SOL Blitz

A.1: The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

1. Kristen heard that it is 82° Fahrenheit outside. She knows that

, where

F represents the temperature in degrees Fahrenheit and C represents the temperature in degrees Celsius. Which is closest to the temperature outside, in 5degrees Celsius?

A. 28 B. 63 C. 90 D/ 180

2. What is the value of the expression

when x = 5 and y = 1?

3. The length of a certain rectangle is six more than three times its width. If the width of the rectangle is

4 units, what is its length? units 4. Which statement could be represented by the expression n2 + 4n?

A. The square of a number increased by four B. The square of the product of a number and four C. The sum of two times a number and four times a number D. The square of a number increased by four times the number

A.2a: The student will apply the laws of exponents to perform operations on expressions.

1. Simplify each expression.

a) x3 • x5 _______ B) (3x4y6)3 ________ C) x15 x21 __________

2. When simplified, (2x3y4)3 is equivalent to –

A. 6x9y12 B. 6x6y7 C. 8x9y12 D. 8x6y7

3. When simplified, what is the exponent for x?

(x-5)4

(x3)7 x

1

x6

41

6

18

x8 27x12y18

8

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(2x – 5)

(2x + 5)

(2x – 3)

(2x + 3)

(2x + 1)

(2x – 1)

A.2b: The student will add, subtract, multiply, and divide polynomials. *

1. A rectangle is given below. Find the perimeter. 7x + 5

A. 10x + 4 B. 10x2 + 4 C. 20x + 8 3x – 1 D. 20x2 + 8

2. Using the rectangle above, find the area. Area = 3. What is the quotient of 8x3 + 12x and 2x?

A. 4x2 + 6 B. 4x3 + 6x C. 6x2 + 10 D. 6x3 + 10x

4. What is the quotient of 3x2 – 20x – 7 and 3x + 1?

A. x – 7 B. x + 7 C. x + 3 D. x – 3 5. Which expression is equivalent to (4x2 – 3x + 9) + (7x2 – 11) – (x2 – 7x + 2)?

A. 10x2 - 10x – 22 C. 10x2 + 4x – 4

B. 10x6 + 4x2 – 4 D. 11x2 + 4x + 4

A.2c: The student will factor first- and second- degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.

1. What is the complete factorization of 3v2 + 9v?

A. v(3v + 9) B. 3(v2 + 3v) C. 3v(v + 3) D. 3v2(1 + 3v) 2. What is the factored form of 4x2 – 8x + 3? Choose two factors from the box below and write them in the space provided.

21x2 + 8x - 5

(2x – 3) (2x – 1)

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3. What is the complete factorization of 3x2 – 48? A. 3(x2 – 16) C. 3(x – 8)(x + 2)

B. 3(x – 4)(x + 4) D. 3(x – 4)2

A.3: The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form.

1. What is √

A. √

B. 8√

C. √

D. 8

2. In simplest radical form, √ is equivalent to –

A. 13 √ C. 13 √

B. 13 √ D. 13 √

3. Which of the following simplifies to 8√ ?

A. √ B. √ C. √ D. √

A.4a: The student will solve literal equations (formulas) for a given variable.

1. Which inequality is equivalent to 4x – 2y < 8?

A. y < 2x – 4 B. y > 2x – 4 C. y < -2x – 4 D. y > -2x – 4

2. Solve for C:

A. C = F – 32 x

C. C =

B. C =

D. C =

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Subtraction Property of Equality

Additive Identity Substitution Property

Division Property of Equality

Distributive Property Associative Property

3. Identify any equivalent expressions:

A.4b: The student will justify steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets.

1. If 2n = 6, what property of equality justifies writing p + 2n = 4p + 15

as p + 6 = 4p + 15 ? A. Addition property C. Transitive property B. Symmetric property D. Substitution property

2. Jerri wrote these steps when solving an equation:

Steps Justification

17(x + 3) = 6 – 4 Given Problem

17x + 51 = 6 – 4 Distributive Property

17x + 51 = 2 Substitution Property

17x = -49 Subtraction Prop. Equality

x =

Division Prop. Equality

Select a property from the box to justify each step. Write your answer in each box. 3. Which is an example of the symmetric property?

