sparks math level 2 test 1

SAT Math Level 2 Practice Test I

293

SAT MATH LEVEL 2 PRACTICE TEST I ANSWER SHEET

1 ®000® 11 ®0000 21 0®000 31 ®0 1000 41 ®000 19 2 00000 12 ®0000 22 00000 32 ®SCOCE) 42 ®0000 3 ®0000 13 ®0©00 23 CD(DC)00 33 00000 43 ®®1000 4 ®®©©® 14 ®0©00 24 c&ecoo 34 c&eocio 44 ®®©©O 5 ®®©OZ 15 ®00000 25 ®000® 35 (D0000 45 (Deco® 6 ®0000 16 ®0000 26 ®0000 36 ®01000 46 ®0000 7 ®©©00 17 .CDCDOCC) 27 ®©©OC) 37 ®0©00 47 ®®000 8 00000 18 00000 28 ®0000 38 ®0000 48 ®ecoo 9 ®0000 19 ®0©00 29 ®0©00 39 ®®000 49 1200000 10 ®0000 20 00000 30 (Docom 40 ®0000 50 ®0000

GO ON TO THE NEXT PAGE

MATHEMATICS LEVEL 2 TEST

REFERENCE INFORMATION

THE FOLLOWING INFORMATION IS FOR YOUR REFERENCE IN ANSWERING SOME OF THE

QUESTIONS IN THIS TEST.

1 Volume of a right circular cone with radius r and height h: V = —nr 2 h

3 1 Lateral area of a right circular cone with circumference of the base c and slant height: S = — 2c

Volume of a sphere with radius r: V = 4 —3Tr

3 3

Surface area of a sphere with radius r: S = 4nr2

1 Volume of a pyramid with base area B and height h: V =

3—Bh

DO NOT DETACH FROM BOOK.


MATHEMATICS LEVEL 2 TEST

For each of the following problems, decide which is the BEST of the choices given. If the exact numerical value is not one of the choices, select the choice that best approximates this value. Then fill in the corresponding oval on the answer sheet.

Notes: (1) A calculator will be necessary for answering some (but not all) of the questions in this test. For each question you will have to decide whether or not you should use a calcuator. The calculator you use must be at least a scientific calculator; programmable calculators and calculators that can display graphs are permitted.

(2) For some questions in this test you may need to decide whether your calculator should be in radian or degree mode.

(3) Figures that accompany problems in this test are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. All figures lie in a plane unless otherwise indicated.

(4) Unless otherwise specified, the domain of any function f is assumed to be the set of all real numbers x for which fix) is a real number.

(5) Reference information that may be useful in answering the questions in this test can be found on the page preceding Question 1.

USE THIS SPACE FOR SCRATCHWORK. 1. If x = t3 and y = t2 + 4, what is y in terms of x?

(A) x + 4

(B) x 2 + 4

(C) +4

(D) x + 4

(E) ,1;2 + 4

2. x _ 2y 2x

(A) 2x - 2y x - y

(B) x - y 2y- 2x

2 2

(C) 2xy

(D) 2xy

2 2 (E) +

2xy

x Figure 1

MATHEMATICS LEVEL 2 TEST—Continued

USE THIS SPACE FOR SCRATCHWORK. 3. What is the range of y = 3 sin 0?

(A) —3 <y < 3

(B) 0 s y

(C)3 s y 5 1

(D) —1 5 y s 1

(E) —3 5 y 5 3

4. What is the perimeter of a rectangle that has vertices (1, ), (1, 5), and (3, 5)?

(A) 7.17 (B) 9.23 (C) 11.17 (D) 15 (E) 30

2

5. If x, y, and z are nonzero real numbers and if X - Z = yz2

, y

(A) y2 (B) 2z2

(C) y2 -2z2 (D) z 2(y 2 — 1) (E) z2(y 2 + 1)

6. In Figure 1, if sin 0 = 0.29 , then what is the value of ? x

(A) —0.34 (B) 0.18

(C) 0.29 (D) 0.30

(E) 0.96

then x = ?

