Math III Exam Review
N-RN.3 (one question)
1. If 𝑃 and 𝑆 are rational numbers and 𝑅 and 𝑄 are irrational numbers, which of these statements is true?
A. The product of 𝑅 and 𝑄 is always an irrational number.
B. The product of 𝑃 and 𝑆 is always a rational number.
C. The sum of 𝑅 and 𝑄 is always an irrational number.
D. The sum of 𝑃 and 𝑄 is always a rational number.
2. Which statement about rational and irrational numbers is always true?
A. Any irrational number added to any rational number is equal to a rational number.
B. Any irrational number added to any irrational number is equal to a rational number.
C. Any irrational number multiplied by any non-zero rational number is equal to a rational number.
D. Any irrational number multiplied by any non-zero rational number is equal to an irrational number.
3. Which expression results in an irrational number when simplified?
A. √121 + √16
1
B. √6 + 2
4
C. (5) √49
D. (√4)(√9)
4. The length of a rectangular prism is 4√3 units. The height is 3√6 units. If the volume is irrational, which could
be the measure of the width of the rectangular prism?
A. 2√50
B. 4√12
C. 5√8
D. 7√18
N-CN.2 (one question)
5. Which expressions is equivalent to (8 − 3𝑖) − (2 − 9𝑖)?
A. 6 + 6𝑖
B. 6 − 12𝑖
C. 11 + 78𝑖
D. 18 − 6𝑖
6. The circuit law, 𝑉 = 𝐼 ∙ 𝑍, is used in circuit analysis. If 𝐼 = 3𝑖 and 𝑍 = 7𝑖, what is the voltage, 𝑉?
A. 21
B. 21𝑖
C. −21
D. −21𝑖
7. What is the value of 8𝑖 − 2𝑖(3𝑖 + 4)?
A. −2 + 8𝑖
B. 10 + 8𝑖
C. −6
D. 6
8. Which of the following is equivalent to (3 − 2𝑖)2 ?
A. 5 − 12𝑖
B. 6 − 4𝑖
C. 9 + 4𝑖
D. 13 − 12𝑖
9. Which of the following expressions is equivalent to 3𝑖(−5 + 2𝑖) − 2(5 − 4𝑖)??
A. −16 − 23𝑖
B. −16 − 7𝑖
C. −10 − 𝑖
D. 21 −4i
10. Which value is equivalent to 𝑖 57 ?
A. −1
B. – 𝑖
C. 1
D. 𝑖
A-SSE.4 (one question)
11.
Which value is closest to the sum of the first 100 terms of the infinite series shown below?
1 1 1 1
1+ + + +
+⋯
2 4 8 16
A. 1
B. 2
C. 100
D. 200
12.
Which of these expressions can be used to find the sum of the first 12 terms of the series below?
1 1 1
−3 + 1 − + −
+⋯
3 9 27
1 12
A.
−3(1−( )
3
)
1
(1−3)
−1 12
B.
−3(1−( 3 )
1
(1+3)
1 12
C.
−2(1−(3)
)
1
(1+3)
−1 12
D.
)
−2(1−( 3 )
)
1
(1+3)
13.
What is the sum of the first 100 terms of the finite geometric series, if it exists?
120 + 60 + 30 + 15 + ⋯
A. The sum doesn’t exist.
B. 80
C. 240
D. 480
14.
Simplify ∑100
𝑘=1 3 (3)
2 𝑘−1
A.
B.
C.
D.
2
5
6
9
15. The Sanchez family wants to go on a vacation in August, and they begin saving in December. The Sanchez family
expects the vacation to cost $1,700. Each month they will deposit 5% more than the previous month. In December,
they deposit $100. How much will the Sanchez family have saved for their vacation after 9 months?
A. $147.75
B. $1,102.66
C. $2,864.73
D. $6,000.00
16. Bianca derived a formula to determine the value of ∑5𝑛=1 80(0.7)𝑛 . Bianca’s teacher asked her to derive the
formula again after increasing the common ratio by 1. Which expression represents the formula Bianca should have
written after increasing the common ratio by 1?
A.
B.
C.
D.
56(1−1.75 )
1−1.7
57(1−1.75 )
1−1.7
81(1−0.75 )
1−0.7
136(1−1.75 )
1−1.7
A-APR.2 (two questions)
17. Given the function 𝑃(𝑥) = 𝑥 3 + 4𝑥 2 + 𝑘𝑥 + 15, for what value of 𝑘 is (𝑥 + 3) a factor of 𝑃(𝑥)?
A. -26
B. -8
C. 8
D. 26
18. When the polynomial 4𝑥 4 − 13𝑥 2 − 2𝑥 + 1 is divided by the polynomial (𝑥 − 2), what is the remainder?
A. -23
B. 1
C. 9
D. 17
𝑝(𝑥)
19. If 𝑝(𝑥) = 𝑥 4 + 3𝑥 3 − 2𝑥 2 + 4 and 𝑞(𝑥) = 𝑥 + 1, then 𝑔(𝑥) is a polynomial that equals 𝑞(𝑥). What is the
remainder of 𝑔(𝑥) when it is divided by (𝑥 − 2)?
