Math 115 Final Examinationspring, 20151

Math 115 Final ExaminationSpring, 20151

Math 115PreCalculusName______

Final Examination: Spring, 2015Instructor ______

Answer Sheet

Instructions:

This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.

Record your answers and work in this document.

There are 28 problems.

Problems #1-6are multiple choice. Record your choice for each problem.

Problems #7-17 are short answer. Record your answer for each problem.

Problems #18-28 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.

You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.

MULTIPLE CHOICE. Record your answer choices.

1.B

2.D

3.C

4.C

5.D

6.A

SHORT ANSWER. Record your answers below.

7. (a)

(b) (-2, 5)

(c)

8. -6

9.$19,300

10.55.1°F

11.

12. (a) 15°

(b)

13. (a) π/4

(b) π/8

14.0, 180°, 210°, 330°

15. (a)

(b)π

16. (a) right

(b) (7, -5)

17. (a)(-∞, 2) U (2, ∞)

(b)y = 3

(d)Graph B

SHORT ANSWER with Work Shown. Record your answers and work.

Problem Number / Solution
18 / Answer:
Work:
Slope = (9-7)/(-5-3) = 2/-8 = -1/4
Equation will be

19 / Answer:
Work:

Here a = 8, b = -20, c = 13
Use quadratic formula

20 / Answers:
(a)
(b)41
Work for both parts:
(a)

(b)
Put x = -1 in

21 / Answers:
(a) 3 seconds
(b) 159 feet
Work for both parts:
(a)
Height will be maximum at t = -b/2a = -96/(2(-16)) = 3 seconds
After 3 seconds, height will be maximum.
(b)
Maximum height = -16*32+96*3+15 = -144+288+15 = 159 feet
22 / Answer: x = -3
Work:

This gives

The givenequation is undefined x = 4
Solution is x = -3
23 / Answers:
(a) sinθ = -3/5
(b) sin 2θ = -24/25
Work for both parts:
(a)

Sine of a angle is negative in quadrant IV.
sinθ = -3/5
(b)
sin 2θ = 2sinθ cos θ = 2(-3/5)(4/5) = -24/25
24 / Proof:

Hence proved.
25 / Answer: 75.6 ft
Work:
Let height of the tree be h

26 / Answer: 34.75
Work:
Angle C = 180°-40°-63° = 77°
Apply sine law

27 / Answers:
(a)0
(b) 90°
Work for both parts:
(a)
u*v = 5*6+10(-3) = 0
(b)
Since u*v = 0 so the vectors are perpendicular.
Angle = 90°
28 / Answers:
(a)Horizontal
(b) (-1-√33, 4) and (-1+√33, 4)
Work for part (b):
Center = (-1, 4)
c2 = a2-b2 = 49-16 = 33
c = √33
Foci : (-1-√33, 4) and (-1+√33, 4)