7. If f(x) = x 2 and g(x) = + 2 , what is g(f(2)) + f(1)?

(A) 3 (B) 5 (C) 6 (D) 10 2 (E) (V2 + 2) + 1




USE THIS SPACE FOR SCRATCHWORK. 8. If

3- (x 3 ) = 3, then what is the value of x?

(A) 0.50

(B) 1.04 (C) 1.65 (D) 2.08 (E) 4.50

9. Under what conditions is the graph of y = -bx + 1 a vertical line?

(A) If b = 0 (B) IfOsbs 1 (C) If b = -1 (D) For all b (E) For no b

10. Where it is defined,

(A) 0 (B) 1 (C) csc2 0 (D) sin2 0 (E) 1- sin2 8

1 + tan 2 B

tan 2

y

(-5, 5) °—C

11. A portion of the graph of y = f(x) is shown in Figure 2. Assuming the graph continues in the pattern shown, what is the range off?

(A) Real numbers

(B) Real numbers, such that f (x) 0

(1, -1)0—o

(C) Real numbers, excluding integers (D) Real numbers, such that fix) > 0 (E) Integers

Figure 2

(2, —2)o--0

(3, —3)°."--0 o--o

(4, —4)

(E) ,A



USE THIS SPACE FOR SCRATCHWORK. 12. Which of the following is a zero root off x) = 3x 2 — x — 5?

(A) —2.14 (B) —1.59 (C) 0.62 (D) 1.47 (E) 3.33

13. If sin 0 = =a then ws° = 2 ' csc 0

(A) —3

14. If f(x) = x + 3, which of the following equals f (1) x (f (7) + f (2)) 9 f(3)

(A) f(5) (B) fi6) (C) fi7) (D) fi7) + 0.5 (E) f(8)

15. A sphere and a cone have equal volume and radii. If the radius of each of the solids is 3, what is the lateral area of the cone?

(A) 58.29 (B) 77.72 (C) 96.38 (D) 113.10 (E) 116.58

USE THIS SPACE FOR SCRATCHWORK.

Y

Figure 3

(A) y



16. If the graph in Figure 3 is the graph of y = I f (x)I, then which of the following graphs could not be the graph of fix)?

(B) y

y

(E) Y

17. The median of a set of numbers is 7.4. If the greatest number in the set is removed, which of the following choices could not be the median of the new set?

(A) 6.4 (B) 7

(C) 7.4 (D) 9 (E) Not enough information to tell


18. In Figure 4, if cot 0 = 0.25, then what is the value of x?

(A) 1 (B) 2 (C) 4 (D) 16 (E) 32


x Figure 4

19. If the current value of a given object is $15 and it increases in value at a rate of 12.5% annually, what will the object's value be in 14 years?

(A) $59 (B) $67 (C) $71 (D) $78 (E) $83

20. If —2 5 x s 4 and fix) = 1x 2 — 91, then what is the range off?

(A) y a 0 (B) 05 y 57 (C) 5 5 y 5 7 (D) Osy 59 (E) y 5 9

21. What number must be added to each of the numbers 0, 8, and 32 so that they form consecutive terms of a geometric sequence?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

22. If f(x) = f -1 (x) for all real numbers x, what might fix) equal?

(A) x (B) x2 (C) x + 1 (D) 2x (E) 2x2


y

Figure 5



USE THIS SPACE FOR SCRATCHWORK. 23. For which of the following values of 0 is tan0 always greater

than cos 8?

