A. 4.3p d

1. Which function represents p, the water pressure in square inches, as a function of d, the depth, in feet?

Depth in feet (d) Pressure in PSI (p)

10 4.3

20 8.6

30 12.9

40 17.2

50 21.5

B. 0.43p d C. 2.33p d D. 23.3p d

The function is linear because the change in d is constant and the change in p is constant.

Increases by 10

Increases by 4.3

The slope of the linear function is the change in p divided by the change in d or

4.30.43 .

10

An easier way to do this problem is to substitute the table values into the formulas to see which one works.

Choice B is the only one with a slope of 0.43.

2. For one child, a childcare facility charges $300 per month for preschool and $3.50 per hour for each hour of childcare after preschool. The function below can be used to determine the monthly fee for childcare and preschool, where h represents the number of hours spent in childcare after preschool.

If the one-month charges for one child totaled $637.75, what was the total number of hours the child spent in childcare after preschool?

( ) 300 3.5f h h

Since f(h) represents the total monthly fee, substitute $637.75 for f(h) and solve for h.

637.75 300 3.5h

337.75 3.5h

The child spent 96.5 hours in childcare after preschool that month.

337.75 3.5

3.5 3.5

h

96.5 h

300 300

3. An economics teacher plotted the value of a stock on 11 different days during a 500 day period and used line segments to connect them. In the graph shown, the horizontal axis is in days and the vertical axis is measured in dollars.

Based on the graph, which of the following best describes the range of the value of the stock for this 500-day period?

A. 0 500

B. 1 500

C. 10 60

D. 0 80

x

x

y

y

The y-axis displays the values of the stock. The lowest value is about 10 and the highest value is about 60.

4. The set of ordered pairs shown below defines a relation.

{(0, 0), (1, 5), (2, 8), (3, 9), (4, 8), (5, 5), (6, 0)} What is the value of the greatest element in the range of this relation?The range is the set of all y-coordinates or {0,5,8,9}.

These numbers are in numerical order so the greatest element in the range is 9.

5. Mario needs to cut three book shelves from a board that is 1.8 meters long. The second shelf is 15 centimeters longer than twice the length of the first shelf. The remaining shelf is 5 centimeters longer than the first shelf. The equation below represents this situation, where x is the length of the first shelf in meters.

Which of the following is the length, in meters, of the first shelf?

(2 0.15) ( 0.05) 1.8x x x

A. 0.40B. 0.45C. 0.53D. 0.96

The problem states that x denotes the length of the first shelf so solving for x will answer the question.

(2 0.15) ( 0.05) 1.8x x x

4 0.2 1.8x 0.2 0.2 4 1.6x

4 1.6

4 4

x

0.4x The length of the first shelf is 0.4 meters.

6. Bill is planning to drive from his house to a baseball stadium and arrive in time for the beginning of the championship game. His arrival time depends on the traffic. If traffic is light, he will travel at an average speed of 50 miles per hour and arrive 1 hour early. If traffic is heavy, he will travel at an average speed of 30 miles per hour and arrive on time. The equation below can be used to model this situation, where t represents Bill’s driving time, in hours.

What is the distance, in miles, from Bill’s house to the baseball stadium?

50( 1) 30t t

Solve the equation to determine Bill’s driving time if he averages 30 mph.

50( 1) 30t t The question askes for the distance and distance equals rate times time.The rate is 30 mph and the time is 2.5 hours.

(30)(2.5)

75 miles

d rt

d

d

50 50 30t t 30 30t t 20 50 0t

50 50 20 50t 20 50

20 20

t

2.5t

7. The Gross Domestic Product of a country for a given year is the sum of the market values of all goods and services produced within the country during that year. The Gross Domestic Product per capita is found by using the followinig formula. C I G N

SP

Where: S = Gross Domestic Product per capitaC = consumer spendingI = InvestmentG = government purchasesN = net exportsP = population

Which of the following shows the formula solved for C?

