Math 115 (Precalculus) Final Exam

1. Some values for the variables x and y are presented in the table below. If x and y are in a linear relationship, what is the value of y when x = 9?

x 1 3 9 12 y 15 11 −7

(a) y = 0 (b) y = 7

(c) y = 1 (d) y = −1 (e) y = −4

2. When we talk about a quantity associated with an object or a process, what are we talking about?

(a) Some part of the object or process

(b) Some attribute of the object or process that can be measured

(c) The number of objects present or the number of times the process is repeated

(d) The particular type of object or process being considered

(e) The broadest context in which the object or process makes sense

3. Suppose a box a crackers is sitting on the kitchen table. Which of the following would be a quantity associated with the box of crackers?

(a) The salt on the crackers

(b) The weight in ounces of the box

(c) Ten boxes of crackers

(d) The cardboard in the box

(e) The kitchen in which the table sits that supports the box

4. The slope of the line 3x− 4y + 8 = 0 is

(a) m = −4 (b) m = 3 (c) m = 3/4 (d) m = 4/3

(e) m = 8

5. Suppose the radian measure for an angle is θ = −6π/5. What is the degree measure for this angle?

(a) a = 150◦ (b) a = −216◦

(c) a = 36◦ (d) a = −150◦

(e) a = 216◦

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Name:____________________________________________________

Problems 6 and 7 refer to the following situation. You decide to rent a car from a company that charges a $25.50 rental fee plus $0.05 per mile for every mile the car is driven.

6. Which of the following statements are true?

(a) The rate charged per mile driven is a fixed quantity (b) The rental fee is a fixed quantity (c) The cost of renting the car is a fixed quantity (d) Both (a) and (b) are true. (e) Both (b) and (c) are true.

7. Let d be the miles driven in the rental car, and let c be the cost in dollars of renting the car. Which of the following formulas is correct?.

(a) 4d = .054c (b) d = 25.50 + .05c

(c) 4c 4d

= .05 (d) Both (a) and (b) are true.

(e) Both (b) and (c) are true.

8. A particular cookie recipe calls for one cup of flour to start, along with an additional one-half cup of flour for every cup of sugar. Let x represent the amount of flour used (measured in cups) and let y be the amount of sugar used (measured in cups). Which of the following statements is true?

(a) x and y are proportional. (b) 4x and 4y are proportional. (c) The y-intercept is the point (0, 0). (d) Three cups of sugar correspond to 1.5 cups of flour used.

(e) All of the above statements are true.

Problems 9 and10 refer to the following situation. Cole is standing on a level playing field when he throws a ball to Janice. The height H of the ball in feet above the ground s seconds after Cole throws it is given by the function

H = f(s) = 5.5 − 2(s− 1)2

9. The maximum height of the ball above the ground will be

(a) H = 2 feet (b) H = 5.5 feet

(c) H = 3.5 feet (d) H = 7.5 feet

(e) H = 10 feet

10. Janice does not catch the ball. How many seconds will pass before the ball hits the ground?

(a) t = 1 seconds (b) t ≈ 2.5 seconds (c) t ≈ 2.66 seconds (d) t = 3 seconds (e) t ≈ 1.87 seconds

11. Suppose that A is the degree measure for an angle. Which of the following expressions must be equal to sin (A + 720◦)?

(a) sin(−A) (b) −cos(A) (c) −sin(A) (d) cos(A) (e) sin(A)

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12. Suppose that b is the radian or degree measure of an angle. As along as all factors are defined, which of the following expressions is equal to

cot(b) cos(b)

csc(b)

(a) cos2(b) (b) 1

(c) sin2(b) (d) tan(b)

(e) cos3(b)

sin(b)

13. Carlton is drinking a glass of water. When the glass contains 18 mL of water, he places it under the water tap and starts refilling. If 4 mL of water enters flows into the glass every 2.5 seconds, how much water will be in the glass 8 seconds after he started refilling?