A. x = x C. If x = 5y and 5y = 10, x = 10

B. 5 = x so x = 5 D. – 5 + 5 + x = 0 + x

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A.4c: The student will solve quadratic equations algebraically and graphically. *

1. Find one solution to the following quadratic equation:

6x2 = 6x + 12 X =

2. Place a point on the solution(s) to the

quadratic equation graphed on the right.

3. Which of the following is a solution to 2x2 + 2x – 12 = 0?

A. -12 B. -3 C. -2 D. 0

4. Which of the following is the solution set to the equation x2 – 3x – 28 = 0?

A. {-28, 1} B. {-4, 7} C. {-2, 14} D. {0, 28}

A.4d: The student will solve multistep linear equations algebraically and graphically.

1. Solve for x: 3x + 1 = 5x – 3

2 3 x = 2. What value of x will make the equation 3(x + 15) – 6x = -6(x – 3) true?

A. -9 B. -6 C. 2 D. 3

3. The perimeter of a rectangular playing field is 244 feet. If its length is 2 feet longer

than twice its width, what are the dimensions of the field? ft by ft

2 or -1

9

82 40

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A.4e: The student will solve systems of two linear equations in two variables algebraically and graphically.

1. What is the solution to the system of equations shown below. State your answer as

an ordered pair.

{

2. This is the graph of a system of linear equations. Based on the graph, which is the

apparent solution to this system of linear equations?

A. (2, 5)

B. (3, 4)

C. (4, 3)

D. (5, 2) 3. What is the solution to the system of equations shown below?

{

A. (-6, 4) C. (6, -14)

B. (14, -4) D. (-6, -4)

A.4f: The student will solve real-world problems involving equations and systems of equations.

1. In addition to an $80 bonus, Joan earned $8 per hour working last week. Joan’s

total earnings last week were $240. How many total hours did she work last week? hours

2. Tommie paid $17.50 to buy 6 youth tickets and 1 adult ticket to a school play.

Susan paid $22.50 to buy 3 youth tickets and 3 adult tickets to the play. What was the price of an adult ticket?

A. $2.00 B. $2.90 C. $5.50 D. $7.50

( _____, ______)

20

7

2

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3. Ralph spent $132 to buy movie tickets for 20 students and 4 adult chaperones. Adult tickets cost $3 more than student tickets. If A is the price of an adult ticket and S is the price of a student ticket, which system of equations could be used to find the price of each adult and student ticket?

A. {

C. {

B. {

D. {

A.5a: The student will solve multistep linear inequalities in two variables algebraically and graphically.

1. Which graph below correctly represents the solutions to 2x – 7 > 15?

2. What is the solution for the following inequality? Use < or > for the inequality sign.

3(x + 5) – 10 > -2(x + 10)

3. Which of the following could be a solution to 3(x – 3) < 3?

A. 6 B. 5 C. 4 D. 3

x > -5

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Commutative Property Additive Identity Additive Inverse

Addition Property of Inequality

Symmetric Property Division Property of Inequality

A.5b: The student will justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets.

1. Jerri wrote these steps when solving an equation:

Steps Justification

-5x > 3 + - 3 Given Problem

-5x > -3 + 3 Commutative Property

-5x > 0 Additive Inverse

x < 0 Division Prop. Inequality

Select a property from the box to justify each step. Write your answer in each box.

2. In which of these situations was the multiplication property of inequality applied correctly?

A B C D

STEP 1:

STEP 2:

A.5c: The student will solve real-world problems involving inequalities.

1. Mr. Lewis charges a flat fee of $35 a day plus $15 per hour of work. How many

hours must he work in one day if he wishes to make at least $155? hours

2. Lincoln High School is hoping to earn at least $5,100 in ticket sales for the school

play. The cost per ticket was $12. Let t represent the number of tickets sold to the play. Which of the following inequalities could be used to determine how many tickets must be sold in order to reach their goal?

