alg1wrbkfall2015- unlocked.pdf

7/26/2019 Alg1WrBkFALL2015- unlocked.pdf

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Published by

TOPICAL REVIEW BOOK COMPANY

P. O. Box 328

Onsted, MI 49265-0328

www.topicalrbc.com

EXAM PAGE

Reference Sheet .................................................................i

Test 1 .................................................................................1

June 2014 ..........................................................................9

August 2014 ....................................................................19

January 2015 ...................................................................29

June 2015 ........................................................................37

August 2015 ....................................................................47

Correlation of Standards .................................................57

ALGEBRA 1Workbook

Common Core StandardsEdition


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3/64

ALGEBRA 1

Test 1

1

Part I Answer all 24 questions in this part. Each correct answer will receive

2 credits. No partial credit will be allowed. For each question, write on the

space provided the numeral preceding the word or expression that bestcompletes the statement or answers the question.

1. What are the values ofxin the equationx(x 6) = 4(x+ 6)?(1) { 6, 6} (2) {12, 2} (3) {2, 12} (4) {6, 0, 6} 1 _____

2. Which of ordered pairs is nota function?(1) {(0, 9),(9, 0),(1, 2),(3, 4)} (3) {(2, 3),(3, 4),(4, 5),(5, 6)}(2) {(0, 1),(1, 0),(1, 2),(3, 2)} (4) {(2, 3),(2, 4),(4, 5),(4, 6)} 2 _____

3. Iff(x) = |3x 4| + 2, ndf(10).(1) 28 (2) 34 (3) 36 (4) 38 3 _____

4. What is the value of the 1stquartile in the data set below? Scores on a math quiz: 65, 90, 100, 72, 88, 55, 73(1) 65 (2) 73 (3) 90 (4) 55 4 _____

5. What is the length of the missingside of the quadrilateral shownif the perimeter is 5x2+ 2x+ 1?

(1) 4x2 6x+ 2 (3) 4x2+ 8x+ 4

(2) 4x2+ 6x+ 2 (4) 4x2+ 8x 4 5 _____6. What is the product of (x+ 1) and (2x2+ 3x 1)?

(1) 2x2+ 5x2x 1 (3) 2x3+ 3x2+ 3x+ 1

(2) 2x3+ 5x2+ 2x 1 (4) 2x3+ 3x2 3x 1 6 _____

7. Which graph is a correct representation of the functionf(x) = 3x?

(1) (2) (3) (4)7 _____

8. A sequence has an initial value of 10 and each term is twice theprevious term. Which function models this sequence?(1) a(n) = 10(2)n (3) a(n) = 10 + 2n(2) a(n) = 10(2)n 1 (4) a(n) = 10 + 2(n 1) 8 _____

2x2+x 1 3x2 5x

4x2 ?


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2 ALGEBRA 1

Test 1

9. How can b2+ 9b+ 14 be re-written?(1) (b+ 7) (b 7) (3) (b+ 7) (b 2)(2) (b 7) (b 2) (4) (b+ 7) (b+ 2) 9 _____

10. The scatter plot to the right Medication

shows the number of milligramsof a medication in a persons

body for rst three hours afterthe medication is given. Whichequation best models therelationship where his hoursafter medication and mis milligrams

of medication in the body?(1) m= h+ 130(2) m= h 130(3) m= 40h+ 130(4) m= 40h 130 10 ____

11. Using the equationy= ax2+ bx+ cto represent a parabola on a graph,which statement is true?(1) If bis negative, the parabola opens downward.

(2) If ais negative, the parabola opens upward.(3) If ais positive, the parabola opens upward.(4) If cis negative, the parabola opens downward. 11 ____

12. If the function h(x) represents the number of full hours that it takesa person to assemblexsets of tires in a factory, which would be anappropriate domain for the function?(1) the set of real numbers (3) the set of integers

(2) the set of negative integers (4) the set of non-negative integers 12 ____

13. Given the length of three sides of a triangle, which is a right triangle?(1) 10, 26, 24 (2) 20, 12, 18 (3) 30, 15, 26 (4) 40, 50, 80 13 ____

14. Which equation is representedby the accompanying graph?

(1)y= {1;x< 22;x> 2(2)y= {1;x22;x> 2

(3)y= {1;x< 22;x2

(4)y= {1;x22;x2

14_____

150

130

110

90

70

50

30

10

-10

0 1 2 3 4Millig

ramsofMedicationintheBody

Hours Since Medicating


5/64

ALGEBRA 1

Test 1

3

15. A mouse population starts with 2,000 mice and grows at a rate of5% per year. The number of mice after t years can be modeled by theequation,P(t) = 2000(1.05)t. What is the average rate of change in thenumber of mice between the second year and the fth year, roundedto the nearest whole number?(1) 116 (2) 348 (3) 2205 (4) 2553 15 ____

16. Seven less than the product of twice a number is greater than 5 morethan the same number. Which integer satises this inequality?(1) 1 (2) 2 (3) 12 (4) 13 16 ____

17. A sequence is dened recursively byf(1) =16 andf(n) =f(n 1) + 2n.

Findf(4).(1) 32 (2) 30 (3) 28 (4) 34 17 ____

18. Which statement is true aboutthe accompanying graph?(1) It is decreasing when 1 1.(2) It is increasing whenx> 1 andnegative whenx< 0.

(3) It is increasing whenx> 1 andnegative when 1


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4 ALGEBRA 1

Test 1

21. Alex makes ceramic bowls to sell at a monthly craft fair in a nearbycity. Every month, she spends $50 on materials for the bowls from alocal art store. At the fair, she sells each completed bowl for a total of$25 including tax. Which equation expresses Alexs prot as a functionof the number of bowls that she sells in one month?(1) p(x) = 50x+ 25 (3)p(x) = 25x(2)p(x) = 15x+ 25 (4)p(x) = 25x 50 21 ____

22. Which expression is equivalent tox4y4?(1) (x2y2)(x2+y2) (3) (2x2)2 (2y2)2

(2) (x2y2)(x2y2) (4) (x2y2) (x2y2) 22 ____

23. A bottle rocket that was made in science class had a trajectorypath that followed the quadratic equationy= x2+ 4x+ 6. What isthe turning point of the rockets path?(1) (1, 5) (2) (2, 10) (3) (2, 10) (4) (1, 5) 23 ____

24. What is the solution to this system of linear equations:yx= 4 andy+ 2x= 1?

(1) (1, 3) (2) (0, 4) (3) (1, 1) (4) (3, 3) 24 ____

Part II Answer all 8 questions in this part. Each correct answer will receive 2

credits. Clearly indicate the necessary steps, including appropriate formula

substitutions, diagrams, graphs, charts, etc. For all questions in this part, a

correct numerical answer with no work shown will receive only 1 credit. All

answers should be written in the space provided. [16]

25. Find the average rate of change

of the function shown to the right thatrepresents the amount of money in asavings account in Lenders Bank?

26. Factor completely, the expression: 2x3 2x2 12x

Week Balance

1 $128

2 $142 3 $156

4 $170

5 $184


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ALGEBRA 1

Test 1

5

27. Find one point that lies in [The use of the grid is optional.]the solution set of the followingsystem of inequalities:

y1

2x+ 6

y> 3x 1

Justify your answer

28. Solve forx: 2x2+ 4x 16 = 0

29. The product of 16 and 4 less than a number is 208. Find the number.

30. MaryJo decided to solve the equation 3x 2 = x 6 by entering each ofthe expressions into her graphing calculator. To solve the equation as a system,she enteredy

1= 3x 2 andy

2= x 6. When she used the calculator to nd

the intersection, she foundx= 1 andy= 5. Show the work to check to see ifMaryJo found the correct solution forxto the linear equation.

y

x


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6 ALGEBRA 1

Test 1

31. Findf(2) for the function: f(x) ={3x2 1,x< 1

x+ 2,x 1

32. Identify the turning point of the functionf(x) =x2 2x+ 8 by writing itsequation in vertex form.

Show your work.

Part III Answer all 4 questions in this part. Each correct answer will receive 4


substitutions, diagrams, graphs, charts, etc. For all questions in this part, acorrect numerical answer with no work shown will receive only 1 credit. All

answers should be written in pen, except for graphs and drawings, which

should be done in pencil. [16]

33. Graph 2x+y< 7 and state one point in the solution set.y

x


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ALGEBRA 1

Test 1

7

34. Jonathan has been on a diet since January 2013. So far, he has been losingweight at a steady rate. Based on monthly weigh-ins, his weight, w, can bemodeled by the function w= 3m+ 205 where mis the number of months afterJanuary 2013.

a) How much did Jonathan weigh at the start of the diet?

b) How much weight has Jonathan been losing each month?

c) How many months did it take Jonathan to lose 45 pounds?

