PRE Practice Test #3 Calvin  College  Education  Program   http://www.calvin.edu/academic/education/

Answer key found at the end of the test. Sample mathematical definitions and formulas to help you are given on the next two pages, just as they are on the actual test. However, you should try to answer questions by referring to these definitions and formula as little as possible. Constant page turning back and forth will slow you down and can actually over-tax your working memory.

1. Which of the following expressions best exemplifies the commutative property of addition?

A. (14 + 6) (7 + x + y) = 20(7 + x + y) B. (14 + 6) (7 + x + y) = (7 + x + y) (14 + 6) C. (14 + 6) (7 + x + y) = (6 + 14) (y + x + 7) D. (14 + 6) (7 + x + y) = 98 +14x + 14y +42 +6x + 6y

2. The period of a pendulum is proportional to the square root of the length of the pendulum. Which graph shows such a relationship? Period

Period

length

length

A

B

Period

Period

length length

C

D

3. An airplane flew due north for 400 miles, and then it flew due east for 300 miles. At that point how far was the plane from its starting point?

A. 450 miles B. 500 miles C. 600 miles D. 700 miles

4. What is another way to express the area of a rectangle that is 1 square centimeter in area?

A. 0.1 millimeter2 B. 1 millimeter2 C. 10 millimeter2 D. 100 millimeter2

5. What are the roots of the equation y = x2 + 3x – 10 ?

A. 2 and -5 B. 1 and 3 C. -3 and 10 D. 1, 3, and -10

6. The rates at a drive-in movie theatre are $5 per car plus $3 per person. Last night c cars and p people attended the movies. Which of the following expressions gives the total amount, in dollars, collected in fees last night?

A. 5c + p B. 5c + 3p C. 5(c + p) D. 5(c + 3 p)

7. Which of the following represents the intersection of the set of all even integers with the set of all prime numbers?

A. 0 B. 1, 2 C. 2 D. The null set

8. Noelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1.5 times her regular pay. How much does Noelle earn for a week in which she works 42 hours?

A. $126.00 B. $315.00 C. $322.50 D. $378.50

9. If r = 9, b = 5, and g = − 6, what does (r + b − g )(b + g ) equal? A. -20 B. -8 C. 8 D. 20

10. Marlon is bowling in a tournament and has the highest average after 5 games with scores of 210, 225, 254, 231, and 280. In order to maintain this exact average, what must be Marlon’s score for his 6th game?

A. 210 B. 225 C. 240 D. 245

11. What is the percent error in a measurement stated as 2.3 cm when the actual length is really 2 cm?

A. 10% B. 13% C. 15% D. 30%

12. What is (x2 – x -12) divided by (x + 3) ?

A. (x – 4) B. (x + 7) C. (x + 6) D. (x – 3)

13. In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball? A. 4 B. 5 C. 6 D. 7

14. Jerome, Shantay, and Beth shared a submarine sandwich. Jerome ate half the sandwich, Shantay ate a third of the sandwich, and Beth ate the rest. What is the ratio of Jerome’s share to Shantay’s share to Beth’s share? A. 1:3:2 B. 2:3:1 C. 2:1:3 D. 3:2:1

15. What is the sum of the first four terms of an arithmetic sequence if the fifth term is 10 and the seventh term is 14?

A. 6 B. 8 C. 18 D. 20

16. A rectangle has an area equal to 20 square feet and a perimeter equal to 18 feet. What is the shortest side of the rectangle equal to in feet?

A. 2 B. 4 C. 5 D. 8

17. What is the least common multiple of 70, 60, and 50? A. 60 B. 180 C. 210 D. 2100

18. What is the equation of a line that perpendicularly intersects the graph of the equation y = mx + b.

A. y =

1 x+b m

B. y = -mx + b C. y = -

1 x+b m

D. y = mx - b

19. Data for the measured position p of a cart at time t is given in the table below. t

0

1

2

3

4

5

d

14

23

30

38

45

53

Which equation below best represents this data? A. d = 14t + 8 B. d = 8t + 14 C. d = t(8 + 14) D. d = 8t2 + 14

20. The formula for finding the value v of P dollars invested for t years at an P interest rate of i% is given by the formula v = (1 + 0.01i)n What is the formula for P in terms of v, t, and i ? A. P = v - 0.01i n

  v B. P =    1 + 0.01i  C.

P=

n

v (1 - 0.01i) n

D. P = v (1 + 0.0i) n

21. If x and y are real numbers such that x > 0 and y < 0, then which of the following inequalities must be true?

A.

x>y

B. x2 > y2 C.

x >0 y

D.

x < 0 y

22. What is the surface area of a cube having a volume of 27 cm3 ?

A. 9 cm2 B. 18 cm2 C. 27 cm2 D. 54 cm2

23. A very large gumball machine is completely filled with equal numbers of red, white, and green gumballs. If two gumballs are randomly removed from the gumball machine, what is the probability that both of the gumballs are green?

A. 1/3 B. 1/6 C. 1/9 D. 1/27

24. T

Line segment QR intersects line segment ST at the center point of the circle. The measure of angle QAS is 40°. What is the Q degree measure of minor arc TR ? A

A. 40° B. 60° C. 80° D. 320°

S

R

25. Line segment TS intersects line segment QR at the center point of the circle. The measure of angle QTA is 20°. What is the degree measure of minor arc QS ?

T

Q A

A. 20° B. 40° C. 60° D. 320°

S

R

26. What is the degree of rotation symmetry for the design shown here?

A. 36 B. 72 C. π D. 2π

27. The design for the new club emblem is shown here. The outer circle has a radius twice that of the inner circle, and it is made from a material that is twice as expensive as the material used for the inner circle. The total cost of the emblem was $21. How much did it cost to make just the outer circle of the emblem?

A. $10 B. $12 C. $15 D. $18

28.

F(x) 5# 4#

What are the sign and power of the highest order of x in the polynomial that has been graphed here?

3# 2# 1#

x

0# !3#

!2#

!1#

!1# !2# !3# !4# !5#

A. x2 B. -x2 C. x3 D. -x3

0#

1#

2#

3#

29. Which mathematical equation below is equivalent to the verbal expression, “The square of x is 14 less than the product of 15 and x.”

A. x2 = 15x - 14 B. x2 -14 = 15x C. x2 -15x = 14 D. x2 + 15x = 14

30.

45°

Angle x is equal to

x

80°

A. 35° B. 45° C. 55° D. 80°

31. Four points (A, B, C, and D) are uniformly positioned around the circumference of a circle. D is 5 positions counterclockwise from A. B is two positions clockwise from A. C is 5 positions counterclockwise from B. What is the order of the points, going clockwise around the circle and starting with A? A. A, B, C, D B. A, B, D, C C. A, D, C, B D. A, C, B, D

32. Which graph below could represent a function that is quadratic in x?

f(x)

f(x)

x

x

A

B f(x)

f(x)

x

C

x

D

33. A sequence of numbers Sn is given by Sn = n2, where n are the positive integers. Which of the following expressions for Sn is true?

A. Sn =

n

B. Sn – Sn-1 = 2 C. Sn + Sn-1 = Sn+1 D. Sn – Sn-1 = 2n - 1

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

C D B C A B C C B C C A B D D B

17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

D C B D D D C A B B D C A C D A

33. D