SAT 8
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PRACTICE TEST 7 |
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PRACTICE TEST 7
MATH LEVEL 2
ANSWER SHEET
Tear out this answer sheet and use it to complete the practice test. Determine the BEST answer for each question. Then, fill in the appropriate oval using a No. 2 pencil.
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PRACTICE TEST 7 |
357 |
PRACTICE TEST 7
Time: 60 minutes
Directions: Select the BEST answer for each of the 50 multiple-choice questions. If the exact solution is not one of the five choices, select the answer that is the best approximation. Then, fill in the appropriate oval on the answer sheet.
Notes:
1.A calculator will be needed to answer some of the questions on the test. Scientific, programmable, and graphing calculators are permitted. It is up to you to determine when and when not to use your calculator.
2.Angles on the Level 2 test are measured in degrees and radians. You need to decide whether your calculator should be set to degree mode or radian mode for a particular question.
3.Figures are drawn as accurately as possible and are intended to help solve some of the test problems. If a figure is not drawn to scale, this will be stated in the problem. All figures lie in a plane unless the problem indicates otherwise.
4.Unless otherwise stated, the domain of a function f is assumed to be the set of real numbers x for which the value of the function, f (x), is a real number.
5.Reference information that may be useful in answering some of the test questions can be found below.
Reference Information
Right circular cone with radius r and height h: |
Volume = |
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πr2h |
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Right circular cone with circumference of base c |
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and slant height : |
Lateral Area = |
c |
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Sphere with radius r: |
Volume = |
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πr3 |
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Surface Area = 4πr2 |
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Pyramid with base area B and height h: |
Volume = |
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358 |
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PART III / EIGHT PRACTICE TESTS |
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PRACTICE TEST 7 QUESTIONS |
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1. If 3x = 18, 18x = |
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(A)2.6
(B)3
(C)108
(D)2,007
(E)34,012,224
2.A number k is increased by 12. If the cube root of that result equals −3, k =
(A)−39
(B)−27
(C)−15
(D)15
(E)39
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(n!)2 |
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(n − 1)!2 |
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(A)n
(B)2n
(C)n2
(D)(n − 1)2
(E)n4
4. A point Q is in the second quadrant at a distance of
41 from the origin. Which of the following could be the coordinates of Q?
(A)(−1, 41)
(B)(−4, 5)
(C)(−8, 23)
(D)(5, −4)
(E)(−6, 5)
5.tan θ(sin θ) + cos θ =
(A)2 cos θ
(B)cos θ + sec θ
(C)csc θ
(D)sec θ
(E)1
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PRACTICE TEST 7 |
361 |
16. A triangle has sides measuring 3, 5, and 7 inches. |
USE THIS SPACE AS SCRATCH PAPER |
What is the measure of its largest angle? |
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(A)135°
(B)60°
(C)120°
(D)150°
(E)153°
17.Which of the following is the equation of the circle with x-intercept (−3, 0) and y-intercept (0, 3) whose center is in the 2nd quadrant?
(A)(x − 3)2 + (y − 3)2 = 9
(B)(x − 3)2 + (y + 3)2 = 9
(C)(x + 3)2 + (y − 3)2 = 3
(D)(x − 3)2 + (y + 3)2 = 3
(E)(x + 3)2 + (y − 3)2 = 9
18.Cost is a function of the number of units produced as given by: C(n) = 0.02n2 − 42n + 5,000. How many units, n, produce a minimum cost C ?
(A)525
(B)1,050
(C)2,100
(D)17,050
(E)125,000
19.Some number n is added to the three numbers −2, 10, and 94 to create the first three terms of a geometric sequence. What is the value of n?
(A)1
(B)2
(C)3
(D)4
(E)5
20.A right circular cylinder has a height of 15 and a radius of 4. If A and B are two points on the surface of the cylinder, what is the maximum possible length of AB?
(A)15.1
(B)15.5
(C)17
(D)21.2
(E)26
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362 |
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PART III / EIGHT PRACTICE TESTS |
21. Five integers are arranged from least to greatest. If |
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the median is 12 and the only mode is 5, what is the |
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least possible range for the 5 numbers? |
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(A) |
5 |
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(B) |
7 |
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(C) |
8 |
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(D) |
9 |
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(E) |
14 |
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22. Which of the following equations only has roots of 4 |
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and − |
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(A) |
2x3 + x2 − 32x − 16 = 0 |
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2x2 + 7x − 4 = 0 |
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(C) |
2x2 − 9x − 4 = 0 |
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2x2 − 7x − 4 = 0 |
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(E) |
4(2x + 1) = 0 |
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23. What is the maximum value of f (x) = 7 − (x − 6)2? |
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−7 |
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−6 |
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1 |
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6 |
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(E) |
7 |
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24. If sec θ < 0 and cot θ > 0, then in which quadrant |
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does θ lie? |
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(A) |
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(B) |
II |
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(C) |
III |
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(D) |
IV |
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II or III |
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25. What is the sum of the integers from 1 to 100? |
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4,950 |
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5,000 |
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5,050 |
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(D) |
9,900 |
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(E) |
10,100 |
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PRACTICE TEST 7 |
363 |
26. The ellipse given by the equation 9x2 + 4y2 − 36x − |
USE THIS SPACE AS SCRATCH PAPER |
12y + 18 = 0 is centered at |
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(A)2, 2
9
(B)4, 4
3
(C)2 , 2
(D)−2, − 3
2
(E)(−2, −3)
27.Which of the following lines are asymptotes of the
graph of |
f (x) = 2(x − 4) ? |
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I.x = 4
II.x = ±1
III.y = 0
(A)I only
(B)II only
(C)I and II only
(D)II and III only
(E)I, II, and III
28.On a construction job, there is a 0.08 probability a certain tool is in error of 2% or more. If 4 tools are used, what is the probability that all of them are in error of 2% or more?
(A)0.00004
(B)0.0005
(C)0.02
(D)0.40
(E)0.32
29. If cos 2θ = |
2 |
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cos2 θ − sin2 θ |
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(A) −1
7
(B)
2
2
(C)
7
49
(D)
4
1
(E)
7
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