35. Yolanda owns 4 rabbits. She expects the number of rabbits to doubleevery year.

a) After how many years will she have 64 rabbits?

b) Write an equation to model this situation. [The use of the grid is optional.]y

x


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8 ALGEBRA 1

Test 1

36. Create a box plot for the ages of people listed below: 40, 25, 20, 15, 40, 40, 45, 60, 7, 10, 52, 34, 38

Part IV

Answer one question in this part. The correct answer will receive 6credits. Clearly indicate the necessary steps, including appropriate formula

substitutions, diagrams, graphs, charts, etc. For all questions in this part, a

correct numerical answer with no work shown will receive only 1 credit. All

answers should be written in the spaces provided.[6]

37. Graph the system of equations: y= x2+ 3x 1State the solution to the system. 2y 1 =x

y

x


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ALGEBRA 1

June 2014

9

y

x

y

x

y

x

y

x

Year Balance, in Dollars

0 380.00

10 562.49

20 832.63

30 1232.49

40 1824.39

50 2700.54

Part I Answer all 24 questions in this part. Each correct answer will receive 2credits. No partial credit will be allowed. For each statement or question,choose the word or expression that, of those given, best completes thestatement or answers the question. Record your answers in the spaceprovided. [48]

1. When solving the equation 4(3x2+ 2) 9 = 8x2+ 7, Emily wrote4(3x2+ 2) = 8x2+ 16 as her rst step. Which property justies Emilys rst step?(1) addition property of equality(2) commutative property of addition(3) multiplication property of equality(4) distributive property of multiplication over addition 1 _____

2. Ofcials in a town use a function, C, to analyze trafc patterns.C(n) represents the rate of trafc through an intersection where nis thenumber of observed vehicles in a specied time interval. What would

be the most appropriate domain for the function?

(1) {2, 1, 0, 1, 2, 3, } (3) {0, 12

, 1, 1 12

, 2, 2 12

}

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

3. IfA= 3x2

+ 5x 6 andB= 2x2

6x+ 7, thenABequals(1) 5x2 11x+ 13 (2) 5x2+ 11x 13 (3) 5x2 x+ 1 (4) 5x2x+ 1 3 _____

4. Given: y+x> 2 y3x 2

Which graph shows the solution of the given set of inequalities?

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

5. Which value ofxsatises the equation 73

9

28 20x+

= ?

(1) 8.25 (2) 8.89 (3) 19.25 (4) 44.92 5 _____

6. The accompanying table shows the averageyearly balance in a savings account where interestis compounded annually. No money is depositedor withdrawn after the initial amount is deposited.Which type of function best models the given data?(1) linear function with a negative rate of change(2) linear function with a positive rate of change(3) exponential decay function(4) exponential growth function 6 _____


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10 ALGEBRA 1

June 2014

1

48

32

192

6

16

y

x5432

64

80

176

96

112

128

144

160

7. A company that manufactures radios rst pays a start-up cost, and thenspends a certain amount of money to manufacture each radio. If the cost ofmanufacturing rradios is given by the function c(r) = 5.25r+ 125, then thevalue 5.25 best represents(1) the start-up cost(2) the prot earned from the sale of one radio(3) the amount spent to manufacture each radio(4) the average number of radios manufactured 7 _____

8. Which equation has the same solution asx2 6x 12 = 0?(1) (x+ 3)2= 21 (2) (x 3)2= 21 (3) (x+ 3)2= 3 (4) (x 3)2= 3 8 _____

9. A ball is thrown intothe air from the edge of a48-foot-high cliff so thatit eventually lands on theground. The accompanyinggraph shows the height,y,of the ball from the groundafterxseconds.

For which interval is the balls

height alwaysdecreasing?(1) 0 x2.5 (3) 2.5


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ALGEBRA 1

June 2014

11

x 3 4 6 7 8

F(x) 9 17 65 129 257

(1,40)

(2,110)

(4,180)

(6,230)

(8,350)

(10,390)

Elapsed Time(hours)

DistanceTraveled

(miles)

14. Which system of equations has the same solution as the system below?

2x+ 2y= 16 3xy= 4

(1) 2x+ 2y= 16 (2) 2x+ 2y= 16 (3)x+y= 16 (4) 6x+ 6y= 48 6x 2y= 4 6x 2y= 8 3xy= 4 6x+ 2y= 8 14 ____

15. The table below represents the functionF.

The equation that represents this function is(1)F(x) = 3x (2)F(x) = 3x (3)F(x) = 2x+ 1 (4)F(x) = 2x+ 3 15 ____

16. John has four more nickels than dimes in his pocket, for a totalof $1.25. Which equation could be used to determine the number ofdimes,x, in his pocket?(1) 0.10(x+ 4) + 0.05(x) = $1.25 (3) 0.10(4x) + 0.05(x) = $1.25(2) 0.05(x+ 4) + 0.10(x) = $1.25 (4) 0.05(4x) + 0.10(x) = $1.25 16 ____

17. Iff(x) =1

3x+ 9, which statement is always true?

(1)f(x) < 0 (3) Ifx< 0, thenf(x) < 0.

(2)f(x) > 0 (4) Ifx> 0, thenf(x) > 0. 17 ____

18. The Jamison family kept alog of the distance they traveledduring a trip, as represented bythe accompanying graph. Duringwhich interval was their averagespeed the greatest?(1) the rst 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 18 ____

19. Christopher looked at his quiz scores shown below for the rst andsecond semester of his Algebra class.

Semester 1: 78, 91, 88, 83, 94

Semester 2: 91, 96, 80, 77, 88, 85, 92

Which statement about Christophers performance is correct?(1) The interquartile range for semester 1 is greater than theinterquartile range for semester 2.(2) The median score for semester 1 is greater than the median scorefor 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 thirdquartile for semester 1. 19 ____


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12 ALGEBRA 1

June 2014

20. The graph ofy=f(x)is shown to the right.Which point could be

used to ndf(2)?(1)A (3) C(2)B (4)D

20 ____

21. A sunower is 3 inches tall at week 0 and grows 2 inches each week.Which function(s) shown below can be used to determine the height,f(n),of the sunower in nweeks?

I. f(n) = 2n+ 3 II.f(n) = 2n+ 3(n 1) III. f(n) =f(n 1) + 2 wheref(0) = 3

(1) I and II (2) II, only (3) III, only (4) I and III 21 ____

22. A cell phone company charges $60.00 a month for up to 1 gigabyte of data.The cost of additional data is $0.05 per megabyte. If drepresents the number ofadditional megabytes used and crepresents the total charges at the end of themonth, which linear equation can be used to determine a users monthly bill?(1) c= 60 0.05d (3) c= 60d 0.05(2) c= 60.05d (4) c= 60 + 0.05d 22 ____

23. The formula for the volume of a cone is V=1

3r2h. The radius, r,

of the cone may be expressed as

(1)3Vh

(2)V

h3 (3) 3

V

h (4)

1

3

V

h

23 ____

24. The diagrams below represent the rst three terms of a sequence.

Assuming the pattern continues, which formula determines an ,the number of shaded squares in the nth term?(1) an= 4n+ 12 (2) an= 4n+ 8 (3) an= 4n+ 4 (4) an= 4n+ 2 24 ____

y

xC

D

B

A

Term 3Term 2Term 1


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ALGEBRA 1

June 2014

13

Part II Answer all 8 questions in this part. Each correct answer will receive 2


substitutions, diagrams, graphs, charts, etc. For all questions in this part, acorrect numerical answer with no work shown will receive only 1 credit. All

answers should be written in pen, except for graphs and drawings,

which should be done in pencil.[16]

25. Draw the graph ofy= x 1 on the set of axes below.

26. The breakdown of a sample of a chemical compound is represented by thefunctionp(t) = 300(0.5)t, wherep(t) represents the number of milligrams of thesubstance and trepresents the time, in years. In the functionp(t), explain what0.5 and 300 represent.

27. Given 2x+ ax 7 > 12, determine the largest integer valueof awhenx= 1.

y

x


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14 ALGEBRA 1

June 2014

28. The vertex of the parabola represented by f(x) =x2 4x+ 3 has coordinates(2, 1). Find the coordinates of the vertex of the parabola dened byg(x) =f(x 2).Explain how you arrived at your answer.

[The use of the set of axes below is optional.]

29. On the set of axes below, draw the graph of the equationy=

3

4x+ 3.

Is the point (3, 2) a solution to the equation? Explain your answer based on thegraph drawn.

y

x

y

x


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ALGEBRA 1

June 2014

15

Sun Mon Tues Wed Thurs

Week 1 4 3 3.5 2 2

Week 2 4.5 5 2.5 3 1.5

Week 3 4 3 1 1.5 2.5

30. The functionfhas a domain of {1, 3, 5, 7} and a range of {2, 4, 6}.Couldfbe represented by {(1, 2), (3, 4), (5, 6), (7, 2)}? Justify your answer.

31. Factor the expressionx4+ 6x2 7 completely.

32. Robin collected data on the number of hours she watched television onSunday through Thursday nights for a period of 3 weeks. The data are shownin the table below.

Using an appropriate scale on the number line below, construct a box plot for the15 values.


