There are 28 problems.

Problems #1-6 are 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.

 

 

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: | 7 – 5x | ≤ 3.
A.
B.
C.
D. 1. ______ [4/5, 2]
(–∞, 4/5]
(–∞,4/5] ∪ [2, ∞)
(–∞, 2] ∪ [4/5, ∞) 2. Which of the following polynomials has a graph which exhibits the end behavior of
downward to the left and upward to the right?
2. _______ A.
B.
C.
D. f (x) = –2x3 + 6x2 – x
f (x) = –5x4 – 5x3 – 1
f (x) = 4x5 + 2x + 6
f (x) = 3x6 + 3x2 – x vvvv 3. Express as an equivalent expression: 9 log x – log (y + 3) + log 1
A. 9x +1 log y+3 B. log ( 9 x − y − 2 ) C. log x9
log ( y + 3) D. x9 log y +3 3. ______ Page 1 of 7 MATH 115 Precalculus
4. Determine the interval(s) on which the function is decreasing. A. ( −2.5, 1) B. ( −∞, −1) and ( 3, ∞ ) C. ( −1, 3) D. ( −∞, −2.5) and (1, 4.5) 5. Which of the functions corresponds to the graph? Summer
ummer, 2016, V1.3
4. ______ 5. ______ A. f ( x ) = e− x + 2
B. f ( x ) = e x + 2
C. f ( x ) = −e x + 2
D. f ( x ) = e− x + 1 Page 2 of 7 MATH 115 Precalculus Summer, 2016, V1.3 6. Which of the functions corresponds to the graph? 6. ______ A. f (x) = 3 – cos x
B. f (x) = 2 + cos x
C. f (x) = 2(1 – cos x)
D. f (x) = 2 – sin x
SHORT ANSWER:
7. Points (–6, 5) and (4, 3) are endpoints of the diameter of a circle.
(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________ (b) What is the center of the circle? Answer: ____________ (c) What is the equation of the circle? Answer: ___________________________ 8. Find the value of the logarithm: log % & ' '(% ). Answer: ____________ 9. A salesperson earns a base salary of $1,650 per month and a commission of 8.2% on the
amount of sales. If the salesperson has a paycheck of $4,725 for one month, what was the
amount of sales for the month?
Answer: _____________ Page 3 of 7 MATH 115 Precalculus Summer, 2016, V1.3 10. A bowl of soup at 200° F. is placed in a room of constant temperature of 60° F. The
temperature T of the soup t minutes after it is placed in the room is given by T(t) = 60 + 140 e – 0.075 t Find the temperature of the soup 30 minutes after it is placed in the room. (Round to the nearest
degree.) Answer: ________
1 11. Given the function *+,- = 7 − 4 ,, find a formula for the inverse function.
Answer: __________________ 12. (a) State the reference angle associated with 300°. Answer: ________ (b) Convert 300° to radians. Leave the answer in terms of π. Answer: ________ 13. Given y = 6 sin(8x – π), state the
(a) period Answer: ________ (b) phase shift Answer: ________ 14. Solve the trigonometric equation (sin x)(2sin x + 1) = 0 in the interval [0, 360°).
Answer: _________________ Find the exact value of arcsin &sin 9: (b) Find the exact value of arccos &sin 9: 15. (a) ; ( ) Answer: ________ ) Answer: ________ 2 16. For the parabola given by (x + 5) = –8(y – 4), find the following:
(a) direction parabola opens (to the left, right, up, or down) Answer: ___________ (b) vertex Answer: ___________ (c) focus Answer: ___________
Page 4 of 7 MATH 115 Precalculus
17. Let f ( x ) = x
2 Summer, 2016, V1.3
. x −4
(a) State the domain. Answer: _________________ (b) State the horizontal asymptote. Answer: _________________ (c) State the vertical asymptote(s). Answer: _________________ (d) Which of the following represents the graph of f ( x ) = x
x2 − 4 GRAPH A. GRAPH B. GRAPH C. GRAPH D. ? Answer: ______________ Page 5 of 7 MATH 115 Precalculus Summer, 2016, V1.3 SHORT ANSWER, with work required to be shown, as indicated. 18. Find the equation for a line which passes through the points (–8, 9) and (–6, 3). Write the
equation in slope-intercept form. Show work. 2 19. Find the exact solutions and simplify as much as possible: 5x + 1 = 8x. Show work. 20. Let f (x) = 4x2 – 6 and g(x) = x – 3.
(a) Find the composite function ( f o g )( x) and simplify. Show work.
(b) Find ( f o g )( −2) . Show work. 21. A projectile is launched from a platform 12 feet high with an initial velocity of 80 feet per second,
2
The height h of the projectile at t seconds after launch is given by h = –16t + 80t + 12 feet.
(a) How many seconds after launch does the projectile attain maximum height?
(b) What is the maximum height? 22. Solve: Show work. Show work. x+7
24
+ 2
= 0 . Show work.
x+3 x −9 23. Suppose that sin θ = 5/13 and that θ is a Quadrant II angle.
(a) Find the exact value of cos θ. Show work. (b) Find the exact value of sin 2θ. Show work. 2 24. Prove the identity (sin x + cos x) = 1 + sin(2x) Page 6 of 7 MATH 115 Precalculus Summer, 2016, V1.3 25. From a point 63 feet from the base of a redwood tree, the angle of elevation to the top of the
tree is 51.8°. Find the height of the tree to the nearest foot. Show work.
(sketch is not to scale) 26. For the triangle ABC, we are given that A = 48°, B = 62°, and c = 35.0. Find the length of side b, rounded to the nearest tenth. Show work. => = 〈9, –3〉 and ?
=> = 〈4, 12〉.
27. Let <
(b) => ∙ ?
=>. Show work.
Calculate the dot product < (c) => and ?
=>. Round the result to the nearest degree. Show work.
Determine the angle between < 28. An ellipse has the equation +A B (-C
; + +E F G-C
9H =1 (a) Is the major axis horizontal or vertical?
(b) Find the exact values of the foci of the ellipse. Show work. Page 7 of 7

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