(a) 12.8 mL (b) 30.8 mL

(c) 22.5 mL (d) 10 mL

(e) 38 mL

14. The implied domain of the function y = f(x) = ln(2x− 1) is the set of

(a) all real numbers (b) all real numbers except x = 0

(c) all real numbers x > 0 (d) all real numbers x > 1/2

(e) all real numbers x < 1

15. Let a and b be distinct real numbers. Which of the following statements is true about the rational function

y = f(x) = 3(x− b)

(x−a)(x− b)

(a) The function f has a vertical asymptote only at x = a.

(b) The function f has a vertical asymptote only at x = b.

(c) The function f has a vertical asymptote at x = a and at x = b.

(d) The function f has no vertical asymptotes.

(e) The function f has an x-intercept at x = b.

16. Let u and v be the values of two varying quantities and suppose that u changes at a constant rate of −4.4 with respect to v. Which of the following statements is true? (a) v = −4.4r (b) 4v = −4.44u (c) u = −4.4v (d) 4u = −4.44v

(e) u = v − 4.4

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17. Sheryl is riding on a teeter-totter. Suppose θ is the measure of the angle between the ground and Sheryl’s highest point on the teeter-totter, and suppose the bar between Sheryl and the pivot has slope m = 2.8 when Sheryl is at the highest point. Which of the following statements is true?

(a) tan(θ) = 2.8 (b) tan(2.8) = θ

(c) sin(θ) = −2.8 (d) cos(θ) = −1

(e) cos(θ) = 2.8

18. At practice one afternoon, Jan ran seven laps on a one-half mile track at a constant speed of three miles per hour. Which of the following is a constant quantity in this situation?

(a) the speed in miles per hour that Jan ran (b) the total number of laps that Jan ran

(c) the total time that Jan ran (d) the total hours required to run one lap

(e) all of the above

19. Suppose that a > 0. If we know that b = ac, then we also know that

(a) b = loga(c) (b) c = logb(a)

(c) a = logc(b) (d) b = logc(a)

(e) c = loga(b)

20. Let u be the radian or degree measure of an angle. Assuming all factors are defined, which of the following expressions is equal to

sin(u)

csc(u) +

1

sec2(u) + tan2(u)

(a) cot(u) (b) 2 tan2(u)

(c) 2 csc(u) + tan(u) (d) tan2(u)

(e) sec2(u)

21. What is the inverse function for y = f(x) = 1 2

(3x + 5)?

(a) x = g(y) = 1 3 (2y − 5) (b) y = g(x) =

2

3x + 5

(c) y = g(x) = 5 − 2x

3 (d) x = g(y) = 1

2 (3y + 5)

(e) x = g(y) = 5 −y

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22. Consider the triangle shown in the diagram below. To the nearest tenth, what is the length of Side a?

(a) a ≈ 29.4 inches (b) a ≈ 69.6 inches (c) a ≈ 83.0 inches (d) a ≈ 37.9 inches (e) a ≈ 24.6 inches

23. Annabeth needs to know the dimensions of a triangular piece of property whose boundaries are shown below. She can measure two sides directly, but unfortunately, one side lies in a lake and cannot be reached. To the nearest tenth of a foot, what is the length of the unknown side?

(a) c ≈ 108.8 feet (b) c ≈ 149.8 feet (c) c ≈ 163.0 feet (d) c ≈ 100.0 feet (e) c ≈ 130.9 feet

24. Nancy starts eating a bowl of soup at noon, and it takes her twenty minutes to finish. Which of the following is a varying quantity in this situation?

(a) the bowl (b) the weight of soup in the bowl in ounces since noon

(c) the time (d) the total time in minutes that passes while Nancy eats

(e) Nancy

25. As an ice cube melts, its mass in grams changes at a constant rate with respect to the number of minutes since it began melting Five minutes after the ice cube began to melt, its mass was ten grams. Seven minutes after the ice cube began to melt, its mass was seven grams. What was the constant rate of change?

(a) 2 grams per minute (b) −1 gram per minute (c) −1.5 grams per minute (d) 0.7143 grams per minute (e) 1.4 grams per minute

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Name __________________________________________

Date___________________

Please sign (or type) your name below the following honor statement:

I have completed this final examination myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this final examination.