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16 ALGEBRA 1

June 2014

Part III Answer all 4 questions in this part. Each correct answer will receive

4 credits. Clearly indicate the necessary steps, including appropriate

formula substitutions, diagrams, graphs, charts, etc. For all questions inthis part, a correct numerical answer with no work shown will receive

only 1 credit. All answers should be written in pen, except for graphs and

drawings, which should be done in pencil. [16]

33. Write an equation that denes m(x) as a trinomial wherem(x) = (3x 1)(3 x) + 4x2+ 19.

Solve forxwhen m(x) = 0.

34. A rectangular garden measuring12 meters by 16 meters is to have awalkway installed around it with awidth ofxmeters, as shown in theaccompanying diagram. Together,the walkway and the garden have

an area of 396 square meters.

Write an equation that can be usedto ndx, the width of the walkway.

Describe how your equation models the situation.

Determine and state the width of the walkway, in meters.

16 mx

x

x x

12 mGarden

Walkway


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ALGEBRA 1

June 2014

17

35. Caitlin has a movie rental card worth $175. After she rents the rst movie,the cards value is $172.25. After she rents the second movie, its value is$169.50. After she rents the third movie, the card is worth $166.75.

Assuming the pattern continues, write an equation to deneA(n), the amount ofmoney on the rental card after nrentals.

Caitlin rents a movie every Friday night. How many weeks in a row can sheafford to rent a movie, using her rental card only? Explain how you arrived atyour answer.

36. An animal shelter spends $2.35 per day to care for each cat and $5.50 perday to care for each dog. Pat noticed that the shelter spent $89.50 caring forcats and dogs on Wednesday.

Write an equation to represent the possible numbers of cats and dogs that couldhave been at the shelter on Wednesday.

Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday.Are Pats 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 atthe shelter on Wednesday. How many cats were at the shelter on Wednesday?


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18 ALGEBRA 1

June 2014

y

x

Number of Products

(hundreds)

Cost(hundreds

ofdollars)

1 2 3 4

10

20

30

40

50

Part IV

Answer the question in this part. A correct answer will receive 6 credits.

Clearly indicate the necessary steps, including appropriate formula

substitutions, diagrams, graphs, charts, etc. A correct numerical answerwith no work shown will receive only 1 credit. The answer should be written

in pen. [6]

37. A company is considering building a manufacturing plant. They determinethe weekly production cost at siteAto beA(x) = 3x2while the production cost atsiteBisB(x) = 8x+ 3, wherexrepresents the number of products, in hundreds,andA(x) andB(x) are the production costs, in hundreds of dollars.

Graph the production costfunctions on the accompanyingset of axes and label themsiteAand siteB.

State the positive value(s) ofxforwhich the production costs at thetwo sites are equal. Explain howyou determined your answer.

If the company plans on manufacturing 200 products per week, which siteshould they use? Justify your answer


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ALGEBRA 1

August 201419


1. Which statement is notalways 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. 1 _____

2. A satellite television company charges a one-time installation fee and amonthly service charge. The total cost is modeled by the functiony= 40 + 90x.Which statement represents the meaning of each part of the function?(1)yis the total cost,xis the number of months of service, $90 isthe installation fee, and $40 is the service charge per month.(2)yis the total cost,xis the number of months of service, $40 isthe installation fee, and $90 is the service charge per month.(3)xis the total cost,yis the number of months of service, $40 isthe installation fee, and $90 is the service charge per month.

(4)xis the total cost,yis the number of months of service, $90 isthe installation fee, and $40 is the service charge per month. 2 _____

3. If 4x2 100 = 0, the roots of the equation are(1) 25 and 25 (2) 25, only (3) 5 and 5 (4) 5, only 3 _____

4. Isaiah collects data fromtwo different companies,each with four employees.

The results of the study,based on each workers ageand salary, are listed in theaccompanying tables.

Which statement is trueabout these data?(1) The median salaries in both companies are greater than $37,000.(2) The mean salary in company 1 is greater than the mean salary in company 2.(3) The salary range in company 2 is greater than the salary range in company 1.(4) The mean age of workers at company 1 is greater than the meanage of workers at company 2. 4 _____

5. Which point isnoton the graph represented byy=x2+ 3x 6?(1) (6, 12) (2) (4, 2) (3) (2, 4) (4) (3, 6) 5 _____


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20 ALGEBRA 1

August 20146. A company producesxunits of a product per month, where C(x) representsthe total cost andR(x) represents the total revenue for the month. The functionsare modeled by C(x) = 300x+ 250 andR(x) = 0.5x2+ 800x 100. The prot isthe difference between revenue and cost whereP(x) =R(x) C(x). What is thetotal prot,P(x), for the month?(1)P(x) = 0.5x2+ 500x 150 (3)P(x) = 0.5x2 500x+ 350(2)P(x) = 0.5x2+ 500x 350 (4)P(x) = 0.5x2+ 500x+ 350 6 _____

7. What is one point that liesin the solution set of the systemof inequalities graphed?(1) (7, 0)(2) (3, 0)(3) (0, 7)(4) (3, 5) 7 _____

8. The value of thex-intercept for the graph of 4x 5y= 40 is

(1) 10 (2)4

5 (3)

4

5 (4) 8 8 _____

9. Sam and Jeremy have ages that are consecutive odd integers.

The product of their ages is 783. Which equation could be used tond Jeremys age,j, if he is the younger man?(1)j 2+ 2 = 783 (2)j 2 2 = 783 (3)j 2+ 2j= 783 (4)j 2 2j= 783 9 _____

10. A population that initially has 20 birds approximately doubles every10 years. Which graph represents this population growth?

(1) (2) (3) (4) 10 ____

11. Letfbe a function such thatf(x) = 2x 4 is dened on the domain2 x6. The range of this function is(1) 0 y8 (2) 0 y< (3) 2 y6 (4)


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ALGEBRA 1

August 201421

13. Which graph shows a line where each value ofyis three more thanhalf ofx?

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

13 ____

14. The accompanying table shows theaverage diameter of a pupil in a personseye as he or she grows older.What is the average rate of change, inmillimeters per year, of a persons pupildiameter from age 20 to age 80?(1) 2.4 (3) 2.4(2) 0.04 (4) 0.04 14 ____

15. Which expression is equivalent tox4 12x2+ 36?(1) (x2 6)(x2 6) (3) (6 x2)(6 +x2)(2) (x2+ 6)(x2+ 6) (4) (x2+ 6)(x2 6) 15 ____

16. The third term in an arithmetic sequence is 10 and the fth term is 26.If the rst term is a1, which is an equation for the nth term of thissequence?(1) an= 8n+ 10 (3) an= 16n+ 10

(2) an= 8n 14 (4) an= 16n 38 16 ____

17. The graph of the equationy= ax2is shown.

Ifais multiplied by 1

2, the

graph of the new equation is(1) wider and opens downward(2) wider and opens upward

(3) narrower and opens downward(4) narrower and opens upward

17 ____

18. The zeros of the functionf(x) = (x+ 2)2 25 are(1) 2 and 5 (2) 3 and 7 (3) 5 and 2 (4) 7 and 3 18 ____


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22 ALGEBRA 1

August 201419. During the 2010 season, football player McGees earnings, m, were0.005 million dollars more than those of his teammate Fitzpatricks earnings, f.The two players earned a total of 3.95 million dollars. Which system of equationscould be used to determine the amount each player earned, in millions of dollars?(1) m+f= 3.95 (3) f 3.95 = m m+ 0.005 =f m+ 0.005 =f

(2) m 3.95 =f (4) m+f= 3.95 f+ 0.005 = m f+ 0.005 = m 19 ____

20. What is the value ofxin the equation x + =2

3

1

6

5

6?

(1) 4 (2) 6 (3) 8 (4) 11 20 ____

21. The accompanying table shows thenumber of grams of carbohydrates,x,and the number of Calories,y, of sixdifferent foods.

Which equation best represents the lineof best t for this set of data?(1)y= 15x (3)y= 0.1x 0.4(2)y= 0.07x (4)y= 14.1x+ 5.8 21 ____

22. A function is graphed onthe set of axes to the right.Which function is related tothe graph?

(1) (3)

(2) (4)22 ____

23. The function h(t) = 16t2

+ 144 represents the height, h(t), in feet, ofan object from the ground at tseconds after it is dropped. A realisticdomain for this function is(1) 3 t 3 (3) 0 h(t) 144(2) 0 t 3 (4) all real numbers 23 ____

24. Iff(1) = 3 andf(n) = 2f(n 1) + 1, thenf(5) =(1) 5 (2) 11 (3) 21 (4) 43 24 ____


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ALGEBRA 1

August 201423

Part II Answer all 8 questions in this part. Each correct answer will receive2 credits. Clearly indicate the necessary steps, including appropriateformula substitutions, diagrams, graphs, charts, etc. For all questionsin this part, a correct numerical answer with no work shown will receiveonly 1 credit. All answers should be written in pen, except for graphsand drawings, which should be done in pencil.[16]

25. In the equationx2+ 10x + 24 = (x+ a) (x+ b), bis an integer. Findalgebraically allpossible values of b.

26. Rhonda deposited $3000 in an account in the Merrick National Bank, earning4.2% interest, compounded annually. She made no deposits or withdrawals.Write an equation that can be used to ndB, her account balance after tyears.

27. Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3%of his total sales in dollars,x, which can be represented by g(x) = 185 + 0.03x.Jim is paid $275 per week plus 2.5% of his total sales in dollars, x, whichcan be represented byf(x) = 275 + 0.025x. Determine the value ofx, in dollars,that will make their weekly pay the same.

28. Express the product of 2x2+ 7x 10 andx+ 5 in standard form.


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24 ALGEBRA 1

August 201429. Letfbe the function represented

by the accompanying graph.

Letgbe a function such that

g(x) = 12x2+ 4x+ 3.

Determine which function hasthe larger maximum value.

Justify your answer.

30. Solve the inequality below to determine and state the smallest possible value

forxin the solution set. 3(x+ 3) 5x3


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ALGEBRA 1

August 201425

31. The table below represents the residuals for a line of best t.

Plot these residuals on the set of axes below.Using the plot, assess the t of the line for these residuals and justify youranswer.

32. A student was given the equationx2+ 6x 13 = 0 to solve by completing thesquare. The rst step that was written is shown below.

x2+ 6x= 13

The next step in the students process wasx2+ 6x+ c= 13 + c.

State the value of cthat creates a perfect square trinomial.

Explain how the value of cis determined.


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26 ALGEBRA 1

August 2014Part III

Answer all 4 questions in this part. Each correct answer will receive4 credits. Clearly indicate the necessary steps, including appropriateformula substitutions, diagrams, graphs, charts, etc. For all questions inthis part, a correct numerical answer with no work shown will receiveonly 1 credit. All answers should be written in pen, except for graphs anddrawings, which should be done in pencil.[16]

33. On the axes, graphf(x) = |3x|.

Ifg(x) =f(x) 2, how is the graph off(x) translated to form the graph ofg(x)?

If h(x) =f(x 4), how is the graph off(x) translated to form the graph of h(x)?

34. The formula for the area of a trapezoid isA=1

2h(b

1+ b

2). Express b

1in

terms ofA, h, and b2.

The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft.Find the number of feet in the other base.

y

x


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ALGEBRA 1

August 201427

35. Letf(x) = 2x2andg(x) = 2x 4. On the set of axes below, draw the graphsofy=f(x) andy=g(x).

Using this graph, determine and state allvalues ofxfor whichf(x) =g(x).

36. A school is building a rectangular soccer eld that has an area of6000 square yards. The soccer eld must be 40 yards longer than its width.Determine algebraically the dimensions of the soccer eld, in yards.

y

x


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28 ALGEBRA 1

August 2014Part IV

Answer the question in this part. A correct answer will receive 6 credits.Clearly indicate the necessary steps, including appropriate formulasubstitutions, diagrams, graphs, charts, etc. A correct numerical answerwith no work shown will receive only 1 credit. All answers should bewritten in pen, except for graphs and drawings, which should be writtenin pencil. [6]

37. Edith babysits forxhours a week after school at a job that pays $4 an hour.She has accepted a job that pays $8 an hour as a library assistant workingyhours a week. She will work both jobs. She is able to work no more than15hours a week, due to school commitments. Edith wants to earn at least$80 aweek, working a combination of both jobs.

Write a system of inequalities that can be used to represent the situation.

Graph these inequalities on the set of axes below.

Determine and state one combination of hours that will allow Edith to earn atleast$80 per week while working no more than15 hours.


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ALGEBRA 1

January 201529

Part I Answer all 24 questions in this part. Each correct answer will receive 2credits. No partial credit will be allowed. For each statement or question,choose the word or expression that, of those given, best completes the

statement or answers the question. Record your answers in the spaceprovided. [48]

1. The owner of a small computer repair business has one employee, whois paid an hourly rate of $22. The owner estimates his weekly prot usingthe functionP(x) = 8600 22x. In this function,xrepresents the number of(1) computers repaired per week (3) customers served per week(2) hours worked per week (4) days worked per week 1 _____

2. Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds.He converts his speed into miles per hour, as shown below.

40

4 5

3

1

5280

1

60

1

60

1

yd ft

yd

ft

mi

sec

min

min

hr. sec

Which ratio is incorrectlywritten to convert his speed?

(1)3

1

ft

yd (2)

5280

1

ft

mi (3)

60

1

sec

min (4)

60

1

min

hr 2 _____

3. Which equation has the same solutions as 2x2+x 3 = 0?(1) (2x 1)(x+ 3) = 0 (3) (2x 3)(x+ 1) = 0(2) (2x+ 1)(x 3) = 0 (4) (2x+ 3)(x 1) = 0 3 _____

4. Krystal was given $3000 when she turned 2 years old. Her parentsinvested it at a 2% interest rate compounded annually. No deposits orwithdrawals were made. Which expression can be used to determinehow much money Krystal had in the account when she turned 18?(1) 3000(1 + 0.02)16 (3) 3000(1 + 0.02)18

(2) 3000(1 0.02)16 (4) 3000(1 0.02)18 4 _____

5. Which table of values represents a linear relationship?

(1) (2) (3) (4) 5 _____

6. Which domain would be the most appropriate set to use for a functionthat predicts the number of household online-devices in terms of thenumber of people in the household?(1) integers (3) irrational numbers(2) whole numbers (4) rational numbers 6 _____

x f(x)

1 3

0 2

1 1

2 6

3 13

x f(x)

1 12

0 1

1 2

2 4

3 8

x f(x)

1 3

0 1

1 1

2 3

3 5

x f(x)

1 1

0 0

1 1

2 8

3 27


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30 ALGEBRA 1

January 2015

7. The inequality 7 2

3x 9 (2)x> 3

5 (3)x< 9 (4)x<

3

5 7 _____

8. The value in dollars, v(x), of a certain car afterxyears is representedby the equation v(x) = 25,000(0.86)x. To the nearest dollar, how muchmore is the car worth after 2 years than after 3 years?(1) 2589 (2) 6510 (3) 15,901 (4) 18,490 8 _____

9. Which function hasthe samey-intercept asthe accompanying graph?

(1) y x=12 6

4

(2) 27 + 3y= 6x

(3) 6y+x = 18

(4)y+ 3 = 6x

9 _____

10. Fred is given a rectangular piece of paper. If the length of Freds

piece of paper is represented by 2x 6 and the width is representedby 3x 5, then the paper has a total area represented by(1) 5x 11 (2) 6x2 28x+ 30 (3) 10x 22 (4) 6x2 6x 11 10 ____

11. The graph of a linear equation contains the points ( 3, 11) and (2, 1).Which point also lies on the graph?(1) (2, 1) (2) (2, 4) (3) (2, 6) (4) (2, 9) 11 ____

12. How does the graph off(x) = 3(x 2)2+ 1 compare to the graph

ofg(x) =x2?(1) The graph off(x) is wider than the graph ofg(x), and itsvertex is moved to the left 2 units and up 1 unit.(2) The graph off(x) is narrower than the graph ofg(x), and itsvertex is moved to the right 2 units and up 1 unit.(3) The graph off(x)) is narrower than the graph ofg(x), and itsvertex is moved to the left 2 units and up 1 unit.(4) The graph off(x) is wider than the graph ofg(x), and itsvertex is moved to the right 2 units and up 1 unit. 12 ____

13. Connor wants to attend the town carnival. The price of admission tothe carnival is $4.50, and each ride costs an additional 79 cents. If he canspend at most $16.00 at the carnival, which inequality can be used tosolve for r, the number of rides Connor can go on, and what is themaximum number of rides he can go on?(1) 0.79 + 4.50r 16.00; 3 rides (3) 4.50 + 0.79r 16.00; 14 rides(2) 0.79 + 4.50r16.00; 4 rides (4) 4.50 + 0.79r 16.00; 15 rides 13 ____

y

x


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ALGEBRA 1

January 201531

14. Corinne is planning a beach vacation in July and is analyzing the dailyhigh temperatures for her potential destination. She would like to choosea destination with a high median temperature and a small interquartilerange. She constructed box plots shown in the diagram below.