A. -4
B. 6
C. 12
D. 22
20. What is the remainder when 𝑝(𝑥) = 𝑥 3 − 7𝑥 − 6 is divided by (𝑥 − 4)?
A. -42
B. -18
C. 9
D. 30
A-APR.3 (one question)
21. Which of the following functions has the same zeros as the function 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 8?
A. 𝑔(𝑥) = 𝑥 − 4
B. 𝑔(𝑥) = 𝑥 2 − 5𝑥 + 6
C. 𝑔(𝑥) = 2𝑥 2 − 12𝑥 + 16
D. 𝑔(𝑥) = 𝑥 3 − 6𝑥 2 + 8𝑥
22. Which function, when graphed, would have the same zero(s) as the function below?
A.
B.
C.
D.
𝑓(𝑥) = 𝑥(𝑥 + 6)
𝑓(𝑥) = 𝑥(𝑥 − 6)
𝑓(𝑥) = (𝑥 + 6)2
𝑓(𝑥) = (𝑥 − 6)2
23. What are the zeros of the polynomial function below?
𝑓(𝑥) = (𝑥 2 − 16)(𝑥 + 5)𝑥
A. −5, −4, 0, 4
B. −4, 0, 4, 5
C. −5, −4, 4
D. −5, 0, 4
24. Which function has zeros −4, 2, and 0?
A. 𝑓(𝑥) = 𝑥 3 + 2𝑥 2 − 8𝑥
B. 𝑓(𝑥) = 𝑥 3 − 2𝑥 2 − 8𝑥
C. 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 8
D. 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 8
25. Let the function 𝑓(𝑥) = (𝑥 + 4)(𝑥 2 − 36)(𝑥 2 + 25). What are all the x-intercepts for the graph of 𝑓(𝑥)?
A. −4, 6
B. −6, −4, 6
C. −6, 4, 6
D. −6, −5, 4, 5, 6
26. Which of these functions best represents the graph shown below?
A.
B.
C.
D.
𝑓(𝑥) = (𝑥 + 2)(𝑥 − 3)
𝑓(𝑥) = (𝑥 + 3)(𝑥 − 2)
𝑓(𝑥) = 𝑥(𝑥 + 2)(𝑥 − 3)
𝑓(𝑥) = 𝑥(𝑥 + 3)(𝑥 − 2)
27. Which function best represents the graph below?
A.
B.
C.
D.
𝑔(𝑥) = 𝑥(𝑥 − 2)2 (𝑥 + 3)
𝑔(𝑥) = (𝑥 − 2)2 (𝑥 + 3)
𝑔(𝑥) = 𝑥(𝑥 − 2)(𝑥 + 3)
𝑔(𝑥) = (𝑥 − 2)(𝑥 + 3)
A-APR.6 (one question)
28. Which fraction is equal to
A.
B.
C.
D.
B.
C.
D.
𝑦 2 +19𝑦+18
in simplest form?
9
37
4
18
𝑦+4
𝑦+18
5𝑦+4
19𝑦+18
2𝑥 2 −18
29. What is
A.
𝑦 2 +5𝑦+4
2𝑥 2 +18
𝑥−3
reduced to lowest terms?
𝑥+3
𝑥+3
𝑥−3
(𝑥−3)(𝑥−3)
𝑥 2 +9
(𝑥−3)(𝑥+3)
𝑥 2 +9
30.What value must be substituted for 𝑘 so that
𝑥+4
𝑥 2 +7𝑥+𝑘
A. 3
B. 4
C. 12
D. 28
31. Which of the following is equivalent to
A. 𝑥
B. 𝑥 2
𝑥
C.
D.
𝑥−1
−6𝑥
𝑥−7
𝑥 3 −7𝑥 2
𝑥−7
?
can be reduced to
1
?
𝑥+3
A-REI.2 (one question)
32. Solve
5
2𝑥−2
=
15
𝑥 2 −1
A. 𝑥 = 1
B. 𝑥 = 5
𝑦
𝑦
33. Solve 5 + 2 = 7
A. 𝑥 = 2
34.
𝑥
Solve 𝑥−5
+
B. 𝑥 = 5
3
𝑥+2
=
C. 𝑥 = 1, 5
D. no solution
C. 𝑥 = 7
D. 𝑥 = 10
C. 𝑥 = −3, 5
D. no solution
7𝑥
(𝑥−5)(𝑥+2)
A. 𝑥 = −3
B. 𝑥 = 5
35. Solve √𝑥 − 3 + 5 = 𝑥
A. 𝑥 = 4
B. 𝑥 = 7
C. 𝑥 = 4, 7
D. no solution
36. Solve √3𝑥 + 7 = 𝑥 − 1
A. 𝑥 = −1
B. 𝑥 = 6
C. 𝑥 = −1, 6 D. no solution
37. After an accident, police can determine how fast a car was traveling before the driver put on his brakes by using
the equation 𝑠 = √30𝑓𝑑. 𝑠 represents the speed in miles per hour, 𝑓 represents the coefficient of friction, and
𝑑 represents the length of the skid in feet. Suppose the coefficient of friction is 0.6, if you were driving 35 miles
per hour, how many feet would it take for you to stop?