A.

B.

C.

D.

PSC

I G NPS

CI G N

C PS I G N

C PS I G N

C I G N

P S PP

PS C I G N I G N I G N

or

PS I G N C

C PS I G N

8. Taylor has a total of $25 to spend on dinner, which includes a 6.5% sales tax and a 20% tip. Taylor used the inequality shown below to calculate the amount in dollars, a, she can spend before tax and tip.

1.2( 0.065 ) 25a a

Which of the following shows the solution to this inequality?

A. 22.74

B. 22.34

C. 19.76

D. 19.56

a

a

a

a

1.2( 0.065 ) 25a a

1.2 0.078 25a a

1.278 25a 1.278 25

1.278 1.278

a

19.56181534...a

9. Which graph shows the solution to the inequality shown below?

15 7 2( 10) 35n n A.

2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

B.

2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

C.

2 1 0 1 2 3 4

5 6 7 8 9 10 11 12

D.

2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

15 7 2( 10) 35n n

Since requires a solid circle and < requires an open circle, the answer is D.

15 7 2 20 35n n 15 5 20 35n 20 20 20

5 5 15n 5 5 15

5 5 5

n

1 3n

10. The out-of-pocket costs to an employee for health insurance and medical expenses for one year are shown in the table below.

Type of Cost Definition Cost to Employee

PremiumTotal amount employee pays insurance company for the policy

$3,626

DeductibleAmount of medical expenses employee pays before insurance company pays for anything $500

Co-paymentPercentage of medical expenses after the first $500 that employee has to pay 20%

According to the plan outlined in the table, total annual health care costs, C, depend on the employee’s medical expenses for that year. If x represents the total medical expenses of an employee on this plan and , which of the following equations can be used to determine this employee’s total health care costs for that year?

500x

This employee has paid the $500 deductible plus 20% of the amount over $500 which is . The employee has also paid the premium. The sum of all three costs will determine the total cost C.

500 x

3,626 500 0.20( 500)C x

A. 3,626 500 0.20( 500)

B. 3,626 500 0.20

C. 3,626 500 0.20( 500)

D. 3,626 500 0.20

C x

C x

C x

C x

11. Karen works as a salesperson for a local marketing company. Using the equations shown below, the company calculates her monthly earnings based upon her total sales for the month.

Total Sales for the Month (s in dollars)

Earnings Equation

$5,000s 1,600 0.1E s

$5,000s 1,600 0.1 0.15( 5000)E s s

where: E represents total monthly earnings before taxes and withholdings represents the dollar amount of her total sales

Karen’s total sales were greater than $5,000 in October. If her total monthly earnings for October were $3,000, what was the value of her total monthly sales, s?

Use the second row of the table because s > $5,000. Substitute $3,000 for E and solve for s.

3,000 1,600 0.1 0.15( 5000)s s 3,000 1,600 0.1 0.15 750s s 3,000 0.25 850s

850 850 2150 0.25s2150 0.25

0.25 0.25

s

8600s

12. Roger went to a garage sale where hardback books sold for $5 each and paperback books sold for $2.50 each. He has $20 to spend. The equation below can be used to find how many books of each type Roger can buy, where x is the number of hardback books and y is the number of paperback books.

Which of the following shows the graph of this equation.5 2.5 20x y

y

xA.

1 2 3 4 5 6 7 8 9 10 11

987654321

1 2 3 4 5 6 7 8 9 10 11

987654321

B.

1 2 3 4 5 6 7 8 9 10 11

987654321

1 2 3 4 5 6 7 8 9 10 11

987654321

C.

D.

Use x and y intercepts.

(a) Let x = 0

5(0)+2.5y = 20

(b) Let y = 05x + 2.5(0) = 20

x = 4 (4,0) is the x-int

The answer is A.

y = 8 (0,8) is the y-int

5x = 205 20

5 5

x

2.5 20y 2.5 20

2.5 2.5

y

13. An architect designed an outdoor staircase for a house. The relationship between the height of the steps and the length of the tread is modeled by the equation

57 95 0.x y

Which of the following represents the slope of the line defined by this equation?

