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Омский Государственный Технический Университет
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334

PRACTICE TEST 6 QUESTIONS

1. If

2a + 2b

= 9,

then

1

=

a + b

 

1

 

 

 

2

1

(A) 9

4

(B)

9

 

(C)

2

3

 

(D)

9

4

 

(E)9

2.If f (x) = e2x, then f (ln 2) =

(A)2

(B)e2

(C)4

(D)e4

(E)ln 4

3.

If 23 (23n )(2) =

1

, then n =

 

 

 

 

 

4

 

 

 

 

 

(A)

−

5

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

(B)

−2

 

 

 

(C)

−

2

 

 

 

 

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

 

 

 

(D)

−

2

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

(E)

−

1

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

4.

If x = 4 − y and x ≠ ±y,

y − x

=

x2

− y2

 

 

 

 

 

 

 

 

 

 

 

 

 

(A)

−4

 

 

 

(B)

−

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

(C)

−

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

 

 

 

 

 

 

 

 

 

1

(D)

2

 

(E)

1

4

 

PART III / EIGHT PRACTICE TESTS

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PRACTICE TEST 6

335

5. What is the reciprocal of 8 − 3i?

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1

 

 

 

 

(A)

 

 

 

8

 

(B)

 

8 + 3i

 

 

55

 

 

 

 

 

(C)

 

8 − 3i

 

 

55

 

 

 

 

 

(D)

 

8 + 3i

 

 

73

 

 

 

 

 

(E)

1

 

 

 

 

 

 

 

 

 

11

 

 

 

 

 

6.What is the solution set to x + x − 4 > 4?

(A){x: 0 < x < 4}

(B){x: x > 4}

(C){x: x < 0}

(D){x: x < 0 or x > 4}

(E){x: x < −4 or x > 0}

7.An equation of the line parallel to 8x − 2y = 5 and containing the point (−2, 2) is

(A)y − 2 = 4(x − 2)

(B)y = 4x + 5

2

(C) y = 4x − 5 2

(D) y + 2 = 4(x − 2)

(E) y = 4x + 10

8. If

x + 3

≤ 0, then which of the following describes x?

 

x − 7

(A)

−3 ≤ x < 7

(B)

x < 7

(C)

x ≤ −3 or x ≥ 7

(D)

−3 ≤ x ≤ 7

(E)

x ≤ −3 or x > 7

9. Which of the following expressions represents the statement “x is proportional to h and inversely proportional to the square of r”?

(A) x = khr2

(B) x = kh(−r2)

(C) x = kh r 2

(D) x = kh r

(E) x = k hr 2

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336

 

 

 

 

 

PART III / EIGHT PRACTICE TESTS

10. What is the vertex of the parabola given by f (x) =

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4x2 − 6x + 9?

 

 

 

3

,

135

 

(A)

 

 

 

 

 

4

16

 

 

 

 

 

3

(B)2 , 9

(C)

 

−

3

−

27

 

,

4

 

 

 

 

4

 

 

1

(D)2 , 7

3 27

(E)4 , 4

11.If 270 ≤ θ ≤ 360° and cos θ = 0.43, then csc θ =

(A)−1.11

(B)−0.90

(C)0.90

(D)1.11

(E)2.33

12.What are the zeroes of f (x) = 6x3 − 5x2 − 25x?

(A){− 52 , 53}

(B){− 53 , 52}

(C){− 52 , 52 , 53}

(D){− 53 , 0, 52}

(E){− 52 , 0, 53}

13.The probability that there will be a lightning storm

tomorrow is 1 and, independently, the probability that 8

there will be a lightning storm the day after tomorrow

is 1 . What is the probability that there will be a storm 11

tomorrow but not the day after tomorrow?

1

(A)

88

1

(B)

8

5

(C)

44

(D)19

88

91

(E)

88

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PRACTICE TEST 6

 

 

 

 

337

14. An operation is defined on any three real numbers by

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a ▪ b ▪ c = ac − b. If 3 ▪ n ▪ 1 =

1

, then n =

 

 

27

 

 

 

 

 

 

 

 

 

 

 

 

(A)

−3

 

 

 

 

 

 

(B)

−2

 

 

 

 

 

 

(C)

2

 

 

 

 

 

 

 

 

 

 

(D)

4

 

 

 

 

 

 

 

 

 

 

(E)

5

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

15.

