Pre-Calculus homework
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MATH115Fall19Izmirli.pdf
MATH 115 Precalculus Fall, 2019, V1.4
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MATH 115 FINAL EXAMINATION
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 | 9 – 7x | 12 and write interval notation for the solution set. 1. _______
A. [−3, 3
7 ]
B. [− 3
7 , 3]
C. (−∞, − 3
7 ]
D. (−∞, − 3
7 ] ∪ [3, ∞)
2. Which of the following polynomials has a graph which exhibits the end behavior of upward to
the left and downward to the right? 2. _______
A. f (x) = 4x3 + 2x + 6
B. f (x) = 5x4 + 3x3 – x
C. f (x) = –6x5 + 6x3 – x
D. f (x) = –3x6 – 5x3 – 1
3. Write as an equivalent expression: log (x2 + 3) – 4 log y + log 1 3. ______
A. 6 log( )
log(4 )
x
y
B. 2
4
3 1 log
x
y
+
C. 2
4
3 log
x
y
+
D. ( )2log 4 4x y+ −
vvvv
MATH 115 Precalculus Fall, 2019, V1.4
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4. Determine the interval(s) on which the function is increasing. 4. ______
A. (1, 5)
B. (– 0.5, 3)
C. (–2, 2)
D. ( )5.0, −− and (5, 6.5)
5. Which of the functions corresponds to the graph? 5. ______
A. ( ) 2xf x e= −
B. ( ) xf x e= −
C. ( ) 1xf x e−= +
D. ( ) 1xf x e−= −
MATH 115 Precalculus Fall, 2019, V1.4
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6. Which of the functions corresponds to the graph? 6. ______
A. f (x) = 2 sin x + 1
B. f (x) = sin(2x) + 1
C. f (x) = 2 – cos x
D. f (x) = 2 cos x + 1
SHORT ANSWER:
7. Points (–5, 7) and (1, 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: log3 ( 1
81 ). Answer: ____________
9. Mark, a resident of Metropolis, pays Metropolis an annual tax of $70 plus 1.7% of his annual
income. If Mark paid $1,141 in tax, what was Mark’s income?
Answer: _____________
MATH 115 Precalculus Fall, 2019, V1.4
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10. A bowl of soup at 180 F. is left in a room of temperature 70 F to cool.
After t minutes, the temperature T of the soup is given by T(t) = 70 + 110e – 0.075 t
Find the temperature of the soup 10 minutes after it is left in the room. (Round to the nearest degree.)
Answer: ________
11. Given the function 𝑓(𝑥) = 1
8 𝑥 − 5, find a formula for the inverse function.
Answer: __________________
12. (a) State the reference angle associated with 315°. Answer: ________
(b) Convert 315° to radians. Leave the answer in terms of . Answer: ________
13. Given y = 4 sin(6x – ), state the
(a) period Answer: ________
(b) phase shift 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 3𝜋
2 ) Answer: ________
(b) Find the exact value of arcsin (tan 5𝜋
4 ) Answer: ________
16. For the parabola given by (x + 3)2 = 8(y – 1), find the following:
(a) direction parabola opens (to the left, right, up, or down) Answer: ___________
(b) vertex Answer: ___________
(c) focus Answer: ___________
MATH 115 Precalculus Fall, 2019, V1.4
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17. Let 2
2
3 3 ( )
4
x f x
x
+ =
− .
(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
2
2
3 3 ( )
4
x f x
x
+ =
− ? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
MATH 115 Precalculus Fall, 2019, V1.4
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SHORT ANSWER, with work required to be shown, as indicated.
18. Find the equation for a line which passes through the points (–3, 17) and (9, 5). Write the
equation in slope-intercept form. Show work.
19. Find the exact solutions and simplify as much as possible: 2x2 + 9 = 12x. Show work.
20. Let f (x) = 3x2 + 9 and g(x) = x – 4.
(a) Find the composite function ))(( xgf and simplify. Show work.
(b) Find )1)(( −gf . Show work.
21. A projectile is launched from a platform 15 feet high with an initial velocity of 72 feet per second,
The height h of the projectile at t seconds after launch is given by h = –16t2 + 72t + 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: 2
0 11 56
4 16
x
x x =
+ +
+ − . Show work.
23. Suppose that sin = 1/8 and that is a Quadrant II angle.
(a) Find the exact value of cos . Show work.
(b) Find the exact value of sin 2. Show work.
24. Prove the identity (sin x + cos x)2 − 1 = sin 2x
MATH 115 Precalculus Fall, 2019, V1.4
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25. From a point 42 feet from the base of a redwood tree, the angle of elevation to the top of the
tree is 55.7°. 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 = 40, B = 63, and c = 38.0.
Find the length of side b, rounded to the nearest hundredth. Show work.
27. Let u = 5, 10 and v = –12, 6.
(b) Calculate the dot product u • v. Show work.
(c) Determine the angle between u and v. Round the result to the nearest degree. Show work.
28. An ellipse has the equation (𝑥 − 2)2
9 +
(𝑦 − 4)2
36 = 1
(a) Is the major axis horizontal or vertical?
(b) Find the exact values of the foci of the ellipse. Show work.