(A) 0° < 0 < 45° (B) 45° < 8 < 90° (C) 90° < 0 < 135° (D) 135° < 0 < 180°

(E) Not possible

24. What is the domain of the function: f(x) = 3 1 2x + 2x

2 - 24x

(A) x<-4 orx> 3 (B) -4 <x< 8

(C) x * -4, 0, 3

(D) x> 0 (E) x pd 0, 8

25. For all 0, (3-t's(-(3))(7t-coo) .

(A) 1 (B) x2 cos(-0)

(C) 5t 2 cos 0

(D) 7t 2 cos(-0)

(E) ncos 20

26. The graph ofy = fix) is shown in Figure 5. Which of the following statements must be true?

I. if (x)I z 0 II. f(x) = -f(-x)

III. If x 1 > x 2 , then r(x 1 ) < f (x2 )

(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III



USE THIS SPACE FOR SCRATCHWORK. 27. If 36x 4 - 126x2 + 108 = 0, which of the following is not a valid

value of x:

(A) -1.41 (B) -1.22 (C) 0 (D) 1.22 (E) 1.41

28. f is a function. Suppose the following two statements are true off

I. f has a root at x = 2. II. The graph of y = f(x) has exactly two asymptotes,

at x = -1 and y = 1.

Which of the following functions could be f?

(A) fix) = x - x + 1

29. f1x) = x 3 + 2x2 - 8x. For what values of x is f (x) a 0?

(A) x a 2

(B) x s 0 (C) Osxs 2 and xa 5

(D) -4 sxs0 andxa 2 (E) -4 sxs2

30. Point (-4, 3) is located on a circle in the coordinate plane given by the equation (x + 1)2 + (y + 1)2 = r2 . If r is the radius of the circle, which of the following points must also lie on the circle?

(A) (-6, -2.8) (B) (-3.9, 2) (C) (1, 2.7) (D) (-1, -4) (E) (2, 3)

}

ex+1 if x 0 31. f(x) = —x 2 + 2 if x < 0



What is the range off?

(A) y 1

(B) y 2 (C) y > 0 (D) y < 0 (E) All real numbers

32. For what value(s) of x is the inverse of the function f(x) = not defined?

(A) x s 0

(B) x < 0 (C) x = 0 only

(D) x > 0

(E) x a (31

33. If a and b are nonzero real numbers and (3.92)a = (7.86) b, what is

11 ? 2 the value of (-- a

(A) 0.44 (B) 0.66 (C) 0.90 (D) 1.5

(E) 2.3

34. In an arithmetic sequence a n , a s = 5 and a„ = 20. What is a100?

(A) 430 (B) 435 (C) 465 (D) 470 (E) 535



USE THIS SPACE FOR SCRATCHWORK. 35. A monkey sits atop a tree and sees two birds. He can look at one

of the birds by tilting his head up at an angle of 01 above the horizontal. He can look at the second bird by tilting his head down at an angle of 02 below the horizontal. If both birds are a horizontal distance of d meters from the tree (i.e., one is flying directly above the other), how far apart vertically are the two birds, in meters?

d (A) 5 (B) d(sin 01 + sin 02) (C) d(cos 01 + cos 02 ) (D) d tan(611 + 02 ) (E) d(tan 01 + tan 02)

36. Jim owns a small business. By Jim's estimate, he has a 40% chance of making a $5000 profit in the next year and a 60% chance of losing $2000. If an "expected profit" is the product of a profit and the probability of making that profit, what is Jim's expected profit in the next year?

(A) —$200 (B) $800 (C) $2200 (D) $3000 (E) $7000

37. /-'4 has initial point (-2, 2) and terminal point (2, 5). L; has initial point (1, 5) and terminal point (-2, 4). What is ii — 0

(A) (4, 3)

(B) (7, 2) (C) (2, 6) (D) (-1, 3) (E) (7, 4)

38. If f -1(x) = 11x2 for x > 0, then f 2) =

(A) 0.18

(B) 0.43 (C) 0.60 (D) 22 (E) 44




USE THIS SPACE FOR SCRATCHWORK. 39. sin-1(sin 45°) =

(A) .0123 (B) .707 (C) 15°

(D) 45° (E) 90°

40. In a given geometric sequence g„,g4 = 5 and g, = 11.25. What is

g14 4. g17?