If (x − 2)

 

= 64, then x =

 

 

 

 

2

 

 

 

 

 

(A)

4

 

 

 

 

 

 

 

 

 

 

(B)

8

 

 

 

 

 

 

 

 

 

 

(C)

14

 

 

 

 

 

 

 

 

 

 

(D)

16

 

 

 

 

 

 

 

 

 

 

(E)

18

 

 

 

 

 

 

 

 

 

16.

If sin 2θ =

2

, then

1

 

 

=

 

 

sin θ cosθ

 

 

 

5

 

 

 

(A)1

5

5

(B)

4

5

(C)

2

(D)5

(E)10

17.What does the angle 480° equal in radian measure?

2π

(A)

3

4π

(B)

3

8π

(C)

3

(D) 16π 3

5π

(E)

2

18. If f (x) = x2 + 2x − 3 , what value does the function x2 − 1

approach as x approaches 1?

(A)−4

(B)−2

(C)1

(D)2

(E)4

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(a − b)
(b − a) , then

338

19.If 4i is a zero of the polynomial p(x), then which of the following must be a factor of p(x)?

(A)−4i

(B)x2 + 16

(C)x2 + 17

(D)x2 − 16

(E)x2 − 8ix + 16i2

20. If, for all a ≠ b, f (a, b) = f ( 5, 3) =

(A)−1

(B)3 − 5

(C) (−2 − 15) 2

(D)1

(E)2

21.If f (x) = 2x + 6 and g[ f (−9)] = −3, then g(x) could be which of the following?

(A)x − 3 2

(B)x + 1 3

(C)15 − x

(D)− x

4

(E)x − 9

22.Which of the following is an x-intercept of the hyper-

bola x2 − y2 = 1?

89

(A)(−2 2, 0)

(B)(2, 0)

(C)(−3, 0)

(D)(4, 0)

(E)(8, 0)

PART III / EIGHT PRACTICE TESTS

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PRACTICE TEST 6

23.What is the length of segment AB in Figure 1?

(A)3.6

(B)6.4

(C)6.7

(D)7.5

(E)45

24. For x ≠ −1 and x ≠

1

, if f (x) = 1 − 3x and g(x) =

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

f

 

3x

2

+ 2x − 1, then

 

 

 

(x) =

 

 

 

 

g

 

(A)

 

1

x2

−

3

x

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

−1

(B) x + 1

1

(C) x + 1

−1

(D)x − 1

(E)3x2 + 5x − 2

25.If f (x) = 3x for all real values of x and f −1(n) = −2, then n =

(A)−9

(B)−6

(C)3 2

(D)1

9

(E)9

26.If logb 4 = 16, then b =

(A)0.25

(B)0.50

(C)1.09

(D)2

(E)4

27.cot (arcsin 0.4) =

(A)0.44

(B)0.56

(C)0.92

(D)2.29

(E)2.36

339

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z

B (0, 5, 3)

y

(4, 0, 1) A

x

Figure 1

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340

PART III / EIGHT PRACTICE TESTS

28. If cos (45 + 2x)° = sin (3x)°, then x =

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(A)18°

(B)27°

(C)45°

(D)22.5°

(E)9°

29.What is the center of the circle x2 + y2 − 8x + 2y + 8 = 0?

(A)(4, −1)

(B)(1, 4)

(C)(2, 1)

(D)(−4, 1)

(E)(−2, 1)

30. If f (x) = 3 x + x , then f [ f (4)] = 2

(A)12 + 2 2

(B)20

(C)14 2

(D)8

(E)16

31.What is the range of the piecewise function

(A)y ≥ 0

(B)y ≥ 5

(C)4 ≤ y ≤ 8

(D)y > 4

(E)All real numbers.