Which destination has a median temperature above 80 degrees andthe smallest interquartile range?(1) Ocean Beach (3) Serene Shores(2) Whispering Palms (4) Pelican Beach 14 ____

15. Some banks charge a fee on savings accounts that are left inactive foran extended period of time. The equationy= 5000(0.98)xrepresents thevalue,y, of one account that was left inactive for a period ofxyears.What is they-intercept of this equation and what does it represent?(1) 0.98, the percent of money in the account initially(2) 0.98, the percent of money in the account afterxyears(3) 5000, the amount of money in the account initially(4) 5000, the amount of money in the account afterxyears 15 ____

16. The equation for the volume of a cylinder is V= r2h. The positivevalue of r, in terms of hand V, is

(1) r V

h= (2) r V h= (3) r= 2Vh (4) r

V=

2 16 ____

17. Which equation has the same solutions asx2

+ 6x 7 = 0?(1) (x+ 3)2= 2 (2) (x 3)2= 2 (3) (x 3)2= 16 (4) (x+ 3)2= 16 17 ____

18. Two functions,y= |x 3| and 3x+ 3y= 27, are graphed on the same setof axes. Which statement is true about the solution to the system of equations?(1) (3, 0) is the solution to the system because it satises the equationy= |x 3|.(2) (9, 0) is the solution to the system because it satises the equation 3x+ 3y= 27.(3) (6, 3) is the solution to the system because it satises both equations.(4) (3, 0), (9, 0), and (6, 3) are the solutions to the system of equations

because they all satisfy at least one of the equations. 18 ____

19. Miriam and Jessica are growing bacteria in a laboratory. Miriam usesthe growth functionf(t) = n2twhile Jessica uses the functiong(t) = n4t,where nrepresents the initial number of bacteria and tis the time, in hours.If Miriam starts with 16 bacteria, how many bacteria should Jessica startwith to achieve the same growth over time?(1) 32 (2) 16 (3) 8 (4) 4 19 ____


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32 ALGEBRA 1

January 201520. If a sequence is dened recursively byf(0) = 2 and

f(n+ 1) = 2f(n) + 3 for n 0, thenf(2) is equal to(1) 1 (2) 11 (3) 5 (4) 17 20 ____

21. An astronaut drops a rock off the edge of a cliff on the Moon. Thedistance, d(t), in meters, the rock travels after tseconds can be modeled

by the function d(t) = 0.8t2. What is the average speed, in meters persecond, of the rock between 5 and 10 seconds after it was dropped?(1) 12 (2) 20 (3) 60 (4) 80 21 ____

22.When factored completely, the expressionp4 81 is equivalent to(1) (p2+ 9)(p2 9) (3) (p2+ 9)(p+ 3)(p 3)(2) (p2 9)(p2 9) (4) (p+ 3)(p 3)(p+ 3)(p 3) 22 ____

23. In 2013, the United States Postal Service charged $0.46 to mail a letterweighing up to 1 oz. and $0.20 per ounce for each additional ounce. Whichfunction would determine the cost, in dollars, c(z), of mailing a letterweighingzounces wherezis an integer greater than 1?(1) c(z) = 0.46z+ 0.20 (3) c(z) = 0.46(z 1) + 0.20(2) c(z) = 0.20z+ 0.46 (4) c(z) = 0.20(z 1) + 0.46 23 ____

24. A polynomial function contains the factorsx,x 2, andx+ 5.

Which graph(s) below could represent the graph of this function?

(1) I, only (2) II, only (3) I and III (4) I, II, and III 24 ____

Part II Answer all 8 questions in this part. Each correct answer will receive2 credits. Clearly indicate the necessary steps, including appropriateformula substitutions, diagrams, graphs, charts, etc. For all questionsin this part, a correct numerical answer with no work shown will receive only1 credit. All answers should be written in pen, except for graphs anddrawings, which should be done in pencil. [16]

25. Ms. Fox asked her class Is the sum of 4.2 and 2rational or irrational?Patrick answered that the sum would be irrational.State whether Patrick is correct or incorrect. Justify your reasoning.


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ALGEBRA 1

January 201533

26. The school newspaper surveyed thestudent body for an article about clubmembership. The accompanying tableshows the number of students in each

grade level who belong to one ormore clubs.

If there are 180 students in ninth grade, what percentage of the ninth gradestudents belong to more than one club?

27. A function is shown in the accompanying table. Ifincluded in the table, which ordered pair, (4, 1) or (1, 4),would result in a relation that is no longer a function?Explain your answer.

28. Subtract 5x2+ 2x 11 from 3x2+ 8x 7. Express the result as a trinomial.

29. Solve the equation 4x2 12x= 7 algebraically forx.

x f(x)

4 2

1 4

0 2

3 16


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34 ALGEBRA 1

January 201530. Graph the followingfunction on the set ofaccompanying axes.

f(x) = {|x|, 3 x< 1 4, 1 x 8

31. A gardener is planting two types of trees:

TypeAis three feet tall and grows at a rate of 15 inches per year. TypeBis four feet tall and grows at a rate of 10 inches per year.

Algebraically determine exactly how many years it will take for these trees to bethe same height.

32. Write an exponential equationfor the graph shown to the right.

Explain how you determined theequation.

f(x)

x


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ALGEBRA 1

January 201535

Part III Answer all 4 questions in this part. Each correct answer will receive4 credits. Clearly indicate the necessary steps, including appropriateformula substitutions, diagrams, graphs, charts, etc. For all questions in

this part, a correct numerical answer with no work shown will receive only1 credit. All answers should be written in pen, except for graphs anddrawings, which should be done in pencil. [16]

33. Jacob and Zachary go to the movie theater and purchase refreshments fortheir friends. Jacob spends a total of $18.25 on two bags of popcorn and threedrinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks.

Write a system of equations that can be used to nd the price of one bag ofpopcorn and the price of one drink.

Using these equations, determine and state the price of a bag of popcorn and theprice of a drink, to the nearest cent.

34. The graph of an inequality isshown to the right.a) Write the inequality represented

by the graph.

b) On the same set of axes, graph theinequalityx+ 2y< 4.

c) The two inequalities graphed on the set of axes form a system. Oscar thinksthat the point (2, 1) is in the solution set for this system of inequalities. Determineand state whether you agree with Oscar. Explain your reasoning.


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36 ALGEBRA 1

January 201535. A nutritionist collected information aboutdifferent brands of beef hot dogs. She made atable showing the number of Calories and theamount of sodium in each hot dog.

a) Write the correlation coefcient for the line ofbest t. Round your answer to the nearest hundredth.

b) Explain what the correlation coefcient suggests in the context of this problem.

36. a) Given the functionf(x) = x2+ 8x+ 9, state whether the vertex representsa maximum or minimum point for the function. Explain your answer.

b) Rewritef(x) in vertex form by completing the square.

Part IV Answer the question in this part. A correct answer will receive 6 credits.Clearly indicate the necessary steps, including appropriate formulasubstitutions, diagrams, graphs, charts, etc. A correct numerical answerwith no work shown will receive only 1 credit. All answers should bewritten in pen, except for graphs and drawings, which should be written

in pencil. [6]

37. New Clarendon Park is undergoing renovations to its gardens. One gardenthat was originally a square is being adjusted so that one side is doubled inlength, while the other side is decreased by three meters.

The new rectangular garden will have an area that is 25% more than the originalsquare garden. Write an equation that could be used to determine the length of aside of the original square garden.

Explain how your equation models the situation.

Determine the area, in square meters, of the new rectangular garden.


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ALGEBRA 1

June 2015

37


1. The cost of airing a commercial on television is modeled by the functionC(n) = 110n+ 900, where nis the number of times the commercial is aired.Based on this model, which statement is true?(1) The commercial costs $0 to produce and $110 per airing up to $900.(2) The commercial costs $110 to produce and $900 each time it is aired.(3) The commercial costs $900 to produce and $110 each time it is aired.

(4) The commercial costs $1010 to produce and can air an unlimitednumber of times. 1 _____

2. The accompanying graphrepresents a joggers speed during her20-minute jog around her neighborhood.

Which statement best describes whatthe jogger was doing duringthe 912 minute interval of her jog?(1) She was standing still.(2) She was increasing her speed.(3) She was decreasing her speed.(4) She was jogging at a constant rate. 2 _____

3. If the area of a rectangle is expressed asx4 9y2, then the productof the length and the width of the rectangle could be expressed as(1) (x 3y)(x+ 3y) (3) (x2 3y)(x23y)

(2) (x

2

3y)(x

2

+ 3y) (4) (x

4

+y)(x 9y) 3 _____

4. Which table represents a function?

(1) (3)

(2) (4) 4 _____

5. Which inequality isrepresented in the graph?

(1)y 3x+ 4

(2)y 3x+ 4

(3)y 4x 3

(4)y 4x 35 _____

2018141210642

2

4

6

8 16

8

0

0

x 0 1 0 1

f(x) 0 1 1 0

x 2 4 2 4

f(x) 3 5 7 9

x 3 5 7 9

f(x) 2 4 2 4

x 0 1 1 0

f(x) 0 1 0 1

y

4 3 2 1 0 1 2 3 45x

51

2

3

4

5

1

2

3

4

5


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38 ALGEBRA 1

June 2015

6. Mos farm stand sold a total of 165 pounds of apples and peaches.She sold apples for $1.75 per pound and peaches for $2.50 per pound.If she made $337.50, how many pounds of peaches did she sell?(1) 11 (2) 18 (3) 65 (4) 100 6 _____

7. Morgan can start wrestling at age 5 in Division 1. He remains in thatdivision until his next odd birthday when he is required to move up to thenext division level. Which graph correctly represents this information?