A. 30 feet
B. 47 feet
C. 68 feet
D. 81 feet
A-REI.4.a (one question)
38. What number should be added to both sides of the equation to complete the square? 𝑥 2 + 10𝑥 = 3
A. 5
B. 25
C. 50
D. 100
39. For what value of 𝑝 is the expression (𝑥 − 𝑝)2 + 5 is equivalent to the expression 𝑥 2 − 14𝑥 + 54?
A. -49
B. -7
C. 7
D. 49
40. What is the value of ℎ is needed to complete the square in order to find the vertex?
𝑥 2 + 2𝑥 + 7 = (𝑥 − ℎ)2 + 6
A. ℎ = 1, vertex (1, 6)
B. ℎ = 1, vertex (-1, 6)
C. ℎ = −1, vertex (1, 6)
D. ℎ = −1, vertex (-1, 6)
41. The equation 2𝑥 2 − 5𝑥 = −12 is rewritten in the form 2(𝑥 − 𝑝)2 + 𝑞 = 0. What is the value of 𝑞?
A.
167
16
B.
71
8
C.
25
8
D.
25
16
A-REI.4.b (one question)
42. Solve 5𝑥 2 − 180 = 0
A. 𝑥 = −6
B. 𝑥 = 6
C. 𝑥 = ±6
D. No real solution
43. What are the solutions of −4𝑥 2 − 72 = 0?
A. ±2𝑖√3
B. ±3𝑖√2
C. ±2√3
D. ±3√2
44. What are the values of 𝑥 that satisfy the equation 3 − 27𝑥 2 = 0?
A. 𝑥 = ±3
B.
𝑥=±
C.
1
𝑥=±
1
3
D. 𝑥 = ±2√6
9
45. What are the solutions of 𝑥 2 + 10𝑥 + 40 = 5?
A. 10 ± 𝑖√5
C. 5 ± 𝑖√10
B. −10 ± 𝑖√5
D. −5 ± 𝑖√10
46. Which equation has −3 ± 5𝑖 as its solutions?
A. 𝑥 2 + 6𝑥 = −34
C. 𝑥 2 + 6𝑥 = −14
B. 𝑥 2 + 3𝑥 = 4
D. 𝑥 2 + 3𝑥 = 2
A-REI.11 (one question)
47. For what values of 𝑥 does 𝑓(𝑥) = 𝑔(𝑥) if 𝑓(𝑥) = 𝑥 3 + 3𝑥 2 and 𝑔(𝑥) = 𝑥 + 3?
A. −3, −1, 1
B. −3, 1, 3
C. −1, 1, 3
D. −3, −1, 3
1
2
48. For what values of 𝑥 does 𝑓(𝑥) = 𝑔(𝑥) if 𝑓(𝑥) = |2𝑥 − 1| + 5 and 𝑔(𝑥) = − 𝑥 + 9?
A. −2, 10
B. −2, 8
C. −2, 2
D. 8, 10
3
49. For what values of 𝑥 does 𝑓(𝑥) = 𝑔(𝑥) if 𝑓(𝑥) = 2𝑥 and 𝑔(𝑥) = 2 𝑥 + 1?
A. 2, 4
B. 0, 1
C. 4, 1
D. 2, 0
50. At approximately what point or points do the graphs of 𝑓(𝑥) = 𝑥 2 − 3𝑥 − 8 and 𝑔(𝑥) = −6 + log 4 𝑥 intersect?
A. (3.6949, −5.4324)
B. (3.7824, −5.0403)
C. (0.0093, −8.0280)𝑎𝑛𝑑 (3.6949, −5.4324)
D. (0.0507, −8.1497)𝑎𝑛𝑑 (3.7824, −5.0403)
51. Since January 2010, a grape farmer has been growing red and green grapes. The number of red grape vines can
be modeled by the function 𝑓(𝑥) = 1,000(1.03)𝑥 , where 𝑥 is the number of years since January 2010. The
number of green grape vines can be modeled by the function 𝑔(𝑥) = 20𝑥 + 1,125, where 𝑥 is the number of
years since January 2010. In what year will the number of each type of grape vine be approximately equal?
A. 2013
B. 2015
C. 2017
D. 2019
1
52. Let 𝑓(𝑥) = 14𝑥 3 + 28𝑥 2 − 46𝑥 and 𝑔(𝑥) = 2𝑥 + 7. Which is the solution set to the equation 12 𝑓(𝑥) = 𝑔(𝑥)?
A.
B.
C.
D.
{−3, 0, 1}
{−3, −1, 2}
{−2, 1, 3}
{1, 5, 11}
F-IF.4 (two questions)
53.
54.
1
During which interval is the graph of 𝑓(𝑥) = − 2 𝑥 2 + 3𝑥 − 2.5 positive?