32. If vector

r

= (−1,

r

−4), then

v

−8) and vector u = (2,

r

+ v =

 

 

vector u

 

 

(A)(−1, −12)

(B)(3, 4)

(C)(−12, −1)

(D)(−3, −4)

(E)(1, −12)

33.A cube has edges of length 5. If P and Q are points on its surface, what is the maximum straight-line distance from P to Q?

(A)5 2

(B)10 2

(C)5 3

(D)3 5

(E)15

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PRACTICE TEST 6

 

 

 

341

 

 

 

 

 

 

 

 

1

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34. If f (x) = 4

x

 

=

4

, then

f log2

 

 

256

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

(A)

 

 

 

 

 

 

 

65,536

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

(B)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

(C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16

 

 

 

 

 

 

 

 

 

(D)3 3

(E)16

35.For x ≠ 0, if 3−2 − 6−2 = x−2, then x =

(A)3 3

(B)2 3

(C)±12

(D)± 2 3

(E)±6

36.If f (x) = x and h(x) is obtained by shifting f (x) down

5 units, right 1 unit, and reflecting it over the line y = −5, then h(3) =

(A)−9

(B)−7

(C)−5

(D)−3

(E)3

37.If the lines y1 = (n + 1)x + 12 and y2 = (2n − 3)x + 2 are parallel, then n could equal which of the following?

(A)−4

(B)−0.78

(C)0.67

(D)1.28

(E)4

38.If f (x) = x2 + 6 for all x ≥ 0, then the graph of f −1(x) intersects the x-axis at

(A)zero points.

(B)exactly one point.

(C)exactly two points.

(D)exactly three points.

(E)f −1 is undefined.

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342

39.Thirteen students receive the following grades on a math test:

60, 78, 90, 67, 88, 92, 81, 100, 95, 83, 83, 86, 74.

What is the interquartile range of the test scores?

(A)14

(B)83

(C)15

(D)16

(E)40

40.What is the value of n if the determinant of matrix X is given as:

det X =

9

−3

= 0?

 

4

n

 

(A)−12

(B)− 4 3

(C)− 3 4

3

(D)

4

4

(E)

3

41. In Figure 2, which of the following must be true?

I.

cot x = 3

 

4

II.cos x = sin y

III.tan x = tan y

(A)I only

(B)II only

(C)II and III only

(D)I and II only

(E)I, II, and III

42.Which of the following statements does not describe a positive correlation?

(A)A person’s height and weight

(B)The percentage of registered voters and the percentage of actual voters

(C)The number of DVD owners and total DVD sales

(D)The value of a car and its age

(E)A student’s GPA and SAT scores

43.The graph of which of the following is symmetric with respect to the origin?

(A)y = x2 − 1

(B)y = x3 − 2x

(C)y2 = x + 8

(D)y = − x + 1

(E)y = (x + 3)2

PART III / EIGHT PRACTICE TESTS

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x

5

3

y

4

Figure 2

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PRACTICE TEST 6

44.The graph of y = −4x + 10 can be expressed as a set of parametric equations. If x = 3 + t and y = f (t), then what does f (t) equal?

(A)−4t − 2

(B)−4t − 22

(C)4t − 2

(D)1 t + 7

4

(E)−4t − 12

45.If x0 = 2 and xn+1 = 3 −4xn , then x4 =

(A)−8

(B)−2

(C)2

(D)4

(E)8

46.In a group of 40 of Ms Jones’s students, students are either sophomores or juniors (but not both) and study either geometry or algebra 2 but not both. If 18 sophomores study geometry, 16 students are juniors, and 13 students study algebra 2, how many juniors study algebra 2?

(A)6

(B)7

(C)8

(D)9

(E)10

47.How long is the base of an isosceles triangle if the

other two sides measure 8 cm, and each base angle measures 41°?

(A)5.3

(B)7.9

(C)13.9

(D)11.3

(E)12.1

48.A committee of 3 people is to be selected from a group of 6 women and 4 men. Assuming the selection is made randomly, what is the probability that the committee consists of 2 women and 1 man?

1

(A) 30

1

(B)

8

1

(C)

4

(D)1

3

1

(E)

2

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