A. 12t < 5,100 B. 12t > 5,100 C. t < 5,100 – 12 D. t > 5,100 – 12

8

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A.5d: The student will solve systems of linear inequalities.

1. Which of the following could be a solution to the system of linear inequalities

shown below?

{

A. (3, -3) B. (0, -5) C. (1, 1) D. (4, 0)

2. Which system of linear inequalities matches the graph below?

A. {

B. {

C. {

D. {

A.6: The student will graph linear equations and linear inequalities in two variables.

1. Which graph best represents the following inequality?

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2. Which of the following points would be on a vertical line containing the point (-3, 4)? A. (0, 4) B. (-3, 1) C. (4, -3) D. (0, 0)

3. Jess described a function as

“three fourths a number x minus two equals y.” Plot three points that appear on this line. All points graphed must have integer values.

¾x – 2 = y y = ¾x - 2

A.6a: The student will determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined.

1. What is the slope of the line that passes through (-2, 5) and (3, 9)? Use the / to represent the fraction bar.

2. What is the slope of the line represented by the following equation?

4x – y + 3 = 0

A. -1 B.

C.

D. 4

3. What is most likely the slope of the line graphed on the coordinate plane?

A. -3

B. 0

C. 3

D. Undefined

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A.6b: The student will write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

1. Candice plotted the points (2, 5) and (4, -1) and then drew a line through these two

points. What is the equation of the line that she drew? A. y = 3x – 1 B. y = -3x + 1 C. y = -3x + 11 D. y = 3x + 5

2. Which is an equation for the line that contains (1, 2) and has a slope of 4?

A. y = 2x – 4 B. y = -2x + 4 C. y = 4x – 2 D. y = 4x + 2

3. What is the equation of the line graphed at the right?

4. What is the equation of the line graphed at the right?

A. y = -2x + 3

B. y = 2x + 3

C. y =

x – 2

D. y =

x – 2

**the line is supposed to go through the point (3,0) though it

appears to be slightly off

A.7a: The student will determine whether a relation is a function.

1. Which of the following sets of ordered pairs is a function?

A. {(3,4), (2,3), (3,-2), (4,1)} C. {(2,5), (-1,9), (6,3), (-1,-2)}

B. {(1,3), (-2,5), (4,5), (3,-2)} D. {(5,6), (-2,3), (10,1), (-2, -9)}

y = 2

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2. Look at the graphs below. Circle all of the graphs that do not represent functions. There may be more than one answer.

3. Which of the following could be added to the domain so that this relation would no

longer represent a function? A. A B. E C. 150 D. 550

A.7b: The student will determine the domain and range.

1. What is the range of the function shown at right?

A.

B. C. D.

2. What is the third element in the domain of the relation shown in the table?

0

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3. What is the domain of the graph shown at the right?

A. {x | x

B. {x | x > 3}

C. {y | y > 3}

D. {y | y }

A.7c: The student will determine the zeros of a function.

1. Which quadratic equation has zeros of 5 and 7?

A. y = x2 – 5x B. y = x2 – 2x – 35 C. y = x2 – 3x – 28 D. y = x2 – 12x + 35

2. What is one root of the function f(x) = x2 – x – 6? x = 3. Plot on the graph the zero(s) of the 4. Plot on the graph the zero(s) of the

function defined by f(x) = x(x + 2). function defined by f(x) = 2x – 4.

3 or -2

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A.7d: The student will determine the x- and y- intercepts. *

1. What are the x- and y- intercepts of the line with equation 4x + 5y = 40?

A. (10, 0) and (0, 8) C. (0, 10) and (8, 0)

B. (-10, 0) and (0, -8) D. (0, -10) and (-8, 0)

2. Which of the following points represents the x-intercept of the equation

y =

A. (0, -4) B. (-4, 0) C. (1, 0) D. (0, 1)

3. Which of the following functions have x-intercepts at 3? Circle all that apply.

y = x + 3 y = (x – 3)(2x + 1) f(x) =

x – 2

y = x2 – 3x f(x) = 3x y =

A.7e: The student will find the values of a function for elements in its domain.