A. 1 < 𝑥 < 5
C. 𝑥 < 1 and 𝑥 > 5
B. 1 ≤ 𝑥 ≤ 5
D. 𝑥 ≤ 1 and 𝑥 ≥ 5
During which of following intervals is the graph of 𝑓(𝑥) = 3𝑥 3 + 10𝑥 2 − 𝑥 − 12 = 0 positive?
55.
56.
A. 𝑥 > 0
B. 𝑥 > 1
C. −3 < 𝑥 < −1
D. −2 < 𝑥 < 0
During which of the following intervals is the graph of 𝑓(𝑥) = 𝑥 3 + 𝑥 2 − 6𝑥 negative?
A. 𝑥 < −3
B. 𝑥 < 0
C. −3 < 𝑥 < 0
D. 𝑥 > 2
𝜋
What is the 𝑦-intercept of 𝑦 = sin(𝜃 + 2 )?
A. (0,0)
57.
B.
𝜋
2
<𝜃<
𝜋
2
3𝜋
2
60.
𝜋
D. (0, 2 )
1
C.
𝜋
2
<𝜃<𝜋
D. 𝜋 < 𝜃 < 2𝜋
Which function has a period of 4𝜋 and an amplitude of 8?
A. 𝑦 = −8 sin 8𝜃
59.
C. ( 2 , 0)
During which of the following intervals is the graph of 𝑦 = 2 cos 𝜃 increasing?
A. 0 < 𝜃 <
58.
𝜋
B. (0, 1)
1
2
C. 𝑦 = −8 sin 𝜃
B. 𝑦 = 8 sin 2𝜃
D. 𝑦 = 4 sin 8𝜃
Which of the following describes the end behavior of 2𝑥 4 − 20𝑥 2 + 18?
A. 𝑥 → −∞ 𝑓(𝑥) → +∞, 𝑥 → +∞ 𝑓(𝑥) → +∞
B. 𝑥 → −∞ 𝑓(𝑥) → +∞, 𝑥 → +∞ 𝑓(𝑥) → −∞
C. 𝑥 → −∞ 𝑓(𝑥) → −∞, 𝑥 → +∞ 𝑓(𝑥) → +∞
D. 𝑥 → −∞ 𝑓(𝑥) → −∞, 𝑥 → +∞ 𝑓(𝑥) → −∞
Which rational function is decreasing in the interval (−∞, 1) and is symmetric over the line 𝑥 = 1?
A.
C.
B.
D.
F-BF.3 (two questions)
61. The graph 𝑓(𝑥) = 3𝑥 is translated 2 units to the right and down 6 units resulting in 𝑔(𝑥). Which of the following
functions represents 𝑔(𝑥)?
A. 𝑔(𝑥) = 3(𝑥−2) − 6
C. 𝑔(𝑥) = 3(𝑥−6) − 2
B. 𝑔(𝑥) = 3(𝑥+2) − 6
D. 𝑔(𝑥) = 3(𝑥+6) − 2
62. The function 𝑓(𝑥) = 3(2)𝑥 models the growth of a bacteria culture. What is the change that occurs to the
graph if 𝑓(𝑥 + 𝑘) is graphed and 𝑘 < 0?
A. The graph moves up 𝑘 units
B. The graph moves down 𝑘 units
C. The graph moves left 𝑘 units
D. The graph moves right 𝑘 units
63. Which function is a phase shift of 𝑦 = sin 𝜃 by 5 units to the left?
A. 𝑦 = 5 sin 𝜃
B. 𝑦 = sin 𝜃 + 5
C. 𝑦 = sin(𝜃 + 5)
D. 𝑦 = sin 5𝜃
64. Which function is a translation of 𝑦 = cos 𝜃 by 5 units down?
A. 𝑦 = −5 cos 𝜃
B. 𝑦 = cos(−5𝜃)
C. 𝑦 = cos(𝜃 − 5)
D. 𝑦 = cos 𝜃 − 5
𝜋
𝜋
65. Which function is a translation of 𝑦 = sin 𝜃 that is 3 units up and 2 units to the left?
𝜋
𝜋
A. 𝑦 = sin(𝜃 + 3 ) + 2
𝜋
𝜋
B. 𝑦 = sin (𝜃 − 2 ) + 3
𝜋
𝜋
𝜋
𝜋
C. 𝑦 = sin (𝜃 + 2 ) + 3
D. 𝑦 = sin (𝜃 − 3 ) − 2
66. The figure below shows the graph of the function 𝑔(𝑥).
If 𝑓(𝑥) = |2𝑥| + 3, how is 𝑔(𝑥) related to 𝑓(𝑥)?