5A.

33

B. 22

C. 33

D. 5

Solve for y to get the equation in the form y = mx + b so that m will be the slope.

57 95 0x y 57 57x x

95 57y x 95 57

95 95

y x

57

95y x

57 19 3

95 19 5m

3

5

14. An engineer needs to determine the slope between two points on a gondola ride in order to evaluate the power requirements when the gondola is full of passengers. A coordinate grid has been placed over a diagram between the two points, as shown below. For estimation purposes, a straight line between the two points can be used to find the slope.

Assuming the cable runs in a straight line, what is the slope of the line between the two points shown?

2 1

2 1

y ym

x x

1 1,x y

2 2,x y

70 30

180 20

40

160

1

4

15. In a technical drawing class, students are analyzing the side view of a house that has been positioned on a coordinate grid, as shown.

Which of the following equations best represents the line that contains ?PQ

Determine the slope by using the formula or by counting.

2 1

2 1

10 12 2 2

11 6 5 5

y ym

x x

5A. 14.4

25

B. 272

2C. 14.4

52

D. 275

y x

y x

y x

y x

orrise 2

run 5m

-2

+5

Now use the point-slope formula to determine the equation of the line.

1 1( )y y m x x Note that after determining the slope of the segment, only choice C has the correct slope.

212 ( 6)

5y x

212 2.4

5y x

12 12 2

14.45

y x

1 1,x y

2 2,x y

16. On the coordinate grid, line l is perpendicular to . AB

�������������� �

What is the slope of line l ?

Use the slope formula to find the slope of . The slope of line l will be the opposite reciprocal since the lines are perpendicular.

AB�������������� �

2 1

2 1

y ym

x x

The opposite reciprocal is 2.

2 0

0 ( 4)

2

4

1

2

1 1,x y

2 2,x y

17. David is training for a marathon. He writes down the time and distance for each training run and then records the data on a scatter plot. He has drawn a line of best fit on the scatter plot, as shown below.

Which statement best expresses the meaning of the slope as a rate of change for this line of best fit?

A. It represents the number of miles he will have to run to finish the marathon.

B. It represents the average speed, in miles per hour, of his training runs.

C. It represents the number of hours he will need to finish the marathon.

D. It represents the distances, in miles, that he ran while he was training.

The slope of a line is vertical change over horizontal change or change in miles over change in hours. Therefore, the units on the slope would be miles per hour.

18. Joel graphed the line shown on the coordinate plane shown. What is the x-coordinate of the point at which this line intersects the x-axis?

First write an equation for the line that is graphed. It is easiest to use y = mx + b because the y -intercept is 11 as shown on the graph. The slope can be determined by using the slope formula.

2 1

2 1

y ym

x x

Using b = 11 and m = -2 and substituting into y = mx + b gives y = -2x + 11.

The x-intercept has a y-coordinate of 0, so substitute 0 for y in the equation of the line and solve for x to get the x-intercept.

?,0

2 11y x

1 1,x y

2 2,x y

7 11

2 0

4

2

2

0 2 11x 11 11

11 or 5.5

2x

11 2

2 2

x

11 2x

19. Russ bought 3 medium and 2 large submarine sandwiches for a total of $29.95. Stacy bought 4 medium and 1 large submarine sandwiches for a total of $28.45. Which statement shows the cost of each medium and each large submarine sandwich?

A. Each medium sandwich costs $5.69 and each large sandwich costs $6.89.B. Each medium sandwich costs $5.69 and each large sandwich costs $6.39.C. Each medium sandwich costs $5.39 and each large sandwich costs $6.89.D. Each medium sandwich costs $5.39 and each large sandwich costs $6.39.

