27. If x 2a =p5, what does x 7a equal?

A. 125 5
p
B. 25 5
C. 125
D. 625
p
E. 5 5

28. A stock went up 20% the first week, up 30% the second week, and down 10% the third week.
What was its percent increase to the nearest percent over the three weeks?
A. 35
B. 40
C. 45
D. 50
E. 70

3x 5 y
29. Which of the following is equivalent to + ?
2 y 3x
9x 2 + 15 y 2
A.
6x y
9x + 16 y 2
2
B.
6x y
12x 2 + 11 y 2
C.
6x y
9x + 10 y 2
2
D.
6x y
9x + 11 y 2
2
E.
6x y

1
30. With 0 ≤ θ < 2π, sin θ > on what interval?
2
π 2π
 ‹
A. ,
3 3
B. (0, π)
π 2π
• ˜
C. ,
3 3
π 5π
 ‹
D. ,
6 6
π 5π
• ˜
E. ,
6 6

6
 p
31. What is the value of log2 32?
3
A.
2
B. 5
5
C.
2
7
D.
2
9
E.
2
3
n
32. What is an = 3 as a recursive formula?
4
9 3
A. a1 = , an = an−1 ·
4 4
3
B. a1 = 3, an = an−1 ·
4
3
C. a1 = 4, an = an−1 ·
4
9 4
D. a1 = , an = an−1 ·
4 3
4
E. a1 = 3, an = an−1 ·
3

33. If f (x) = 2x 2 + a goes through 3, 5 , what is f (7)?

A. 45
B. 55
C. 65
D. 75
E. 85

34. Which is y = x 5 shifted 3 up and 7 to the right?

A. y = (x − 7)2 + 3
B. y = (x − 7)2 − 3
C. y = (x − 3)2 + 7
D. y = (x + 7)2 + 3
E. y = (x + 7)2 − 3

35. The perimeter of a square is equal to the circumference of a circle. The circle has radius 4 meters.
What is the area of the square in square meters?
A. 16π2
B. 4π2
C. 2π2
D. 4π
E. 2π

7
 1 1
36. Which of the following is equivalent to + ?
x 2 − 4 x 2 + 3x − 10
2x + 5
A.
x3 + 5x 2 − 4x − 20
7
B.
x + 5x − 4x − 20
3 2
2x + 7
C.
x 3 + 5x 2 − 10x − 20
7
D.
x + 3x − 4x − 20
3 2
2x + 7
E.
x + 5x 2 − 4x − 20
3

x 1
+
37. Which of the following equals 5 3 ?
3 1
−
4 3
4(3x + 5)
A.
25
3x + 5
B.
5
3x + 5
C.
6
4(3x + 4)
D.
25
3x + 4
E.
5
10
38. Given f (x) = , for what values of t does f (t) = t ?
x +3
A. −2 or 5
B. 2
C. 2 or 5
D. −4 or 3
E. −5 or 2

39. What is the weight in pounds expressed in scientific notation of 57 million bricks if each brick
weighs 4 pounds?
A. 2.28 × 108
B. 2.28 × 109
C. 2.28 × 101 0
D. 1.14 × 109
E. 4.56 × 109

8
40. Kevin ran a 6 mile cross country course in 31 minutes and Robert took 35 minutes for the same
course. To the nearest tenth what was the difference in their speeds in miles per hour?
A. 1.0
B. 1.1
C. 1.2
D. 1.3
E. 1.4

41. What is the value of log4 8?

2
A.
3
B. 3
5
C.
2
D. 2
3
E.
2

42. t = 23 − .008a models the temperature on June 17 in near Denver, where a is the height above
sea level. According to the model what would be the temperature at 3, 000 meters?
A. −1◦ C
B. 3◦ C
C. 5◦ C
D. 7◦ C
E. 9◦ C

9
43. Temperature in Fahrenheit is related to temperature in Centigrade by the formula F = C+
5
32. An increase of 10 degrees Fahrenheit is equivalent to an increase in how many degrees
Centigrade.
40
A.
9
50
B.
9
C. 6
D. 12
E. 18