(1) (3)

(2) (4)

7 _____

8. Which statement is notalways true?(1) The sum of two rational numbers is rational.

(2) The product of two irrational numbers is rational.(3) The sum of a rational number and an irrational number is irrational.(4) The product of a nonzero rational number and an irrationalnumber is irrational. 8 _____

9. The graph of the function

f(x) = x+4 is shown. The

domain of the function is(1) {x|x> 0} (3) {x|x> 4}(2) {x|x 0} (4) {x|x 4}

9 _____

10. What are the zeros of the function f(x) =x2 13x 30?(1) 10 and 3 (2) 10 and 3 (3) 15 and 2 (4) 15 and 2 10 ____

11. Joey enlarged a 3-inch by 5-inch photograph on a copy machine.He enlarged it four times. The table below shows the area of the

photograph after each enlargement.

What is the average rate of change of the area from the originalphotograph to the fourth enlargement, to the nearest tenth?(1) 4.3 (2) 4.5 (3) 5.4 (4) 6.0 11 ____

5 7 9 11 13 15

5

4

3

2

1Division

Age

5 7 9 11 13 15

5

4

3

2

1Division

Age

5 7 9 11 13 15

5

4

3

2

1Division

Age

5 7 9 11 13 15

5

4

3

2

1Division

Age

Enlargement 0 1 2 3 4

Area (square inches) 15 18.8 23.4 29.3 36.6

f(x)

x


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ALGEBRA 1

June 2015

39

y

x

g(x)

x

1

1

t(time, in days) 0 2 4

f(t)(bacteria) 25 15,625 9,765,625

3

5

9

9

5

3

1

0

1

2

3

4

12. Which equation(s) representthe accompanying graph?

I y= (x+ 2)(x2 4x 12)

II y= (x 3)(x2

+x 2) III y= (x 1)(x2 5x 6)

(1) I, only(2) II, only(3) I and II(4) II and III 12 ____

13. A laboratory technician studied the population growth of a colony

of bacteria. He recorded the number of bacteria every other day, asshown in the partial table below.

Which function would accurately model the technicians data?

(1) f(t) = 25t (2) f(t) = 25t+ 1 (3) f(t) = 25t (4) f(t) = 25(t+ 1) 13 ____

14. Which quadratic function has the largest maximum?(1) h(x) = (3 x)(2 +x) (3) k(x) = 5x2 12x+ 4

(2) (4)

14 ____

15. Iff(x) = 3xandg(x) = 2x+ 5, at which value ofxisf(x)


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40 ALGEBRA 1

June 2015

0.5 0.5 0.6 0.7 0.75 0.8

1.0 1.0 1.1 1.25 1.3 1.4

1.4 1.8 2.5 3.7 3.8 4

4.2 4.6 5.1 6 6.3 7.2

Term 1 Term 2 Term 3 Term 4

I II III

an n 4

a1 2

an a

n 1 4 a

n 4n 2

17. The function V(t) = 1350(1.017)trepresents the value V(t), in dollars, of acomic book tyears after its purchase. The yearly rate of appreciation of thecomic book is(1) 17% (2) 1.7% (3) 1.017% (4) 0.017% 17 ____

18. When directed to solve a quadratic equation by completing the

square, Sam arrived at the equation x

=

5

2

13

4

2

. Which equation

could have been the original equation given to Sam?

(1)x2+ 5x+ 7 = 0 (3)x2 5x+ 7 = 0

(2)x2+ 5x+ 3 = 0 (4)x2 5x+ 3 = 0 18 ____

19. The distance a free falling object has traveled can be modeled bythe equation d=

1

2at2, where ais acceleration due to gravity and tis

the amount of time the object has fallen. What is tin terms of aand d?

(1) t da=

2 (2) t

d

a=

2 (3) t da

d=

2

(4) t d

a=

22

19 ____

20. The accompanying table shows the annualsalaries for the 24 members of a professional

sports team in terms of millions of dollars.

The team signs an additional player to a contract worth 10 milliondollars per year. Which statement about the median and mean is true?(1) Both will increase. (3) Only the mean will increase.(2) Only the median will increase. (4) Neither will change. 20 ____

21. A student is asked to solve the equation 4(3x 1)2 17 = 83.The students solution to the problem starts as

4(3x 1)2= 100(3x 1)2= 25

A correct next step in the solution of the problem is

(1) 3x 1 = 5 (3) 9x2 1 = 25

(2) 3x 1 = 25 (4) 9x2 6x+ 1 = 5 21 ____

22. A pattern of blocks isshown to the right.

If the pattern of blocks continues,which formula(s) could be usedto determine the number of

blocks in the nth term?

(1) I and II (2) I and III (3) II and III (4) III, only 22 ____


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ALGEBRA 1

June 2015

41

23. What are the solutions to the equationx2 8x= 24?

(1)x= 4 2 10 (3)x= 4 2 2

(2)x= 4 2 10 (4)x= 4 2 2 23 ____

24. Natasha is planning a school celebration and wants to have live musicand food for everyone who attends. She has found a band that willcharge her $750 and a caterer who will provide snacks and drinks for$2.25 per person. If her goal is to keep the average cost per person

between $2.75 and $3.25, how many people,p, must attend?(1) 225


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42 ALGEBRA 1

June 2015

26. Alex is selling tickets to a school play. An adult ticket costs $6.50 and astudent ticket costs $4.00. Alex sellsxadult tickets and 12 student tickets.Write a function,f(x), to represent how much money Alex collected fromselling tickets.

27. John and Sarah are each saving money for a car. The total amount of moneyJohn will save is given by the functionf(x) = 60 + 5x. The total amount ofmoney Sarah will save is given by the functiong(x) =x2+ 46. After how manyweeks,x, will they have the same amount of money saved? Explain how youarrived at your answer.

28. If the difference (3x2 2x+ 5) (x2+ 3x 2) is multiplied by1

2x2, what is

the result, written in standard form?

29. Dylan invested $600 in a savings account at a 1.6% annual interest rate. Hemade no deposits or withdrawals on the account for 2 years. The interest wascompounded annually. Find, to the nearest cent, the balance in the account after2 years.


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ALGEBRA 1

June 2015

43

30. Determine the smallest integer that makes 3x+ 7 5x< 15 true.

31. The residual plots from two different sets of bivariate data are graphed below.

Explain, using evidence from graphAand graphB, which graph indicates thatthe model for the data is a good t.

32. A landscaper is creating a rectangular ower bed such that the width is halfof the length. The area of the ower bed is 34 square feet. Write and solve anequation to determine the width of the ower bed, to the nearest tenthof a foot.

0.6

0.4

0.2

0

0.2

0.4

0.6

5

4

3

2

1

0

1

2

3

2 4 6 8 10 12

2 4 6 8 10 12


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44 ALGEBRA 1

June 2015

Part III Answer all 4 questions in this part. Each correct answer will receive4 credits. Clearly indicate the necessary steps, including appropriate formulasubstitutions, diagrams, graphs, charts, etc. Utilize the information providedfor each question to determine your answer. Note that diagrams are notnecessarily drawn to scale. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit. All answers shouldbe written in pen, except for graphs and drawings, which should be donein pencil.[16]

33. Albert says that the two systems of equations shown below have the samesolutions.

Determine and state whether you agree with Albert. Justify your answer.

34. The equation to determine the weekly earnings of an employee at TheHamburger Shack is given by w(x), wherexis the number of hours worked.

w(x) =

{10x, 0 x 40

15(x 40) + 400,x> 40

Determine the difference in salary, in dollars, for an employee who works 52hours versus one who works 38 hours.

Determine the number of hours an employee must work in order to earn $445.Explain how you arrived at this answer.

First System Second System

8x 9y 48

12x 5y 21

8x 9y 48

8.5y 51


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ALGEBRA 1

June 2015

45

35. An on-line electronics store must sell at least $2500 worth of printers andcomputers per day. Each printer costs $50 and each computer costs $500. Thestore can ship a maximum of 15 items per day.

On the set of axes, graph asystem of inequalities thatmodels these constraints.

Determine a combination of

printers and computers thatwould allow the electronicsstore to meet all of theconstraints. Explain howyou obtained your answer.

36. An application developer released a new app to be downloaded. The tablebelow gives the number of downloads for the rst four weeks after the launch ofthe app.

Write an exponential equation that models these data.

Use this model to predict how many downloads the developer would expect in the26th week if this trend continues. Round your answer to the nearest download.

Would it be reasonable to use this model to predict the number of downloadspast one year? Explain your reasoning.

Number of Weeks 1 2 3 4

Number of Downloads 120 180 270 405


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46 ALGEBRA 1

June 2015

Part IV Answer the question in this part. A correct answer will receive 6 credits.Clearly indicate the necessary steps, including appropriate formulasubstitutions, diagrams, graphs, charts, etc. Utilize the information providedfor each question to determine your answer. Note that diagrams are notnecessarily drawn to scale. A correct numerical answer with no work shownwill receive only 1 credit. All answers should be written in pen, except forgraphs and drawings, which should be written in pencil.[6]

37. A football player attempts to kick a football over a goal post. The path of the

football can be modeled by the function h x x x( ) = +1

225

2

32 , wherexis the

horizontal distance from the kick, and h(x) is the height of the football above the

ground, when both are measured in feet.