A. 𝑔(𝑥) = 𝑓(𝑥) − 4
B. 𝑔(𝑥) = 𝑓(𝑥) + 4
C. 𝑔(𝑥) = 𝑓(𝑥 − 4)
D. 𝑔(𝑥) = 𝑓(𝑥 + 4)
67. The cubic function 𝑦 = 𝑥 3 is changed to 𝑦 = −2𝑥 3 − 7. What effect will this have on the function?
A. The graph will be reflected in the y-axis, shifted up 2 units and vertical stretch by a factor of 7.
B. The graph will be reflected in the x-axis, shifted up 7 units and vertical stretch by a factor of 2.
C. The graph will be reflected in the x-axis, shifted down 7 units and vertical stretch by a factor of 2.
D. The graph will be reflected in the y=axis, shifted down 2 units and vertical stretch by a factor of 7.
F-BF.4.a (two questions)
68. What is the inverse, 𝑓 −1 (𝑥), of the function 𝑓(𝑥) = 3𝑥 − 7?
A. 𝑓 −1 (𝑥) =
B. 𝑓
−1 (𝑥)
=
−1 (𝑥)
𝑥−7
3
𝑥+7
3
C. 𝑓
= −3𝑥 + 7
−1 (𝑥)
D. 𝑓
= 7𝑥 − 3
69. Which of the following is the inverse function of 𝑦
A. 𝑦 =
B. 𝑦 =
C. 𝑦 =
𝑥 2 +2
3
2𝑥 2 +2
3
4𝑥 2 +2
3
=
√3𝑥−2
?
2
D. 𝑦 =
𝑥2
3
70. Which expression represents the inverse of 𝑓(𝑥) = 8𝑥 + 13?
A.
B.
x
8
− 13
1
8𝑥 +13
C. log 21(𝑥)
D. log 8 (𝑥 − 13)
71. Given that 𝑓 −1 (𝑥) = 𝑔(𝑥) and 𝑓(𝑥) = 2√𝑥, which expression correctly defines the function 𝑔(𝑥) and its
domain?
A.
B.
C.
D.
𝑥2
2
𝑥2
4
𝑥2
2
𝑥2
4
for all values of 𝑥 ≥ 0
for all values of 𝑥 ≥ 0
for all real values of 𝑥
for all real values of 𝑥
72. What is the inverse of 𝑓(𝑥) = 𝑥 3 + 5?
A.
B.
C.
D.
𝑓 −1 (𝑥) = −𝑥 3 − 5
3
𝑓 −1 (𝑥) = √𝑥 − 5
3
𝑓 −1 (𝑥) = √𝑥 3 − 5
3
𝑓 −1 (𝑥) = 𝑥 − √5
4
3
73. What is the inverse of the equation 𝑦 = √3𝑥 − 4, 𝑥 ≥ ?
A. 𝑦 =
B. 𝑦 =
𝑥 2 +4
3
4−𝑥
3
C. 𝑦 = −
D. 𝑦 = −
, 𝑥≥0
, 𝑥≤4
𝑥 2 +4
3
𝑥+4
3
, 𝑥≥0
, 𝑥 ≥ −4
F-LE.3 (one question)
74. For what positive integer value of 𝑥 will the value of 𝑔(𝑥) = 3𝑥 first exceed the value of 𝑓(𝑥) = 2𝑥 + 25?
A. 3
B. 4
C. 25
D. 26
75. Which statement is true about the functions 𝑓(𝑥) = 2𝑥 2 + 𝑥 + 2 and 𝑔(𝑥) = 2𝑥 + 2, when 𝑥 = 0?
A. The value of 𝑓(𝑥) and the value of 𝑔(𝑥) are the same.
B. The value of 𝑓(𝑥) exceeds the value of 𝑔(𝑥) by 1.
C. The value of 𝑔(𝑥) exceeds the value of 𝑓(𝑥) by 1.
D. The value of 𝑔(𝑥) exceeds the value of 𝑓(𝑥) by 2.
76. Two functions are shown.
𝑓(𝑥) = 1.02𝑥 + 100
𝑔(𝑥) = 50(1.02)𝑥
What is the smallest positive integer in which the value of 𝑔(𝑥) exceeds the value of 𝑓(𝑥)?
A. 60
B. 59
C. 55
D. 50
77. George is comparing the graphs of two function 𝑓(𝑥) = 3𝑥 and 𝑔(𝑥) = 3𝑥 2 + 𝑥 − 1 for different values of 𝑥.
Which statement best compares the values of the function as the value of 𝑥 increases?
A. 𝑓(𝑥) will eventually exceed 𝑔(𝑥) for all real numbers greater than a certain x-value.
B. 𝑔(𝑥) will eventually exceed 𝑓(𝑥) for all real numbers greater than a certain x-value.
C. 𝑓(𝑥) is greater than 𝑔(𝑥) for all values of 𝑥.
D. 𝑔(𝑥) is greater than 𝑓(𝑥) for all values of 𝑥.
78. What is the largest integer value of 𝑥 such that the value of 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 40 exceeds the value of 𝑔(𝑥) =
2(1.5)𝑥 ?
A. 6
B. 8
C. 10
D. 12
79. Which function goes to positive ∞ most quickly as 𝑥 increases?
A. 𝑦 = log(𝑥) + 100
B. 𝑦 = 𝑒 𝑥−9 − 3
C. 𝑦 = 𝑥 2 + 5𝑥 + 6
D. 𝑦 = 3𝑥 5 + 4𝑥 3 − 11𝑥 − 6
F-TF.1 (one question)
80. The diameter of a circle is 8 meters. A central angle of the circle intercepts an arc of 12 meters. What is the
radian measure of the angle?