44. What is the y−intercept of y = (x + 2)(x + 4)(x − 3)?

A. −144
B. −72
C. −24
D. −12
E. 24

9
45. What is the axis of symmetry of a parabola where y is a function of x with x−intercepts of −7
and 11?
A. x = 1
B. x = 2
C. x = 3
D. x = 4
E. x = 5

9C
46. The melting point of zinc is 787◦ Fahrenheit. Fahrenheit to Celsius is related as F = + 32 and
5
Kelvin to Celsius as K = C + 273. Which is closest to the melting point of zinc in degrees Kelvin.
A. 632
B. 662
C. 692
D. 722
E. 752

47. If x 3 = 300, and x is real then x is between which of the following integers?
A. 4 and 5
B. 5 and 6
C. 6 and 7
D. 7 and 8
E. 8 and 9

48. If f (x) = 7 · 2 x , g(x) = 2 · 3 x , and h(x) = f (x) − g(x), what is the value of h(4)?
A. −50
B. −20
C. 10
D. 20
E. 50
p
24 18
49. The expression p is equal to?
4 2
A. 12
B. 18
C. 24
p
D. 12 2
p
E. 9 2

50. What is the volume of a cylinder with diameter 80 cm and height 35 cm?
A. 140π
B. 5600π
C. 22400π
D. 56000π
E. 224000π

10
51. Sphere U has a volume of 7 cubic feet. Sphere V has a radius 3 times that Sphere U . What is
the volume of sphere V in cubic feet?
A. 21
B. 63
C. 112
D. 189
E. 252

1 7
52. If x + = , then x equals what?
8 12
5
A.
12
11
B.
24
1
C.
2
13
D.
24
17
E.
24

53. Which of the following is the equation of a circle with center (3, −1) which goes through (5, 5)?
A. (x − 3)2 + ( y + 1)2 = 10
B. (x − 3)2 + ( y + 1)2 = 40
C. (x − 3)2 + ( y + 1)2 = 1600
D. (x + 3)2 + ( y − 1)2 = 10
E. (x + 3)2 + ( y − 1)2 = 40

54. The area of circle A is 3 times the area of circle B . What is the ratio of the circumference of circle
A to the circumference of circle B ?
p3
A. 3
3
B.
2
p
C. 3
D. 3
E. 9

55. If x + y = 12 and x − y = 7, what is x y ?

81
A.
4
85
B.
4
89
C.
4
95
D.
4

11
 101
E.
4

56. The area of a rectangle is 108 square meters and the length of that rectangle is 3 times the
width. What is the perimeter of the rectangle in meters?
A. 36
B. 48
C. 54
D. 60
E. 72

12
13
 ANSWER KEY
1C, 2D, 3E, 4C, 5A, 6C, 7C, 8C, 9B, 10C, 11B, 12B, 13C, 14E, 15C, 16E, 17A, 18A, 19C, 20A,
21A, 22B, 23D, 24C, 25C, 26B, 27A, 28B, 29D, 30D, 31C, 32A, 33E, 34A, 35B, 36E, 37A, 38E,
39A, 40A, 41E, 42A, 43B, 44C, 45B, 46C, 47C, 48A, 49B, 50D, 51D, 52B, 53B, 54C, 55D, 56B.

−5b
1. (C) 2a + 5b = 0 −→ 2a = −5b −→ a = .
2

2. (D) The solutions are 4i and its conjugate −4i . Taking x minus each, x −4i x +4i = x 2 −16i 2 =

x 2 + 16.

3. (E) s3 =volume, s3 = 27 −→ s = 3. Each of 6 sides are 3 · 3 = 9. 6 · 9 = 54 square inches.

1 x 1 29
4. (C) 8 = a · 4 + 7 −→ 1 = 4a −→ a = . So f (x) = + 7. f (1) = + 7 = .
4 4 4 4
p
5. (A) x = y 5 −→ y = 5 x .