3 2 29.95m l 3(5.39) 2 29.95l 4 1 28.45m l

2 4 1 2 28.45m l 8 2 56.90m l 3 2 29.95m l

5 26.95m

5.39m A medium sandwich costs $5.39 but we need to also determine the cost of a large. Substitute in the top equation and solve for l.

16.17 2 29.95l 2 13.78l

6.89l

5 5

20. A website that sells songs for downloading increased its price per song from $0.99 to $1.29. Macy spent $15.36 downloading songs during the month of the price increase. She downloaded 4 more songs at $0.99 than at $1.29. The set of equations below represents the situation where x is the number of songs Macy downloaded at $0.99 and y is the number of songs she downloaded at $1.29.

What is the exact number of songs Macy downloaded at the $0.99 price?

4

0.99 1.29 15.36

x y

x y

0.99( 4) 1.29 15.36y y 0.99 3.96 1.29 15.36y y

2.28 3.96 15.36y 3.96 3.96

2.28 11.4y 2.28 11.4

2.28 2.28

y

5y 4x y

9x

But y represents the number of songs downloaded at $1.29 and the question asks how many are downloaded at $0.99. Substitute the value of y and solve for x.

21. The expression is equivalent to which of the following?

26 5 3m n q

12 10 6

36 25 9

8 7 5

12 10 6

A.

B.

C. 2

D. 2

m n q

m n q

m n q

m n q

26 5 3

2 2 26 5 3

m n q

m n q

22. Mina simplified the expression shown below:

Her final answer was in the form If she simplified the expression correctly, what is the value of n, the exponent of b?

.m na b

3 6 2 2a b a b

3 6 2 2a b a b

Add exponents to get

Therefore, the value of n is - 4 .

12 10 6m n q

5 4 .a b

23. Which expression is equivalent to the perimeter of the shaded portion of the rectangle?

A. 2 10

B. 2 12

C. 4 14

D. 8 28

x

x

x

x

The consecutive sides of the rectangle are x + 3 and x + 4 units in length. The perimeter is

4x

3x 4x

24. New photo imaging techniques on computers allow artists to distort an image from its original shape. Figure 1 is a square image. Figure 2 is stretched 4 units wider and shrunk 4 units shorter than Figure 1. How many square units greater is the area of Figure 1 than the area of Figure 2?

2Area Figure 1 is .x x x 2 2( 16)x x

2(x + 3) + 2(x + 4) = 2 x + 6+ 2 x + 8=

4x+14

2Area Figure 2 is ( 4)( 4) 16.x x x 2 2 16x x 16

25. Members of the art club want to raise money for their next field trip. They plan to decorate greeting cards with glitter and origami animals made of origami paper. They wrote the expression below to help calculate their total expenses:

( )np ng nc

Which of the following expressions is equivalent to the expression above?

where c = cost of one greeting card, g = cost of glitter per card, p = cost of origami animals per card, and n = number of cards.

A. ( ) C. 3 ( )

B. ( ) D. 3 ( )

n p g c n p g c

n p g c n p g c

( )np ng nc

26. If , which of the following shows the expression below in simplest form?

3x 23 27

3

x

x

A. 3( 3)

B. 3( 3)

C. 3( 9)

D. 3( 9)

x

x

x

x

23 27

3

x

x

3( 3)x

( )n p g nc ( )n p g c

23( 9)

3

x

x

3( 3)( 3)

3

x x

x

27. Charlie needs to simplify the expression below before he substitutes values for x and y.

18 12 9 8

3 4

x y x y

x y

If , which of the following is a simplified version of the expression above?

0 and 0x y

9 5

24 16

6 3 3 2

15 8 6 4

A.

B.

C.

D.

x y

x y

x y x y

x y x y

18 12 9 8

3 4

x y x y

x y

28. Tammy made similar models of a building, with dimensions, in inches, as shown in the diagram below. What is the value, in inches, of x?