4 3- 2 -8 9 (A) —

87 9 8 9

- (B) (C) (D) (E) - 2

41. A right triangle in 3-dimensional space is formed by the points (2, -2, 1), (2, -2, 7), and (5, 2, 1). What is the length of the hypotenuse of the triangle?

(A) 5.00 (B) 6.00 (C) 6.71 (D) 7.81 (E) 10.63

42. Which of the following expresses the polar point (3, 6 ) in rectangular coordinates?

(A) (-1.7, -3.14) (B) (-0.87, 0.5) (C) (1.5, 3.14) (D) (-2.6, 1.5) (E) (0.78, 2.3)


43. (n+1)!x(n-1)! =

(n!) 2

(A) (n + 1)(n - 1)

(B) n+ 1

(C)

(D)(n + 1)(n — 1)

(E) n


44. A circle with equation (x - 3) 2 + (y - 3) 2 = 16 is rotated around the line y = x. What is the volume of the solid that is created?

(A) 256.29 (B) 268.08 (C) 301.97 (D) 312.75 (E) 316.33

45. Suppose the following statement is true: "If the watch costs less than 40 dollars, Jim will buy it." Which of the following statements must also be true?

I. If the watch costs more than 40 dollars, Jim will not buy it.

II. If Jim buys the watch, it costs less than 40 dollars. III. If Jim doesn't buy the watch, the watch costs at least

40 dollars.

(A) I only (B) I and II only (C) III only (D) II and III only (E) None of the three statements must be true.




USE THIS SPACE FOR SCRATCHWORK. 46. An ellipse has equation 100x 2 + 25y2 = 175. What is the length of

the major axis of the ellipse?

(A) 1.51 (B) 2.65 (C) 3.50 (D) 5.29 (E) 7.00

47. Letf(a,b)= la+b xil and g(a, b) = lal + lb x i 2 I . What is g(3, 4) - f(3, 4)?

(A) -2 (B) -1 (C) 0 (D) 2 (E) 18

48. For which of the following is fix) positive for all real values of x?

I. fix) = nbc2 + 4

II. f(x) = sin (x - D

III. f(x) = 2x-1

(A) None (B) I only (C) II only

(D) I and II (E) I and III


49. What is urn —1— ? x — 2 X - 2

(A) 0 (B) 1 (C) 00

(D) -00

(E) The limit does not exist.


50. If mn is an integer, which of the following must also be an integer?

(A) 2mn

(B) m

(C) n

(D) mn + 2n

(E) -- mn

STOP IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON THIS TEST ONLY.

DO NOT TURN TO ANY OTHER TEST IN THIS BOOK.

SAT Math Level 2 Practice Test I Explanations

311

Test

I Exp

lana

tions

312 • Answers to SAT Math Level 2 Practice Test I

Answers to SAT Math Level 2 Practice Test I

Question Number Answer Right Wrong Question Number Answer Right Wrong

1 E 26 E

2 C 27 C

3 E 28 D

4 C 29 D

5 E 30 E

6 D 31 E

7 B 32 C

8 C 33 A

9 E 34 C

10 C 35 E

11 E 36 B

12 D 37 E

13 C 38 B

14 C 39 D

15 E 40 A

16 E 41 D

17 D 42 D

18 B 43 B

19 D 44 B

20 D 45 C

21 C 46 D

22 A 47 D

23 B 48 E

24 C 49 E

25 A 50 A

Calculating Your Score

Your raw score for the SAT Math Level 2 test is based on the number of questions you an-swer correctly and incorrectly. Once you have determined your raw score, use the conver-sion table on page 17 of this book to calculate your scaled score.

To Calculate Your Raw Score

1. Count the number of questions you answered correctly: (A)

2. Count the number of questions you answered incorrectly, and multiply that number by Vt: (B) x 1/4 = (C)

3. Subtract the value in (C) from value in (A): (D)

4. Round the number in (D) to the nearest whole number. This is your raw score: (E)

sparks math level 2 test 1

Documents