6. (C) (x + 4)2 − 25 = 0 −→ x 2 + 8x + 16 − 25 = 0 −→ x 2 + 8x − 9 = 0 −→ x 2 + 9x − x − 9 = 0 −→
(x + 9)(x − 1) = 0 −→ x = 1 or −9. You could also use the quadratic formula, completing the
square, or graphing. Alternate solution: x 2 − 25 = 0 −→ x = 5 or −5x + 4 = 0 −→ x = −4 So
5 − 4 = 1, −5 − 4 = −9.

7. (C) The easiest approach for most student is to take two points (1, 100) and (2, 160). The slope
160 − 100
is = 60. Using y = mx + b and (1, 100), 100 = 60 · 1 + b −→ b = 40. So y = 60x + 40.
2−1
It is easier in a way to realize the daily charge is 60 and the initial charge is 100 − 60 = 40, but
the more methodical approach usually works better.

8. (C) 2 · 8(130−127) = 2 · 83 = 2 · 512 = 4(mod 10).

130
9. (B) 3 AM. = 5 remainder 10. 5 + 10 = 15. 15 − 12 = 3 AM.
120
10. (C) a + b = 3, a − b = 5, adding, 2a = 8 −→ a = 4. You could also use substitution or graphing
to solve the system of linear equations.
p
3
p
3
p3
p
3
11. (B) 160 = 2 · 80 = 22 · 40 = 23 · 20 = 24 · 10 = 25 · 5. 25 · 5 = 23 · 22 · 5 = 2 20.
p p p p
12. (B) 108 = 54 · 2 = 27 · 22 = 9 · 3 · 22 = 33 · 22 . 33 · 22 = 3 · 32 · 22 = 6 3.

13. (C) 4x 2 − i 2 = 4x 2 + 1.

14. (E) 3x + 2i 3x + 2i = 9x 2 + 6i x + 6i x − 4 = 9x 2 + 12i x − 4. 9x 2 + 12i x − 4 3x + 2i =

27x 3 + 18i x 2 + 36i x 2 − 24x − 12x − 8i = 27x 3 + 54i x 2 − 36x − 8i . You could also use the binomial
theorem. (level 5)

15. (C) P(A) · P(B) = 0.8 · 0.7 = 0.56.

14
16. (E) P(A) + P(B) − P(AB) = 0.8 + 0.7 − 0.8 · 0.7 = 1.5 − 0.56 = 0.94.
p p
10 −5/2 1 1 1 10
17. (A) . 10 = 5/2 = 2 . p = .
1000 10 10 · 101/2 100 10 1000

18. (A) b2 − 4ac < 0. b2 − 4 · 4 · 9 < 0 −→ b2 < 144 −→ |b| < 12 −→ − 12, 12 .

19. (C) Take the negative of the y−value, 3, −5 .

20. (A) Dividing, x 2 + 3.

21. (A) The more spread out the data is, the higher the standard deviation, Actually calculating the
standard deviations of wach data set in a time trap.


22. (B) Take the negative of the x−value − 3, 5 .

23. (D) 7 km= 7 · 100 · 1000 = 700, 000 cm. Circumference of tire = 2πr = 2π · 30 = 60π cm.
700, 000
≈ 3, 724 rotations.
60π

4 
24. (C) log2 25 = 3x + 5 −→ log2 220 = 3x + 5 −→ 20 = 3x + 5 −→ 15 = 3x −→ x = 5.

sin x cos π
25. (C) cos x . By the angle sum formula, sin(a + b) = sin a cos b + cos a sin b. So +
2
cos x sin π
= sin x · 0 + cos x · 1 = cos x . It is possible to know this fact or to use making up
2
numbers or graphing to solve.
2x − y + 2x + y 4x
26. (B) = .
(2x + y)(2x − y) 4x 2 − y 2
p p
27. (A) 125 5. x 7 a = x 2 a7/2 , 57/2 = 53 · 51/2 = 125 5.

28. (B) (level 5) 1.2 · 1.3 · .9 = 1.404. (1.404 − 1) · 100 = 40.4% ≈ 40%.

