[PDF] SAT Mathematics Level 2 Practice Test 16.pdf | Plain Text

# 24 1 1. The product of a positive number, its reciprocal, and its square is 15,129. What is the number? (A) 103 (B) 117 (C) 121 (D) 123 (E) 127 2. If �(�)= �2+ 2�+ �, and if �(1 2)= 1, then c = (A) − 1 2 (B) − 1 4 (C) 0 (D) 1 4 (E) 1 2 3. Which of the following intervals contains only those values of x that satisfy |2 x + 5| < 5? (A) −10 < � < −5 (B) −5< � < 0 (C) −5< � < 5 (D) −5< � < 10 (E) 0< � < 5

# 24 2 ENROLLMENT AT PACIFIC HIGH SCHOOL Class Female Male Freshman 150 150 Sophomore 150 100 Junior 200 125 Senior 100 125 Total 600 500 4. Based on the enrollment figures shown in the table above, what is the probability that a student chosen at random is a freshman? (A) 0.14 (B) 0.25 (C) 0.27 (D) 0.55 (E) 1.00 5. For the triangle above, which of the following is an expression for x, in terms of a and ������? (A) � �������� ������ (B) � ��� ������ (C) �������� ������ ������ (D) � ��� ������ (E) �������� ������ ������

# 24 3 6. Which of the following is a root of the equation �3−5.5�2+ 8�− 3.5= 0? (A) 2.7 (B) 1.0 (C) 0 (D) –1.0 (E) –3.5 7. If (�− �)2= 4, which of the following could be a value of 3( x – y)? (A) 6 (B) 12 (C) 18 (D) 24 (E) 48 8. If �(�)= 2�,�(�)= 6,and ℎ(�)= �+8 2 , what is the value of ℎ(�(�(4)))? (A) 6 (B) 7 (C) 8 (D) 10 (E) 11 9. In the xy-plane, the graph of which of the following lines is tangent to the graph of � = �2+ 4? (A) � = 2�+ 2 (B) � = 2�+ 3 (C) � = 2�+ 4 (D) � = 2�+ 5 (E) � = 2�+ 6

# 24 4 10. A certain population has 5 members at time �0 and doubles every 23 minutes. If no members of the population die, what is the size of the population 2.3 hour s after time �0? (A) 30 (B) 50 (C) 320 (D) 15,625 (E) 9.8 × 10 6 11. If �(�)= 2�− 3 and �(�(�))= 0,�ℎ�� � = (A) –3 (B) 0 (C) 9 8 (D) 3 2 (E) 9 4 12. In the xy -plane, the graph of � = (�− 32)+ 5 is shifted 2 units to the right. Which of the following is an equation for the resulting graph? (A) � = (�− 3)2+ 7 (B) � = (�− 3)2+ 3 (C) � = (�− 1)2+ 5 (D) � = (�− 5)2+ 5 (E) � = (�− 5)2+ 7

# 24 5 13. After grading 25 test papers, a teacher realized that the two highest scores should both be changed from 95 to 97. If no changes were made to the other scores, which of the following statistics for the scores must remain the same despite the teacher’s error? (A) Mean (B) Median (C) Mode (D) Range (E) Standard dev iation 14. If 5�−8 3�−2= 4, what is the ratio of x to y? (A) 3 to 5 (B) 5 to 3 (C) 12 to 5 (D) 3 to 1 (E) 4 to 1 15 . How is the volume of a cone affected if the radius of its base is doubled and its height is unchanged? (A) The volume is multiplied by 8 (B) The volume is multiplied by 4 (C) The volume is multiplied by 2 (D) The volume is multiplied by 4 3 (E) The volume is multiplied by 2 3

# 24 6 ℎ(�)= −4.9�2+ ��������+ ℎ0 16. The function h above gives the height, in the meters, of an object propelled vertically for time t seconds, where t ≥ 0. The object’s initial velocity, �������, is 107 meters per second and its initial height ℎ�, is 15.6 meters. What is the maximum height of the object? (A) 107.0m (B) 170.3m (C) 492.3m (D) 519.0m (E) 599.7m 17. Where defined, ��� 2�− ��� 2� = (A) 0 (B) 0.5 (C) 1 (D) 2 (E) 4 18 . If x and y are positive real numbers and � = �2.6, then log y = (A) log (2.6 x) (B) 2.6 + log x (C) log2.6 + log x (D) (2.6)(log x) (E) (log2.6)(log x) 19. In the xy -plane, the distance between the points (3, –5) and ( x, –8) is 7. Which of the following is a possible value for x? (A) –3.32 (B) –1 (C) 4.41 (D) 7.95 (E) 10.62