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

5 3

16 12

x x

4 60 48x

18 12 9 8

3 4 3 4

x y x y

x y x y 15 8 6 4x y x y

12( 5) 16( 3)x x

12 60 16 48x x

3x 4 12x

60 60

16 16x x

29. What is the solution of the equation below?2 3

14 4x x

2 3

14 4x x

2(4 ) 3( 14)x x

8 3 42x x 3 3x x 5 42x 5 42

5 5

x

42 or 8.4

5x

30. Neelam simplified the expression below for a homework assignment.

If Neelam simplified correctly, which of the following is her answer?12 3 7 3x

A. 9 3 3

B. 11 3 3

C. 7 15 3

D. 8 15 3

x

x

x

x

12 3 7 3x

31. Jeannie solved the quadratic equation shown below by factoring.

Which of the following shows a step in solving the equation shown?

2 2 8 0x x

A. ( 2)( 4) 0

B. ( 2)( 4) 0

C. ( 2)( 4) 0

D. ( 2)( 4) 0

x x

x x

x x

x x

2

( 4)( 2

8

)

2 0

0x x

x x

The first step is to factor the quadratic.

2 2 3 3 7 3x

2 3 7 3 3x

9 3 3x

32. Which of the following is the graph of ?2 2 8y x x

2 2 8 0x x

The graph is a parabola that opens up because the leading coefficient is positive. This eliminates choices A and B.

Set y equal to 0 and solve to find the x-intercepts.

The correct graph is C because it has the correct x-intercepts.

( 4)( 2) 0x x 4 0 or 2 0x x

4 or 2x x

33. A ball is kicked from ground level into the air. Its height y, in feet, after x seconds can be represented by the equation What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches ground level again?

240 16 .y x x

Set y = 0 and solve because when the ball is on the ground its height, y, is 0.240 16y x x

The ball is on the ground for a total of 2.5 seconds.

20 40 16x x

0 8 (5 2 )x x 8 0 or 5 2 0x x 8 0

or 2 58 8

xx

2 50 or

2 2

xx

0 or 2.5x x

34. The set T represents several Tauring breeds of cattle. T = {Angus, Devon, Shorthorn, Texas Longhorn} The set Z represents several Zebu breeds of cattle. Z = {Boran, Nelore, Ponwar} What is the total number of elements in the set ?T Z

The number of elements in the cross product of two sets is the number of elements in one set multiplied by the number of elements in the other. 4 x 3 = 12

35. Set D lists the ages of Dianna’s grandchildren. D = {2, 5, 6, 8, 10, 11} Set K lists the ages of Karen’s grandchildren. K = {2, 10, 18} Set P lists the ages of Patrick’s grandchildren. P = {10, 11, 14}What is the greatest age in the set ( ) ?K P D

The set contains any element in either set K or set P which is {2, 10, 11, 14, 18}

K P

The intersection of this set with set D is elements that the sets have in common which is {2, 10, 11}

The greatest element in this set is 11.

A. 7B. 9C. 12D. 20

36. The universal set contains only sets R, S, and T. These sets are related as shown in the Venn Diagram below:Which set represents (~ ) (~ )?R S T S

~ denotes elements not in and in .R S R S

The elements in S, the yellow circle, that are NOT in R make up the set {j, k, m, n}.

~ denotes elements not in and in .T S T SThe elements in S, the yellow circle, that are NOT in T make up the set{d, k, m, n}.

The union of {j, k, m, n} and {d, k, m, n} contains all elements that are in either set. Therefore, the union of the sets is {d, j, k, m, n}.

A. {d, e, f, j}B. {d, j, k, m, n}C. {d, e, f, j, k, m, n}D. {d, e, f, g, j, k, m, n}

37. The Venn diagram below shows the number of students who chose to participate in each of the three sports offered at Sports Camp.

Based on the diagram, what is theTotal number of students who did NOT participate inVolleyball?

Students who did NOT participate in volleyball are represented by the areas that lie outside the highlighted circle that represents Volleyball.

15 + 9 + 11 = 35