On the set of axes below, graph the functiony= h(x) over the interval 0 x 150.

Determine the vertex ofy= h(x). Interpret the meaning of this vertex in thecontext of the problem.

The goal post is 10 feet high and 45 yards away from the kick. Will the ball behigh enough to pass over the goal post? Justify your answer.

y

x


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ALGEBRA 1

August 201547


1. Given the graph of the line represented by the equationf(x) = 2x+ b, if bisincreased by 4 units, the graph of the new line would be shifted 4 units(1) right (2) up (3) left (4) down 1 _____

2. Rowan has $50 in a savings jar and is putting in $5 every week. Jonahhas $10 in his own jar and is putting in $15 every week. Each of them plots

his progress on a graph with time on the horizontal axis and amount in thejar on the vertical axis. Which statement about their graphs is true?(1) Rowans graph has a steeper slope than Jonahs.(2) Rowans graph always lies above Jonahs.(3) Jonahs graph has a steeper slope than Rowans.(4) Jonahs graph always lies above Rowans. 2 _____

3. To watch a varsity basketball game, spectators must buy a ticket atthe door. The cost of an adult ticket is $3.00 and the cost of a student

ticket is $1.50. If the number of adult tickets sold is represented by aand student tickets sold bys, which expression represents the amountof money collected at the door from the ticket sales?(1) 4.50as (2) 4.50(a+s) (3) (3.00a)(1.50s) (4) 3.00a+ 1.50s 3 _____

4. The graph off(x) is shown.Which function could representthe graph off(x)?(1)f(x) = (x+ 2)(x2+ 3x 4)

(2)f(x) = (x 2)(x2+ 3x 4)(3)f(x) = (x+ 2)(x2+ 3x+ 4)(4)f(x) = (x 2)(x2+ 3x+ 4)

4 _____

5. The cost of a pack of chewing gum in a vending machine is $0.75.The cost of a bottle of juice in the same machine is $1.25. Julia has$22.00 to spend on chewing gum and bottles of juice for her team andshe must buy seven packs of chewing gum. If brepresents the numberof bottles of juice, which inequality represents the maximum numberof bottles she can buy?(1) 0.75b+ 1.25(7) 22 (3) 0.75(7) + 1.25b 22(2) 0.75b+ 1.25(7) 22 (4) 0.75(7) + 1.25b 22 5 _____

y

x


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48 ALGEBRA 1

August 2015

5 5

2 6

3 124 7

2 6

y

x

6. Which graph represents the solution ofyx+ 3 andy 2x 2?

(1) (2) (3) (4) 6 _____

7. The country of Benin in West Africa has a population of 9.05 millionpeople. The population is growing at a rate of 3.1% each year. Whichfunction can be used to nd the population 7 years from now?(1)f(t) = (9.05 106)(1 0.31)7 (3)f(t) = (9.05 106)(1 + 0.031)7

(2)f(t) = (9.05 106)(1 + 0.31)7 (4)f(t) = (9.05 106)(1 0.031)7 7 _____

8. A typical cell phone plan has a xed base fee that includes a certainamount of data and an overage charge for data use beyond the plan. Acell phone plan charges a base fee of $62 and an overage charge of $30

per gigabyte of data that exceed 2 gigabytes. If Crepresents the cost andgrepresents the total number of gigabytes of data, which equation couldrepresent this plan when more than 2 gigabytes are used?(1) C= 30 + 62(2 g) (3) C= 62 + 30(2 g)

(2) C= 30 + 62(g 2) (4) C= 62 + 30(g 2) 8 _____

9. Four expressions are shown below.

I 2(2x2 2x 60) III 4(x+ 6)(x 5) II4(x2x 30) IV4x(x 1) 120

The expression 4x2 4x 120 is equivalent to(1) I and II, only (3) I, II, and IV(2) II and IV, only (4) II, III, and IV 9 _____

10. Last week, a candle store received $355.60 for selling 20 candles.Small candles sell for $10.98 and large candles sell for $27.98.How many large candles did the store sell?(1) 6 (2) 8 (3) 10 (4) 12 10 ____

11. Which representations are functions? I III

II{ (1,1), (2,1), (3,2), (4,3), (5,5), (6,8), (7,13) } IVy= 2x+ 1

(1) I and II (2) II and IV (3) III, only (4) IV, only 11 ____

y

x

y

x

y

x

y

x


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ALGEBRA 1

August 201549

12. Iff(x) =2 3

6 5

x

x

+

, thenf

1

2( )=(1) 1 (2) 2 (3) 1 (4) 13

3

12 ____

13. The zeros of the functionf(x) = 3x2 3x 6 are(1) 1 and 2 (2) 1 and 2 (3) 1 and 2 (4) 1 and 2 13 ____

14. Which recursively dened function has a rst term equal to 10and a common difference of 4?(1)f(1) = 10 (3)f(1) = 10 f(x) =f(x 1) + 4 f(x) = 4f(x 1)

(2)f(1) = 4 (4)f(1) = 4 f(x) =f(x 1) + 10 f(x) = 10f(x 1) 14 ____

15. Firing a piece of pottery ina kiln takes place at differenttemperatures for differentamounts of time. The graphshows the temperatures in akiln while ring a piece of

pottery after the kiln is preheatedto 200F. During which timeinterval did the temperature inthe kiln show the greatestaverage rate of change?(1) 0 to 1 hour (3) 2.5 hours to 5 hours(2) 1 hour to 1.5 hours (4) 5 hours to 8 hours 15 ____

16. Which graph representsf(x) =

{|x| x< 1

? x x 1

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

16 ____

17. If f(x) =x2 2x 8 and g(x) =1

4x 1, for which values ofx

isf(x) =g(x)?(1) 1.75 and 1.438 (3) 1.438 and 0(2) 1.75 and 4 (4) 4 and 0 17 ____

x

y

x

y

x

y

x

y


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50 ALGEBRA 1

August 201518. Alicia has invented a new app for smart phones that two companiesare interested in purchasing for a 2-year contract.

CompanyAis offering her $10,000 for the rst month and will increase the amount each month by $5000.

CompanyBis offering $500 for the rst month and will double their payment each month from the previous month.

Monthly payments are made at the end of each month. For which monthlypayment will companyBs payment rst exceed companyAs payment?(1) 6 (2) 7 (3) 8 (4) 9 18 ____

19. The two sets of data below represent the number of runs scored bytwo different youth baseball teams over the course of a season.

TeamA: 4, 8, 5, 12, 3, 9, 5, 2 TeamB: 5, 9, 11, 4, 6, 11, 2, 7Which set of statements about the mean and standard deviation is true?(1) meanA< meanB standard deviationA> standard deviationB(2) meanA> meanB standard deviationA< standard deviationB(3) meanA< meanB standard deviationA< standard deviationB(4) meanA> meanB

standard deviationA> standard deviationB 19 ____

20. If Lylah completes the square forf(x) =x2 12x+ 7 in orderto nd the minimum, she must writef(x) in the general form

f(x) = (x a)2+ b. What is the value of aforf(x)?(1) 6 (2) 6 (3) 12 (4) 12 20 ____

21. Given the followingquadratic functions:

g(x) = x2x+ 6 and

Which statement about these functions is true?(1) Over the interval 1 x 1, the average rate of change for n(x)is less than that forg(x).(2) They-intercept ofg(x) is greater than they-intercept for n(x).(3) The functiong(x) has a greater maximum value than n(x).(4) The sum of the roots of n(x) = 0 is greater than the sum of theroots ofg(x) = 0. 21 ____

22. For which value ofPand WisP+ Wa rational number?

(1)P=1

3and W=

1

6 (3)P=

1

6and W=

1

10

(2)P=1

4and W=

1

9 (4)P=

1

25and W=

1

2 22 ____

23. The solution of the equation (x+ 3)2= 7 is

(1) 3 7 (2) 7 3 (3) 3 7 (4) 7 3 23 ____

x 3 2 1 0 1 2 3 4 5

n(x) 7 0 5 8 9 8 5 0 7


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ALGEBRA 1

August 201551

24. Which trinomial is equivalent to 3(x 2)2 2(x 1)?(1) 3x2 2x 10 (3) 3x2 14x+ 10(2) 3x2 2x 14 (4) 3x2 14x+ 14 24 ____

Part II Answer all 8 questions in this part. Each correct answer will receive2 credits. Clearly indicate the necessary steps, including appropriateformula substitutions, diagrams, graphs, charts, etc. Utilize the informationprovided for each question to determine your answer. Note that diagramsare not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. [16]

25. Each day Toni records the height of a plant for her science lab. Her data are

shown in the table.

The plant continues to grow at a constant daily rate. Write an equation torepresenth(n), the height of the plant on the nth day.

26. On the set of axes below, graph the inequality 2x+y> 1.

Day (n) 1 2 3 4 5

Height (cm) 3.0 4.5 6.0 7.5 9.0

y

x


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52 ALGEBRA 1

August 201527. Rachel and Marc were given the information shown below about the bacteriagrowing in a Petri dish in their biology class.