# 24 7 20. If x is the radian measure of an acute angle and sin (5������ 12 − �)= √2 2, then x = (A) 2������ 3 (B) ������ 3 (C) ������ 4 (D) ������ 6 (E) ������ 12 21. In the xy -plane, the point (2, 1) lies outside of which of the following circles? (A) (�− 2)2+ (�− 1)2= 9 (B) (�− 2)2+ (�+ 1)2= 4 (C) (�− 2)2+ (�+ 1)2= 16 (D) (�− 2)2+ (�+ 2)2= 4 (E) (�− 2)2+ (�+ 2)2= 9 22. If �(�)= 4(3)−2�+ 7�(3)−2�, how many times does the graph of � = �(�) intersect the x-axis? (A) None (B) One (C) Two (D) Three (E) Four 23. What is the least positive integer n for which each of � 3, � 5, � 6, and � 9 is an integer? (A) 9 (B) 23 (C) 2•3•5 (D) 2•5•9 (E) 3•5•6•9

# 24 8 24. The volume of a right circular cylinder is 250. If the height of the cylinder is 4, what is the radius of the cylinder? (A) 3.86 (B) 4.46 (C) 4.97 (D) 9.95 (E) 19.89 25. How many real numbers are solutions of the equation 2�2− �+ 3= 0? (A) None (B) One (C) Two (D) Three (E) Four 26. Which of the following functions has the graph shown in the figure above? (A) �(�)= x2 �2+3 (B) �(�)= x2+3 �2 (C) �(�)= x2 �2−3 (D) �(�)= 3x2 �2+1 (E) �(�)= x2 �3+3

# 24 9 27. When a certain ball is dropped, the height reached on each bounce is 75 percent of the height of the previous bounce. If the height reached on the first bounce is 125 centimeters, what height should be reached on the fifth bounce? (A) 0.49cm (B) 29.66cm (C) 39.55cm (D) 79.10cm (E) 93.75cm 28. In the xy -plane, triangle ABC has vertices A(2,1), B(5,5), and C(15,1). Triangle DEF has vertices whose x- and y-coordinates are each 3 times those of triangle ABC . The area of triangle DEF is how many times the area of triangle ABC ? (A) 3 (B) 4 (C) 4.5 (D) 6 (E) 9 29. How many terms are there in an arithmetic sequence whose first two terms are 3 and 7 and whose last term is 55? (A) 14 (B) 13 (C) 12 (D) 11 (E) 7

# 24 10 30. If the two periods of the periodic function f are shown in the figure above, what is f(186)? (A) –2 (B) –1 (C) 0 (D) 1 (E) 2 �+ � � � � 31. If each variable in the expression above represents a positive number, which of the following operations, taken alone, will have the effect of reducing the value of the entire expression to 1 2 of its original value? I. Dividing c by 2 II. Dividing e by 2 III. Multiplying f by 2 (A) I only (B) II only (C) III only (D) I and III (E) II and III

# 24 11 32. In △ ��� , the measure of ∠� is 102º, the measure of ∠� is 23º, and the length of side RS is 575. What is the length of side ST ? (A) 230 (B) 483 (C) 573 (D) 687 (E) 1,442 33. At time t = 0, a game commission introduced 50 deer into a new state park. The deer population, P, is given by P = 10(5+3�) 1+0.04�, where t is the number of years since the deer were introduced. What value does P approach as t gets infinitely large? (A) 50 (B) 75 (C) 750 (D) 1,250 (E) 3,000 34. If tan x = tan y and 0 < x < ������ 2, which of the following could be a value of y? (A) ������ 2+ � (B) ������− � (C) ������+ � (D) 3������ 2 + � (E) 2������ − �

