Math III Final Exam Review Packet
Name______________________
This review packet is due on Wednesday, May 28th. It is optional, but will be graded for accuracy. It will count as a 50
point test grade.
____
1. The formula for the area A of a square with side s is A = s . Write an expression to represent the area of the
square.
a. (x
____
3)
b. (x
3)
c. x
d.
2. Graph the function f(x) = | x | + 4. Identify its domain and range.
y
a.
–16 –12 –8
y
c.
16
12
12
8
8
4
4
–4
–4
4
8
–12 –8
x
12
–4
–4
–8
–8
–12
–12
4
8
12
x
–16
The domain of the function is all real
numbers. The range of the function is
.
The domain of the function is all real
numbers. The range of the function is
.
y
b.
d.
12
y
12
8
8
4
4
–12 –8
–4
–4
4
8
12
x
–8
–12 –8
–4
–4
4
8
x
–8
–12
–12
The domain of the function is all real
numbers. The range of the function is
.
____
3.
The domain of the function is all integers.
The range of the function is
.
What are the center and radius of a circle with the equation x2 + y2 + 10x – 20y = 19?
a. Center = (-5, 10), r = 12
c. Center = (5, 10) r = 12
b. Center = (25, -100), r = 12
d. Center = (0,0) r = 19
____
4. A study along on a highway measuring vehicle speeds to the nearest 5 miles per hour produced these results.
What was the median speed recorded?
Speed (mph)
40
45
50
55
60
65
Number of Vehicles
3
4
9
7
8
7
a. 50 mph
____
b. 55 mph
c. 56 mph
d. 57 mph
5. Which is the domain for the relationship graphed below?
y
4
2
–4
–2
2
4
x
–2
–4
a.
____
b.
c.
6. The graph of
d.
is the graph of
e.
transformed in what manner?
a. shifted horizontally 2 units to the right, compressed by a factor of
, and shifted up 6 units
b. shifted horizontally 2 units to the right, stretched by a factor of 3, and shifted up 2 units
c. shifted horizontally 2 units to the right, stretched by a factor of 3, and shifted up 6 units
d. shifted horizontally 2 units to the right, stretched by a factor of 3, and shifted down 6 units
e. shifted horizontally 6 units to the right, stretched by a factor of 3, and shifted down 2 units
____
____
____
7. Given
a. 4
, b is equal to
b. 1
c. 2
d. 3
8. If f(x) = abx, what values of b represent exponential decay?
a. b< 0
b. b = 0
c. 0 <b< 1
9. Simplify
a.
d. b> 1
.
b.
c.
d.
e. 60 mph
____ 10. If the equation for a set of population data over x years is y = 3(1.014)x, what does the value 1.014 in the
equation indicate about the population?
a. The population is declining by 1.014% per year.
b. The population is growing by 1.014% per year.
c. The population is declining by 1.4% per year.
d. The population is growing by 1.4% per year.
Use the following information to answer the question(s) below.
A company manufactures several sizes of ice cream cones. The different sizes all have a height of 5 inches,
1
but the radii of the cones vary. The formula for the volume of a cone is 𝑉 = 3𝜋𝑟 2 ℎ.
____ 11. Which equation gives the radius r as a function of the volume V?
a.
.
b.
c.
d.
____ 12. Students earn 9 points per question they answer correctly on the SAT with a 200 point curve. What function
would calculate a student’s score if she answered q questions correctly?
a. f(q) = 200q + 9
b. f(q) = 200q2 + 9q + 100
c. f(q) = 9q + 200
d. f(q) = 9q – 200
____ 13. For which angle is the tangent function undefined?
a. 00
b. 900
c. π rad
____ 14. Simplify
a.
d. 1800
.
b.
c. –10
d. 2
Use the following information to answer the question(s) below.
A Navy Seal in Afghanistan fires a rocket-propelled grenade (RPG). The rocket’s path models the function
f(t) = -16t2 + 435t + 4.3.
____ 15. Does the function have a minimum value, maximum value, or neither?
a. Minimum
b. Maximum
c. Neither
____ 16. What is the y-intercept of the function’s graph?
a. 0
b. -16
c. 435
d. 4.3
____ 17. Suppose you are graphing the function
equation(s) of the vertical asymptote(s) of the graph?
a. x = a
b. x = –b, x = c
, where a, b, and c are real numbers. Identify the
c. x = –a
d. x = b, x = –c
____ 18. Which equation is represented by the graph?
a.
b.
c.
d.
____ 19. If a> 0 in the equation y = ax3, what does this indicate about the shape of the graph?
a. The left and right behavior are both up.
b. The left and right behavior are both down.
c. The left behavior is down and the right behavior is up.
d. The left behavior is up and the right behavior is down.
Use the following information to answer the question(s) below.
In 2001, the population of North Carolina was estimated to be 8 million people. It was reported that the
annual growth rate from 2000 to 2001 was 1.7%. Assume that this annual growth rate in the population
continues.