A.
3
2
B. 2
C. 3
D. 4
81. The radius of a circle is 2 centimeters. A central angle of the circle intercepts an arc of 8 centimeters. What is
the radian measure of the angle?
A. 2
B. 3
C. 4
D. 8
82. A circle has a central angle whose radian measure is 2 and an arc length of 6 meters. What is the diameter of
the circle in inches?
A. 2
B. 3
C. 6
D. 12
83. In a circle, an arc of length 8𝜋 is intercepted by a central angle of
A.
3𝜋
16
cm
B.
16𝜋
3
cm
C.
16𝜋2
3
cm
2𝜋
3
radians. What is the radius of the circle?
D. 12 cm
84. The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the
measure of angle 𝜃 in radians?
𝐴.
3
11
B.
6
11
C.
11
6
D.
11
3
85. What is the approximate length of the arc subtended by an angle of
meters?
A. 12.57 meters
B. 14.14 meters
C. 25.13 meters
4𝜋
3
radians on a circle with a radius of 6.00
D. 28.13 meters
F-TF.2 (one question)
86. William put the tip of his pencil on the outer edge of a graph of the unit circle at the point
this pencil tip through an angle of
4𝜋
3
(0, -1). He moved
radians in the counterclockwise direction along the edge of the circle. At
what angle of the unit circle did William’s pencil tip stop?
A.
𝜋
3
B.
5𝜋
C.
6
7𝜋
6
5𝜋
D.
3
87. Max put the tip of his pencil on the outer edge of a graph of the unit circle at the point (-1, 0). He moved his
𝜋
pencil tip through an angle of radians in the counterclockwise direction along the edge of the circle. At what
6
angle of the unit circle did Max’s pencil tip stop in radians?
A.
7𝜋
6
B.
𝜋
6
C.
5𝜋
6
D.
11𝜋
6
88. A Ferris wheel has a diameter of 114 feet and is 5 feet off the ground. After a person gets on the bottom car,
the Ferris wheel rotates 1700 counterclockwise before stopping. How high above the ground is the car when it
has stopped?
A. 56 feet
B. 62 feet
C. 80 feet
D. 118 feet
89. How many radians are 1800o?
A. 10
B. 10𝜋
C. 180
D. 180𝜋
90. In the right triangle pictured below, the measure of angle A, in radians, is 𝜃. The side adjacent to angle A
measures 6 cm and the side opposite measures 5 cm.
Which of the following values is closest to sin(5𝜃)?
A. -0.3260
B. 0.6402
C. 0.9723
D. 3.2009
F-TF.5 (one question)
91. A mark of T is at the top of a small wheel. The graph shows ℎ, the height in centimeters of the T above the
ground as a function of 𝑥, the angle the wheel has turned.
Which function is best represented by the graph?
A. ℎ(𝑥) = 12 cos 𝑥
𝑥
2
B. ℎ(𝑥) = 12 sin (𝑥 − )
𝜋
C. ℎ(𝑥) = 6 sin (𝑥 + 2 ) + 6
𝜋
D. ℎ(𝑥) = 6 cos (𝑥 + 2 ) + 6
92. An automotive engineer recorded an antilock brake sensor wave with an amplitude of 0.8, a midline of 0.1, and
𝜋
a frequency of . Which equation best represents this wave?
4
A.
B.
C.
D.
𝑦 = 0.1 sin(8𝑥) + 0.8
𝑦 = 0.8 sin(4𝑥) + 0.1
𝑦 = 0.8 sin(8𝑥) + 0.1
𝑦 = 0.1 sin(4𝑥) + 0.8
93. A transmitter sends a radio wave from the top of a 70-foot building. The amplitude of the wave is 1.5, the
midline of the wave is 4, and the frequency of the wave is 𝜋. Which equation best represents this radio wave?
A. 𝑦 = 1.5 sin(2𝑥)
B. 𝑦 = 1.5 sin(2𝑥) + 4
C. 𝑦 = 2 sin(1.5𝑥) + 4
D. 𝑦 = 2 sin(4𝑥) + 1.5
G-GO.10 (one question)
94. In ∆𝐴𝐵𝐶, 𝐴𝐷 = 𝐷𝐵 and 𝐴𝐸 = 𝐸𝐶.
Given the information above, which statement can be proved to be true?
A. Triangle 𝐴𝐵𝐶 is isosceles.
B. ̅̅̅̅
𝐷𝐸 is perpendicular to ̅̅̅̅
𝑨𝑪.
̅̅̅̅ .