9x 2 + 10 y 2
29. (D) .
6x y

π 5π π 5π 1
 ‹  ‹
30. (D) , . sin = sin = . sin(x) is larger than that in the interval between them.
6 6 6 6 2

1/2 5
31. (C) log2 25 = log2 25/2 = .
2
 ‹1
3 9 9 3
32. (A) a1 = 3 = . So a1 = , an = an−1 · .
4 4 4 4

33. (E) 5 = 2·32 + a −→ 5 = 18+ a −→ a = −13, so f (x) = 2x 2 −13 −→ f (7) = 2·72 −13 = 98−13 =
85.

15
34. (A) y = (x − 7)2 + 3.

35. (B) Circumference of circle = 2πr = 2π4 = 8π. 8π is then the perimeter of the square. Each
side of the square is then 2π, so the area of the square is (2π)2 = 4π2 .
1 1 x +5+ x +2 2x + 7 2x + 7
36. (E) + = = = 3 .
(x − 2)(x + 2) (x + 5)(x − 2) (x − 2)(x + 2)(x + 5) (x 2 − 4)(x + 5) x + 5x 2 − 4x − 20

3x + 5 3x + 5
15 15 (3x + 5) · 12 4(3x + 5)
37. (A) = = = .
9−4 5 15 · 5 25
12 12
10
38. (E) t = −→ t 2 + 3t = 10 −→ t 2 + 3t − 10 = 0 −→ t = −5 or 2, by factoring, the quadratic
t +3
formula, completing the square, or graphing.

39. (A) 1 million is 106 , so 57 million is 57 × 106 = 5.7 × 107 . 5.7 · 107 · 4 = 22.8 × 107 = 2.28 × 108 .
6 360 6 360
40. (A) Kevin’s speed = = ≈ 11.61 mph. Robert’s speed = = ≈ 10.59. 11.61 −
31 31 34 34
60 60
10.59 = 1.02 ≈ 1.0.
3 log 8
41. (E) log22 23 = . Alternate solution, using the change of base formula with your calculator
2 log 4
ln 8
or .
ln 4
42. (A) 23 − 0.008 · 3000 = 23 − 24 = −1◦ C.
5 50
43. (B) 10 · = .
9 9
44. (C) 2 · 4 · (−3) = −24. You could also graph it and read the intercept.
−11 + 7
45. (B) Take the average of the intercepts, . x = 2.
2
9C 9C
46. (C) 787 = + 32 −→ 755 = −→ C ≈ 419.4, K = C + 273 −→ K = 419.4 + 273 ≈ 692.
5 5
p
3
47. (C) 6 and 7. With your calculator, 300 = 3001/3 ≈ 6.693. Or take third powers, 53 = 125,
63 = 216, 73 = 343.

48. (A) f (4) = 7 · 24 = 112, g(4) = 2 · 34 = 162. 112 − 162 = −50.

p
49. (B) 6 9 = 6 · 3 = 18.

50. (D) Radius is 40. Volume is πr 2 h. π · 402 · 35 = π · 1600 · 35 = 56000π.

51. (D) 189. 7 · 33 = 7 · 27 = 189.

16
 11 7 1 14 3 11
52. (B) .x= − = − = .
24 12 8 24 24 24
Æ p p
53. (B)
p Use the distance formula to obtain the radius, (5 − 3)2 + (5 − (−1))2 = 4 + 36 = 40 or
2 10. Equation of circle is (x − 3)2 + ( y + 1)2 = 40.

54. (C) The area is proportional

p to the square of the radius and the circumference to the radius, so
you take the square root, 3.

55. (D) Squaring (x + y)2 = 12 −→ x 2 + 2x y + y 2 = 144, (x − y)2 = 7 −→ x 2 − 2x y + y 2 = 49.

95
Subtracting the second equation from the first, 4x y = 95 −→ x y = . Or solve the equations,
4
19 19 5 19 5 95
adding 2x = 19 −→ x = . + y = 12 −→ y = . x y = · = .
2 2 2 2 2 4

56. (B) 48. l w = 108, 3w · w = 108 −→ w2 = 36 −→ w = 6. l = 3w = 3 · 6 = 18. Perimeter

= 2l + 2w = 2 · 18 + 2 · 6 = 36 + 12 = 48

17