Math 115 final exam fall, 2016
MATH 115 FINAL EXAMINATION
Fall, 2016, V4.3
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. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 28 problems.
Problems #1–6 are Multiple Choice.
Problems #7–17 are Short Answer. (Work not required to be shown)
Problems #18–28 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Solve, and express the answer in interval notation: | 3 – 8x | ≤ 21.
A. (–∞, −9/4] ∪ [3, ∞)
B. (–∞, –9/4]
C. [–9/4, 3]
D. [–9/4, ∞)
1. ______
2. Which of the following polynomials has a graph which exhibits the end behavior of
downward to the left and downward to the right?
A. f (x) = –6x5– x3– x2– 5
B. f (x) = 8x3+ 6x2– x + 3
2. _______
C.
D.
f (x) = 5x6+ 7x2+ x
f (x) = –3x4 + 9x2– x – 1
3. Express as an equivalent expression: 8 log y + log 1 – log (x – 3)
3. ________
A.
log
y
8
B.
y +
C.
log
x
(
)
-13D.
-13log 8y + 4 − x
MATH 115 Precalculus
4. Determine the interval(s) on which the function is increasing.
A. (− 4 / 3, 1)
B. (−1,1) and (3,∞)
Fall, 2016, V4.3
4. ______
C. (
)
11/ 3, ∞)
C. f ( x) = −ex
D. ( ) x 1
-40f x = e− +
5. _____
Page 2 of 7
MATH 115 Precalculus
6. Which of the functions corresponds to the graph?
A. f (x) = cos(2x) + 2
B. f (x) = 3 – sin x
C. f (x) = sin x + 3
D. f (x) = 2 cos x + 1
SHORT ANSWER:
7. Points (–7, 2) and (5, 6) are endpoints of the diameter of a circle.
Fall, 2016, V4.3
6. ______
(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________
(b) What is the center of the circle?
(c) What is the equation of the circle?
Answer: ____________
Answer: ___________________________
8. Find the value of the logarithm: log
Answer: ____________
9. Bill, a resident of Metropolis, pays Metropolis an annual tax of $55 plus 1.8% of his annual
income. If Bill paid $1,441 in tax, what was Bill’s income?
Answer: _____________
Page 3 of 7
MATH 115 Precalculus
Fall, 2016, V4.3
10. A can of soda at 71° F. is placed in a refrigerator that maintains a constant temperature of 39°
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 39 + 32 e – 0.058 t
Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the
nearest tenth of a degree.)
Answer: ________
11. Given the function
= 3 − 18 , find a formula for the inverse function.
Answer: __________________
12. (a) State the reference angle associated with 300°.
(b) Convert 300° to radians. Leave the answer in terms of ð.
13. Given y = 9 sin(8x – ð), state the
(a) period
(b) phase shift
Answer: ________
Answer: ________
Answer: ________
Answer: ________
14. Solve the trigonometric equation (cos x)(2cos x + 1) = 0 in the interval [0, 360°).
Answer: _________________
15. (a) Find the exact value of arccos sin
(b) Find the exact value of arcsin tan
16. For the parabola given by (y + 5)2= 8(x – 2), find the following:
(a) direction parabola opens (to the left, right, up, or down)
(b) vertex
(c) focus
Answer: ________
Answer: ________
Answer: ___________
Answer: ___________
Answer: ___________
Page 4 of 7
3x + 1
Fall, 2016, V4.3
17. Let
f (x) =
x − 2
(a) State the domain.
(b) State the vertical asymptote(s).
(c) State the horizontal asymptote.
(d) Which of the following represents the graph of
f x
( )
=
3x + 1
x − 2
Answer: _________________
Answer: _________________
Answer: _________________
Answer: ______________
GRAPH A.
GRAPH C.
GRAPH B.
GRAPH D.
MATH 115 Precalculus
SHORT ANSWER, with work required to be shown, as indicated.
Fall, 2016, V4.3
(a) Find the composite function ( f o g)(x) and simplify. Show work.
(b) Find (
f o g − . Show work.
21. A projectile is launched from a platform 15 feet high with an initial velocity of 48 feet per second.
The height h of the projectile at t seconds after launch is given by h = –16t2 + 48t + 15 feet.
(a) How many seconds after launch does the projectile attain maximum height? Show work.
(b) What is the maximum height? Show work.
22. Solve:
x − 6
x − 4
+
16
x2−16
= 0 . Show work.
23. Suppose that cos è = 5/13 and that è is a Quadrant IV angle.
(a) Find the exact value of sin è.
(b) Find the exact value of sin(2è ).
Show work.
Show work.
24. Prove the identity (sin x + cos x)2− sin(2x) = 1
MATH 115 Precalculus
Fall, 2016, V4.3
25. From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the
tree is 52.3°. Find the height of the tree to the nearest tenth of a foot. Show work.
(sketch is not to scale)
26. For the triangle ABC, we are given that A = 46°, B = 64°, and c = 35.0.
Find the length of side a, rounded to the nearest tenth. Show work.
27. Let = 〈10, –5〉 and = 〈2, 4〉.
(b) Calculate the dot product ∙ . Show work.
(c) Determine the angle between and . Round the result to the nearest degree. Show work.
28. An ellipse has the equation
+
= 1
(a) Is the major axis horizontal or vertical?
(b) Find the exact values of the foci of the ellipse. Show work.