____ 20. What function estimates the population N, in millions, as a function of time t, in years?
a. N(t) = 8(1.017t)
b. N(t) = 8(1.017)t
c. N(t) = 8(0.017t)
d. N(t) = 8(0.017)t
____ 21. Solve
for x.
b. 3, –2
a.
c. 1, 3
d. 1
____ 22. Four students scored 89, 75, 94, and 80 on their Algebra 2 Final. What does the fifth student have to score to
bring the mean score of the group to an 85?
a. 70
b. 75
c. 82
d. 87
____ 23. Simplify
a.
.
b.
c.
d.
____ 24. Solve 2ex+ 4 = 268 for x. Round to the nearest tenth.
a. –1.9
b. –1.2
c. 0.9
d. 2.3
____ 25. Find the x-intercept(s) of the graph of y = x3 – 7x + 6.
a. –3, 1, 2
b. –7
c. 0
d. 6
____ 26. Solve (q + 4)2 = 8.
a. –4 
b. –2 
c.
d. 60
____ 27. Alfonzo opened a savings account at a bank in Boone. He deposited $4,000 at 4.5% interest compounded
continuously. To the nearest cent, how much will he have in his savings account in 12 years if he makes no
additional deposits and no withdrawals?
a. $6,160.00
b. $6,783.53
c. $6,864.03
d. $7,342.71
____ 28. Simplify (4 + 7i) – (8 – 9i) – (7 + 6i).
a. –11 + 4i
b. –11 + 10i
d. –i
c. 25i
____ 29. For the quadratic equation ax2 + bx + c = 0, if b2 – 4ac < 0, then the equation has:
a. No roots
b. one real root
c. two real roots
d. two imaginary roots
____ 30. Solve x2 – 6x + 10 = 0 for x.
a. 6 i
b. 3  2i
c. 6  2i
d. 3 i
____ 31. Factor 3z4 – 147z2 completely.
a. 3z2(z – 7)2
b. 3z2(z + 7)2
c. 3z2(z – 7)(z + 7)
d. 3z2(z – 7)2(z + 7)2
____ 32. Which cubic function is represented by the table of values?
x
–2
–1
0
1
2
y
–45
–10
–1
0
11
a. y = –3x3 + 4x2 + 2x – 1 b. y = 3x3 – 4x2 + 2x – 1 c. y = 4x3 – 5x2 + 2x – 1 d. y = –4x3 + 5x2 + 2x – 1
1
____ 33. Identify the coordinates of the focus of the parabola 𝑦 = − (𝑥 − 1)2 + 3.
8
a. (1, 3)
b. (1, 5)
____ 34. Solve
d. (1, -1)
for x.
b. –3,
a.
____ 35. Solve
a. 1.5
c. (1, 1)
c. –2,
d. –2, 2
.
b. 10.5
c. 36
d. 45
c.
d.
____ 37. Simplify (3 – 2i)2 + (4 + i) – (2 – 7i).
a. 7 + 8i
b. 7 – 4i
c. 15 – 6i
d. 7 – 6i
____ 38. If f(x) = –2x3 + 3x2 – 5x + 7, evaluate f(3).
a. –89
b. –35
c. –8
d. 103
____ 36. Simplify
a.
.
b.
____ 39. Give the exact value for sin 45°.
a.
b.
c.
d.
____ 40. Right ∆𝑆𝑅𝑈 is shown to the right. Find SR.
a. 2√21
c. 2√15
b. √74
____ 41. If f(x) = 2x + 1, what is f -1 (x)
1
a. f -1 (x) = 2x - 1
b. f -1 (x) = − 2
d. √35
c. f
-1
(x) = x + 2
____ 42. What are the solutions to the equation tan 𝜃 = −√3?
𝜋 4𝜋
2𝜋 5𝜋
𝜋 7𝜋
a. ,
b. ,
c. ,
3
3
3
3
6
d. f
d.
6
-1
(x) =
𝑥−1
2
5𝜋 11𝜋
,
6
6
____ 43. Which of the following pairs of angles are coterminal?
5𝜋 15𝜋
7𝜋 17𝜋
5𝜋
𝜋
a. 6 , 6
b. 4 , 4
c. 6 , − 6
d.
7𝜋
9𝜋
,− 4
4
____ 44. Which of the following gives the equation of the trigonometric
function graphed to the right:
a. y = 3sin(2x)
b. y = 3sin(x) + 1
c. y = -3sin(2x) + 1
d. y = -3sin(2x)
____ 45. Give the period of the graph shown on the right:
a. 2
𝜋
2
b.
c. π
d.3
____ 46. If the tangent of an angle is negative and its cosine is positive, in which quadrant does the angle terminate?
a. I
b. II
c. III
d. IV
____ 47. Factor: 8𝑥 3 − 1
a. (2x – 1)(4x2 + 2x + 1)
b. (2x – 1)(2x + 1)
c. (2x – 1)(2x2 + 2x + 1)
____ 48. When inscribed in a certain circle, ∠𝐴𝐵𝐶 intercepts arcs as shown in
the diagram. What is the measure of ∠𝐵𝐴𝐶?
a. 90⁰
b. 70⁰
c. 40⁰
d. 20⁰
d. (x – 4)(x + 2)