̅̅̅̅ is half the length of 𝐵𝐶
C. The length of 𝐷𝐸
D. Triangle 𝐴𝐵𝐶 is congruent to triangle 𝐴𝐷𝐶.
95. In triangle 𝐴𝐵𝐶, 𝑚 < 𝑥 and 𝑚 < 𝐵 = 𝑦. Which of these can be proved using the triangle sum theorem?
A. 𝑚 < 𝐶 = 𝑦
B. 𝑚 < 𝐶 = 𝑥 + 𝑦
C. 𝑚 < 𝐶 = 180𝑜 − 𝑥 + 𝑦
D. 𝑚 < 𝐶 = 180𝑜 − (𝑥 + 𝑦)
96. Find the measure of each angle in the triangle below.
97. Find 𝑆𝑅 in the figure below
98. If 𝐶𝑅 = 24, what is 𝐾𝑅?
A. 6
B. 8
C. 12
99. If 𝑇𝑅 = 12, what is 𝐶𝑃?
A. 16
B. 18
C. 24
D. 16
D. 36
G-GO.11 (one question)
100. Which of these properties is enough to prove that a given parallelogram is also a rectangle?
A. The diagonals bisect each other.
B. The opposite angles are equal.
C. The opposite sides are equal.
D. The diagonals are congruent.
101.
̅̅̅̅.
̅̅̅̅̅ and ̅̅̅̅̅
In the figure below, ̅̅̅̅
𝑃𝑂//𝑀𝑁
𝑃𝑀//𝑂𝑁
Which would be a correct way to begin a proof that shows < 𝑂 ≅< 𝑀?
A. Draw diagonal ̅̅̅̅
𝑃𝑁 and show that a pair of corresponding angles formed by the transversal are congruent.
̅̅̅̅̅ and show that a pair of adjacent interior angles formed by the transversal are congruent.
B. Draw diagonal 𝑂𝑀
̅̅̅̅ and show that a pair of alternate interior angles formed by the transversal are congruent.
C. Draw diagonal 𝑃𝑁
D. Draw diagonal ̅̅̅̅̅
𝑂𝑀 and show that a pair of alternate interior angles formed by the transversal are
complementary.
G-SRT.5 (two questions)
102. What is the value of 𝑥 in the triangle below?
A.
5√3
cm
2
B. 5√3 cm
C. 10 cm
D. 15 cm
103. Which of the figures shown below are similar?
104. If the rectangular prisms are similar, what is the value of 𝑥?
A.
B.
C.
D.
9
10
12
18
105. Triangle 𝑀𝑁𝑃 is a right triangle. Point X is on ̅̅̅̅̅
𝑀𝑃, Point Y is on ̅̅̅̅
𝑃𝑁, and ̅̅̅̅̅
𝑀𝑁 is parallel to ̅̅̅̅
𝑋𝑌.
Which statement must be true?
A. ∆𝑃𝑀𝑁 ≅ ∆𝑃𝑋𝑌
C. ∆𝑃𝑀𝑁~∆𝑃𝑋𝑌
B. 𝑚 < 𝑃𝑀𝑁 − 𝑚 < 𝑋𝑃𝑌
D. 𝑚 < 𝑃𝑀𝑁 > 𝑚 < 𝑃𝑋𝑌
̅̅̅̅ = 8, and ̅̅̅̅
106. Triangle 𝐴𝐵𝐶 is similar to ∆𝐷𝐸𝐹, ̅̅̅̅
𝐴𝐵 = 12, 𝐷𝐸
𝐴𝐶 = 15
̅̅̅̅ ?
What is the length of 𝐷𝐹
A. 6.4
B. 10
C. 11
D. 22.5
G-C.5 (two questions)
107.
A.
B.
C.
D.
108.
Which measurement is closest to the area of the shaded sector in the circle shown below?
12.56 square inches
25.12 square inches
50.24 square inches
75.36 square inches
The drawing shows a semicircular window separated into 3 sections of color glass.
Approximately how many square inches of the tinted glass are red?
A. 15.7
B. 70.7
C. 141.3
D. 282.6
109.
The windshield wiper blade on Julia’s car is 21 inches long. Each swipe of the wiper makes an angle of
85 degrees as pictured below.
To the nearest inch, how far does the tip of the windshield wiper travel with each swipe of the blade?
A.
B.
C.
D.
21 inches
30 inches
31 inches
33 inches
110.
Sally is creating a flower bed that wraps around the corner of her house. She will put edging around the
flower bed 10 feet from the corner of the house in all directions as shown below.
Which is the best estimate of the number of feet of edging that Sally will need?
A. 24
B. 43
C. 48
D. 63
G-GPE.1 (two questions)
111.
A.
B.
C.
D.
112.
What is the equation of the circle that has a center at (−1, −3) and a radius of 4 units?
(𝑥 − 1)2 + (𝑦 − 3)2 = 16
(𝑥 + 1)2 + (𝑦 + 3)2 = 16
(𝑥 − 1)2 + (𝑦 − 3)2 = 2
(𝑥 + 1)2 + (𝑦 + 3)2 = 2
A circle is graphed on the coordinate plane below.
A. 𝑥 2 + (𝑦 − 4)2 = 9
C. (𝑥 + 4)2 + 𝑦 2 = 9
B. (𝑥 − 4)2 + 𝑦 2 = 3
D. 𝑥 2 + (𝑦 + 4)2 = 3
113.
Which equation represents a circle with the center at (−1, 7) and a radius of √17?
A. (𝑥 − 1)2 + (𝑦 + 7)2 = 17
B. (𝑥 + 1)2 + (𝑦 − 7)2 = 17
C. (𝑥 + 1)2 + (𝑦 + 7)2 = √17
D. (𝑥 + 1)2 + (𝑦 − 7)2 = √17
114.