Rachel wants to model this information with a linear function. Marc wants touse an exponential function. Which model is the better choice? Explain whyyou chose this model.

28. A driver leaves home for a business trip and drives at a constant speed of 60miles per hour for 2 hours. Her car gets a at tire, and she spends 30 minuteschanging the tire. She resumes driving and drives at 30 miles per hour for theremaining one hour until she reaches her destination.

On the set of axes, drawa graph that models thedrivers distance from home.

29. How many real solutions does the equationx2 2x+ 5 = 0 have?Justify your answer.

Number of Hours, x 1 2 3 4 5 6 7 8 9 10

Number of Bacteria, B(x) 220 280 350 440 550 690 860 1070 1340 1680

x

300

240

180

120

60

1 2 3 4 5


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ALGEBRA 1

August 201553

30. The number of carbon atoms in a fossil is given by the functiony= 5100(0.95)x, wherexrepresents the number of years since being discovered.

What is the percent of change each year? Explain how you arrived at youranswer.

31. A toy rocket is launched from the ground straight upward. The height ofthe rocket above the ground, in feet, is given by the equation h(t) = 16t2+ 64t,where tis the time in seconds. Determine the domain for this function in thegiven context. Explain your reasoning.

32. Jackson is starting an exercise program. The rst day he will spend 30 minuteson a treadmill. He will increase his time on the treadmill by 2 minutes each day.Write an equation for T(d), the time, in minutes, on the treadmill on day d.

Find T(6), the minutes he will spend on the treadmill on day 6.


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54 ALGEBRA 1

August 2015

Part III Answer all 4 questions in this part. Each correct answer will receive4 credits. Clearly indicate the necessary steps, including appropriate formulasubstitutions, diagrams, graphs, charts, etc. Utilize the informationprovided for each question to determine your answer. Note that diagramsare not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. Allanswers should be written in pen, except for graphs and drawings, whichshould be done in pencil. [16]

33. Graphf(x) =x2andg(x) = 2xforx 0 on the set of axes.State which function,f(x) org(x),has a greater value whenx= 20.Justify your reasoning.

34. Solve forxalgebraically: 7x 3(4x 8) 6x+ 12 9x

Ifxis a number in the interval [4, 8], state all integers that satisfy the giveninequality. Explain how you determined these values.

y

x


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ALGEBRA 1

August 201555

35. The volume of a large can of tuna sh can be calculated using the formulaV= r2h. Write an equation to nd the radius, r, in terms of Vand h.

Determine the diameter, to the nearest inch, of a large can of tuna sh that has avolume of 66 cubic inches and a height of 3.3 inches.

36. The table below shows the attendance at a museum in select years from 2007to 2013.

State the linear regression equation represented by the data table whenx= 0 isused to represent the year 2007 andyis used to represent the attendance. Roundall values to the nearest hundredth.

State the correlation coefcient to the nearest hundredthand determine whetherthe data suggest a strong or weak association.

Attendance at Museum

Year 2007 2008 2009 2011 2013Attendance (millions) 8.3 8.5 8.5 8.8 9.3


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56 ALGEBRA 1

August 2015

Part IV Answer the question in this part. A correct answer will receive 6 credits.Clearly indicate the necessary steps, including appropriate formulasubstitutions, diagrams, graphs, charts, etc. Utilize the informationprovided to determine your answer. Note that diagrams are not necessarilydrawn to scale. A correct numerical answer with no work shown will receiveonly 1 credit. All answers should be written in pen, except for graphs anddrawings, which should be written in pencil.[6]

37. A rectangular picture measures 6 inches by 8 inches. Simon wants to builda wooden frame for the picture so that the framed picture takes up a maximumarea of 100 square inches on his wall. The pieces of wood that he uses to buildthe frame all have the same width.

Write an equation or inequality that could be used to determine the maximumwidth of the pieces of wood for the frame Simon could create.

Explain how your equation or inequality models the situation.

Solve the equation or inequality to determine the maximum width of the piecesof wood used for the frame to the nearest tenth of an inch.


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Correlationof

Standards


60/64

58

JUNE 2014

A-REI.A

F-IF.B

A-APR.A

A-REI.D

A-REI.B

F-LE.A

F-LE.B

A-REI.B

F-IF.B

A-REI.B

S-ID.C

A-SSE.B

N-RN.B

A-REI.C

F-LE.A

A-CED.A

F-IF.A

F-IF.B

S.ID.A

F.IF.A

F.IF.A

A.CED.A

A.CED.A

F.LE.A

Correlation of Standards

AUGUST 2014

N-RN.B

F-LE.B

A-REI.B

S-ID.A

A-REI.D

A-APR.A

A-REI.D

F-IF.C

A-CED.A

F-LE.A

F-IF.A

F-LE.A

A-CED.A

F-IF.B

A-SSE.A

F-LE.A

F-BF.B

F-IF.C

A-CED.A

A-REI.B

S-ID.B

F-IF.C

F-IF.B

F-IF.A

QUESTION STANDARD

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

TEST 1

A.REI.3

F.IF.1

F.IF.2

S.ID.2

A.APR.1

A.APR.1

F.IF.7

F.LE.2

A.SSE.2

S.ID.6

F.IF.4

F.IF.5

8.GB.6

F.IF.7

F.IF.6

A.SSE.1

F.IF.3

F.IF.4

S.ID.5

A.REI.10

A.CED.2

A.SSE.2

F.IF.4

A.REI.11


61/64

Correlation of Standards 59

25

26

27

28

29

30

31

32

33

34

35

36

37

TEST 1

F.IF.6

A.SSE.3

A.REI.12

A.REI.4

A.CED.1

A.REI.11

F.IF.2

F.IF.8

A.REI.12

N.Q.1

F.IF.7

S.ID.1

A.REI.6

JUNE 2014

F.IF.C

F.LE.B

A.REI.B

F.BF.B

A.REI.D

F.IF.A

A.SSE.A

S.ID.A

A.REI.B

A.CED.A

F.BF.A

A.CED.A

A.REI.D

AUGUST 2014

A-SSE.B

F-BF.A

A-REI.C

A-APR.A

F-IF.C

A-REI.B

S-ID.B

A-REI.B

F-BF.B

A-CED.A

A-REI.D

A-CED.A

A-CED.A

QUESTION STANDARD


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60 Correlation of Standards

QUESTION STANDARD

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

JANUARY 2015

A-SSE.A

N-Q.A

A-SSE.B

F-BF.A

F-LE.A

F-IF.B

A-REI.B

F-IF.A

F-IF.C

A-APR.A

A-REI.D

F-BF.B

A-CED.A

S-ID.A

F-IF.B

A-CED.A

A-REI.B

A-REI.D

A-SSE.B

F-IF.A

F-IF.B

A.SSE.A

A-CED.A

A-APR.B

AUGUST 2015

F-BF.B

A-CED.A

A-SSE.A

A-APR.B

A-CED.A

A-REI.D

F-LE.A

F-BF.A

A-SSE.A

A-REI.C

F-IF.A

F-IF.A

A-SSE.B

F-IF.A

F-IF.B

F-IF.C

A-REI.D

F-LE.A

S-ID.A

A-SSE.B

F-IF.C

N-RN.B

A-REI.B

A-APR.A

JUNE 2015

F-LE.B

N-Q.A

A-SSE.A

F-IF.A

A-REI.D

A-REI.C

F-IF.C

N-RN.B

F-IF.A

A-SSE.B

F-IF.B

A-APR.B

F-LE.A

F-IF.C

F-LE.A

S-ID.C

A-SSE.A

A-REI.B

A-CED.A

S-ID.A

A-REI.A

F-BF.A

A-REI.B

A-CED.A


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Correlation of Standards 61

QUESTION STANDARD

25

26

27

28

29

30

31

32

33

34

35

36

37

JANUARY 2015

N-RN.B

S-ID.B

F-IF.A

A-APR.A

A-REI.B

F-IF.C

A-CED.A

F-LE.A

A-CED.A

A-REI.D

S-ID.C

F-IF.C

A-CED.A

JUNE 2015

F-BF.B

F-BF.A

A-REI.D

A-APR.A

A-CED.A

A-REI.B

S-ID.B

A-CED.A

A-REI.C

F-IF.A

A-CED.A

A-CED.A

F-IF.B

AUGUST 2015

F-BF.A

A-REI.D

S-ID.B

F-IF.B

A-REI.B

F-LE.B

F-IF.B

A-CED.A

F-LE.A

A-REI.B

A-CED.A

S-ID.C

A-CED.A


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A quick reference guidefor the

NEWCOMMON CORE STANDARDS of ALGEBRA 1

Loaded with lots of examples

AVAILABLE ONLY AT THE

TOPICAL REVIEW BOOK COMPANY

Written by:

MaryAnn Casey

Topical Review Book Company

ALGEBRA 1

MADE EASYCommon Core Standards

Edition

alg1wrbkfall2015- unlocked.pdf

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