would be the most appropriate domain for the function?

1) {…-2,-1,0,1,2,3,…} 2) {…-2,-1,0,1,2,3}

35) If , which statement is always true?

1) f(x) < 0 3) If x < 0, then f(x) < 0.

2) f(x) > 0 4) If x > 0, then f(x) > 0.

2 212 8 9 8 7x x

1) 4 12 2) 4 8 3) 4 4 4) 4 12n n n na n a n a n a n

1 1 13){0, ,1,1 ,2,2 } (4){0,1,2,3...}

2 2 2

1( ) 3

2f x x


Practice Test 4

Open Ended

1 Solve | 4 5 | 13x algebraically for x.

2 Solve the equation below algebraically, and express the result in simplest radical form:

3 Express in simplest form 3 9

2 6 6 2

y

y y

4 What is the common ratio of the geometric sequence shown below?

-2, 4, -8, 16, …

5 A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees

Fahrenheit, of the soup recorded over a 10-minute period.

Write an exponential regression equation for the data, rounding all values to the nearest thousandth.

6 Find the third term in the recursive sequence , where .

7 Determine the sum of the first twenty terms of the sequence whose first five terms are

5, 14, 23, 32, and 41.


8 The height, in inches, of 10 high school varsity basketball players are 78, 79, 79, 72, 75, 71, 74, 74, 83,

and 71. Find the interquartile range of this data set.

9 The table below shows the number of new stores in a coffee shop chain that opened during the years

1986 through 1994. Using to represent the year 1986 and y to represent the number of new

stores, write the exponential regression equation for these data. Round all values to the nearest

thousandth.

10 Determine the solution of the inequality | 3 – 2x | ≥ 7. ( the use of the graph below is optional)

11 The data collected by the biologist showing the growth of a colony of bacteria at the end of each hour

are displayed in the table below.

Write an exponential regression equation to model these data. Round all values to the nearest

thousandth.

Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of

bacteria in the colony at the end of 7 hours.


12 Graph the inequality for x. Graph the solution on the line below.

13 Find the sum of the first eight terms of the series

14 Emma recently purchased a new car. She decided to keep track of how many gallons of gas she

used on five of her business trips. The results are shown in the table below.

Write the linear regression equation for these data where

miles driven is the independent variable. (Round all

values to the nearest hundredth.)

15 Jim purchased a box of jelly beans. The nutrition label on the box stated that a serving of two

jelly beans contains a total of 10 Calories.

On the axes below, graph the function, C, where C (x) represents the number of Calories in x jelly

beans.

Write an equation that represents C (x).

A full box of jelly beans contains 180 Calories. Use the equation to determine the total number

of jelly beans in the box.

Miles Driven Number of

Gallons Used

150 7

200 10

400 19

600 29

1000 51


16 Robert has two jobs. He earns $10 per hour babysitting his neighbor’s children and he earns

$14 per hour working at the coffee shop.

Write an inequality to represent the number of hours, x, babysitting and the number of hours, y,

working at the coffee shop that Robert will need to work to earn a minimum of $425.

Robert worked 20 hours at the coffee shop. Use the inequality to find the number of full hours he

must babysit to reach his goal of $425.

17 On the set of axes below, graph the function | 2 |y x

State the range of the function

State the domain over which the function is increasing.

Graph | 2 | 1y x

State the range of the function

State the domain over which the function is increasing.

18 Over what intervals is the function below increasing

what intervals is it decreasing?

Which quadrants does it occupy?

What is the domain and range


19 For the following graph, describe the features, include: what intervals does it increase/decrease, what

quadrants does it reside in, what are it’s min/max, what are the intercepts, and what are the domain and

range?

20 A cup of soup is left on a countertop to cool. The

table below gives the temperatures, in degrees

Fahrenheit, of the soup recorded over a 10-minute

period.

Write an exponential regression equation for the

data, rounding all values to the nearest thousandth.

21 A wholesale t-shirt manufacturer charges the following prices for t-shirt orders:

$20 per shirt for shirt orders up to 20 shirts.

$15 per shirt for shirt between 21 and 40 shirts.

$10 per shirt for shirt orders between 41 and 80 shirts.

$5 per shirt for shirt orders over 80 shirts.

Graph the step function that represents the

cost for the number of t-shirts purchased

You've ordered 40 shirts and must pay shipping fees of $10.

How much is your total order?


22 Solve algebraically:

[Only an algebraic solution can receive full credit.]

23 Use the data below to write the regression equation (y = ax + b) for the raw test score based on the

hours tutored. Round all values to the nearest hundredth.

Equation:

Create a residual plot on the axes below, using the residual scores in the table above.

Based on the residual plot, state whether the equation is a good fit for the data. Justify your answer


2( ) 2f x x

24 Given the functions g(x), f(x), and h(x) shown below:

g(x)

Order g(x), f(x), and h(x) from greatest to least by average rate of change over the interval 0 2x

25 The graph of ( )f x is shown here:



26) Factor the expression completely.

27) Write an equation that defines as a trinomial where . Solve for x

when .


28) Robin collected data on the number of hours she watched television on Sunday through Thursday

nights for a period of 3 weeks. The data are shown in the table below.

Using an appropriate scale on the number line below, construct a box plot for the 15 values.

29) A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with

a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an

area of 396 square meters.

Write an equation that can be used to find x, the width of

the walkway. Describe how your equation models the

situation. Determine and state the width of the

walkway, in meters.

30) An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each dog.

Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday. Write an equation

to represent the possible numbers of cats and dogs that could have been at the shelter on Wednesday.

Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s

numbers possible? Use your equation to justify your answer. Later, Pat found a record showing that

there were a total of 22 cats and dogs at the shelter on Wednesday. How many cats were at the

shelter on Wednesday?

31) The function f has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}.



32) Express the product of 3x2 - 4x - 5 and x + 3 in standard form.

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