What is the center and the radius of a circle given by the equation 𝑥 2 + 𝑦 2 + 4𝑥 − 10𝑦 + 20 = 0?
A. (−2, 5) 𝑎𝑛𝑑 𝑟 = √20
B. (2, −5) 𝑎𝑛𝑑 𝑟 = √20
C. (−2, 5) 𝑎𝑛𝑑 𝑟 = 3
D. (2, −5) 𝑎𝑛𝑑 𝑟 = 3
115.
The equation 𝑥 2 + 𝑦 2 − 4𝑥 − 8𝑦 − 16 = 0 represents a circle in the standard 𝑥𝑦-coordinate plane.
What is the radius of the circle?
A. 6
B. √20
C. 4
D. √2
G-MG.3 (one question)
116.
To completely cover a spherical ball, a ball company uses a total area of 36 square inches of material.
What is the maximum volume the ball can have?
4
(Note: Surface area of a sphere = 4𝜋𝑟 2 . Volume of a sphere = 3 𝜋𝑟 3 ).
A. 27𝜋 cubic inches
B. 36√𝜋 cubic inches
36
C. 𝜋 cubic inches
D.
√
27
𝜋
cubic inches
117.
Roberto put new carpeting in one room of his house. The area of this room is represented in the scale
drawing below. Scale: 1 inch=5.5 feet
If carpeting costs $5.40 per square foot, what is the total cost of the new carpeting for this room?
A.
B.
C.
D.
118.
$256.50
$282.15
$1,282.50
$1,551.83
A cube-shaped packing box like the one shown below is used to pack a stack of dinner plates.
If the volume of the box is 1,000 cubic inches, what is the maximum circumference of the dinner plates that will
fit in the box, to the nearest tenth of an inch?
A.
B.
C.
D.
15.7 inches
31.4 inches
78.5 inches
99.3 inches
S-ID.4 (one question)
119.
In a set of test scores that are normally distributed, a test score of 76 is 3 standard deviations below the
mean. A score of 88 is 1 standard deviation above the mean. What is the mean of the data?
A. 79
B. 82
C. 84
D. 85
120.
Petra measures how long a particular brand of holiday light bulb remains lit continuously before burning
out. She samples 250 bulbs, and her data forms a normal distribution, with a mean of 100 hours and a standard
deviation of 5 hours. What percent of the bulbs burned out between 105 and 110 hours?
A. 5.0
B. 10.3
C. 13.5
D. 34.0
121.
In a college math class, 500 students took a final exam. The final exam results showed students had an
average score of 65.3% with a standard deviation of 5.2%. The scores on the final exam followed a normal
distribution curve with population percentages as shown below.
How many students scored above 54.9% but below 70.5%?
A. 78
B. 82
C. 341
D. 409
122.
A local peach orchard packages 200 peaches per box. The weights of the peaches are normally
distributed with a mean of 5.5 ounces and a standard deviation of 0.75 ounce. Approximately how many of the
peaches in each box weigh between 4.75 ounces and 6.25 ounces?
A. 34
B. 68
C. 95
D. 136
S-IC.4 (one question)
123. Of 400 teenagers surveyed, 62% do not plan to stay in their communities after finishing their education. Find
the margin of error for the sample.
A. ±2%
B. ±4%
C. ±5%
D. ±6%
124. In a random survey of 1,000 high school students, 65% said that math is their favorite subject. Based on these
survey results, which of these represents a 95% confidence interval for the percentage of all high school
students who would choose math as their favorite subject?
A. 60% to 70%
B. 62.04% to 67.96%
C. 62.5% to 67.5%
D. 63.52 to 66.48%
125. A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0-100. The sample
mean of this survey is 86. The known population standard deviation is 14 for all seniors in the class. Which of
these is a 95% confidence interval for the population mean?
A. [82.72, 89.28]
B. [83.51, 88.49]
C. [83.91, 88.09]
D. [85.92, 86.08]
126. An electrics company conducted a customer satisfaction survey. The survey results showed, with a 95%
confidence level, that 62% to 68% of customers are satisfied with their service. What is the margin of error of
this survey?
A. 3%
B. 6%
C. 65%
D. 95%
127. A state senator requested a survey of registered voters to determine public opinion of a new law. Of the 940
voters who responded to the survey, 61.7% were in favor of the new law, 35.% were opposed, and the rest were
undecided. What is the margin of error of this survey with a 95% level of confidence?
A. ±1.44%
B. ±1.51%
C. ±2.98%
D. ±3.11%
128. A random sampling of 500 adults showed that 203 preferred Brand A potato chips more than all other brands of
potato chips in the survey. Which interval reflects a 95% likelihood of containing p, the population proportion?
A. 0.305 ≤ 𝑝 ≤ 0.508
B. 0.356 ≤ 𝑝 ≤ 0.456
C. 0.363 ≤ 𝑝 ≤ 0.449
D. 0.386 ≤ 𝑝 ≤ 0.426