# 24 12 35. The faces of each of two regular octahedrons are numbers from 1 through 8. In a single throw of the two octahedrons, what is the probability that the sum of the numbers on the two top faces will be 13? (A) 1 4 (B) 1 8 (C) 1 16 (D) 1 32 (E) 1 64 36. Let f be a polynomial function such that the graph of y = f (x) in the xy -pla ne contains the points ( –2,–2), (–1,4), and (2,1). Which of the following must be true about the zeros of f? (A) f has a zero between x = –2 and x = –1 (B) f has a zero between x = –1 and x = 2 (C) f has no zeros (D) f has exactly on zero (E) f has exactly two zeros 37. The diagonals of a square graphed in the xy -plane intersect at the origin. All four vertices of the square lie on the coordinate axes. If the sum of the lengths of the two diagonals is 34.78, what is the sum of the x- coordinates of the vertices of the sq uare? (A) –34.78 (B) –17.39 (C) 0 (D) 17.39 (E) 34.78

# 24 13 38. If f and g are polynomial functions defined for all real numbers and f(x) = g(x)(x – 2) + r for all x, then r = (A) f(–2) (B) f(–1) (C) f(0) (D) f(1) (E) f(2) 39. In the figure above, tan x equals which of the following? (A) sin y (B) cos z (C) tan y (D) cot y (E) tan z 40. The even integers from 2 through 98, inclusive, excluding those that are multiples of 10, are multiplied together. What is the units digit of the result ing product? (A) 0 (B) 2 (C) 4 (D) 6 (E) 8 41. If cot x = 7 8, what is the value of cot4 x? (A) 0.27 (B) 0.29 (C) 0.85 (D) 3.5 (E) 3.67

# 24 14 42. If a, b, and c are distinct real numbers, which of the following could be the graph of � = (�− �)(�− �)(�− �)? (A) (B) (C) (D) (E)

# 24 15 43. In the xy -plane, the graph of y = f(x) is symmetric with respect to the y-axis. Which of the following is tru e? (A) �(−�)= −�(�) (B) �(−�)= �(�) (C) �(�)= −�(�) (D) �(�)= |�(�)| (E) �(�)= −|�(�)| 44. The mean height of the students in class A is equal to the mean height of the students in class B, but the standard deviation of the heights for class A is less than the standard deviation of the heights for class B. If both classes have the same number of students, which of the following must be true? I. The heights of the students in class A are more closely grouped about the mean height than are the heights of the students in class B. II. The median height for class A is less than the median height for class B. III. The range of the heights for c lass A is less than the range of the heights for class B. (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III

# 24 16 45. A great circle is a circle on a sphere whose diameter is the same as the diameter of the sphere . In the figure above, B is a point on a great circle of the sphere centered at O, and A is a point not on this great circle. How many great circles of the sphere contain both A and B? (A) None (B) One (C) Two (D) Three (E) More than three 46. If cos A = 2 5 and ������ < ������ < 2������, what does tan A equal? (A) 2.29 (B) 0.92 (C) –0.92 (D) –2.14 (E) –2.29 47. A box with a square base and no top must have a volume of 8 cubic meters. The materials cost $8 per square meter for the base and $6 per square meter for the sides. To the nearest dollar, what is the minimum cost for the materials need ed to make the box? (Disregard any overlap of materials) (A) $50 (B) $126 (C) $138 (D) $158 (E) $174

# 24 17 48. Any positive integer greater than 1 can be expressed as a product of powers of distinct primes each greater than 1. When each of the following numbers is expressed in this form, the expression for which of these numbers will contain the greatest exponent? (A) 60 (B) 64 (C) 81 (D) 100 (E) 125 49. A surveyor who wanted to calculate the area of a triangular plot of land measured two sides of the plot as 486 feet and 748 feet and measured the angle between these two sides as 71.3º. What is the area of the triangular plot, in acres? (1 acre = 43,560 square feet) (A) 1.3 (B) 3.4 (C) 4.0 (D) 4.2 (E) 8.3 50. If x varies directly as the positive square root of y and if x = 1.2 when y = 0.9, what is the value of y when x = 1.5? (A) 1.01 (B) 1.13 (C) 1.19 (D) 1.26 (E) 1.41

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