1. The function f(x) = 1,200 – 50x gives the distance left to travel after driving x hours.

What is f(9), the distance left to travel after driving 9 hours? miles

2. If f(x) = √

, what is f(5)?

A. √

B.

C.

√

D. 1

3. What are the range values of the function f(x) = -3x2 + 5 for the domain values

{-2, 0, 1}? A. {-31, -4, 5} B. {-7, 2, 5} C. {5, 8, 17} D. {5, 14, 41}

750

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4. What is g(2) for g(x) =

?

A.7f: The student will make connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

1. Look at the graph below. Choose the two factors from the list provided that

represent the graph.

(x – 2) (x + 6) (x – 4) (x + 2) (x – 6) (x + 4) 2. The profit equation for a manufacturing firm is P = x2 – 2,500 where P is profit and x

is the number of units sold. For what number of units sold does the company break even (P = 0)?

A. 50 units sold C. 100 units sold

B. 500 units sold D. 1,250 units sold

A.8: The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent direct variation algebraically and graphically and an inverse variation algebraically.

1. Letter A is one point on a line representing a direct variation. Plot two more points

that also belong on that line. A

8

(x + 4)

(x – 2)

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2. The number of miles, m, a car can travel varies directly with the amount of gas, g, in its fuel tank. If k is the constant of variation, which equation represents that situation?

A.

B.

C. D.

3. Choose two points from the list below that would indicate a direct variation. Circle

the points. (2, 6) (2, 4) (3, 4) (1, 5) (3, 9) (0, 3)

4. An experiment is conducted on a container of gas that is kept at a constant temperature. The pressure, p, on the gas and the volume, v, of the gas vary inversely. What is the equation of inverse variation, assuming that k is the constant?

A. C.

B. D.

A.9: The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.

1. The data set shown has a mean of 37 and a standard deviation of 6.3. Which data

point has a z-score of zero? {26, 29, 32, 33, 35, 36, 37, 39, 40, 44, 45, 48}

2. The data on the annual rainfall for 32

cities is summarized in this histogram.

The mean amount of rainfall for these cities is 32.5 inches.

The standard deviation of the data is 4 inches.

Seattle’s z-score is 1.5. Identify (by shading) the interval that would include Seattle’s z-score.

37

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3. The Math Club sponsored a contest. The results are summarized in the chart below. What is the mean absolute deviation for this data? Round to the nearest hundredth.

A.10: The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.

1. The male and female teachers at

Mercer Middle School recorded the number of years they have been teaching. The box-and-whisker plots summarize the data. Which statement below is false?

A. The teacher with the least number of years teaching is female. B. The range in the years teaching is greater for male teachers than for female

teachers. C. The difference in the maximum number of years teaching for male and female

teachers is 1. D. The median number of years teaching for female teachers is 2 less than the

median for male teachers. 2. The length of the fish caught in two ponds, in inches, is summarized in these box-

and-whisker plots.

There were 24 fish, all of a different length, caught in Taylor Pond.

There were 20 fish, all of a different length, caught in Willow Pond.

How many fish were caught that were at most 9 inches long?

A. 10 B. 11 C. 32 D. 33

Name # Correct

Max 15

Eli 15

Ryanne 13

Clark 12

Grant 11

Rhyse 9

1.83

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A.11: The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.

1. Which is most likely the equation of the line of best fit for the set of data points?

A. y =

C. y =

B. y =

D. y =

2. This table shows the wind chill at 40° F for various wind speeds. What is the

approximate wind chill when the wind speed is 70 miles per hour?

A. 19° F B. 20° F C. 21° F D. 22° F

3. What is the curve of best fit for the data shown below?

Depth (in)

6 7.5 9 10.5 12 13.5

Weight (lbs)

68 137 242 389 586 838

A. y = 10.18x2 + 285.36x – 96.77 B. y = 10.18x2 – 96.77x + 285.36 C. y = 101.79x – 615.79 D. y = -615.79x + 101.79