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# 22 1 2�+ � = −1 5�− 2� = 13 1. If (x, y) is the solution to the system of equations above, what is the value of x? (A) 11 9 (B) 4 3 (C) 11 7 (D) 12 7 (E) 2 2. If 0 < x < 1, which of the following has the greatest value? (A) � (B) �2 (C) �3 (D) 1 (E) 1 2 3. What are all possible values of a for which the expression 22−2 �2− 4 is undefined? (A) –2 only (B) –1 only (C) 2 only (D) –2 and 2 (E) –1 and 1

# 22 2 4. If j = x 2, then x4 + 4 x2 – 5 = 0 is equivalent to which of the following? (A) �2+ 4�− 5= 0 (B) �2+ �− 5= 0 (C) �4+ 4�2− 5= 0 (D) �8+ 4�4− 5= 0 (E) �8+ 4� − 5= 0 5. The sum of a number and its positive square root is 12. What is the number? (A) –4 (B) 3 (C) 4 (D) 9 (E) 16 6. If �(�)= +2 −2, what value does f(x) approach as x approaches 3.5? (A) –1.00 (B) –0.43 (C) 0.27 (D) 2.07 (E) 3.67 7. For positive integers n, the nth term of a given sequence is 1 �2+2. For what value of n is the value of the nth term closest to 0.01? (A) 8 (B) 9 (C) 10 (D) 11 (E) 12

# 22 3 8. If 0 ≤ x ≤ 2 and sin x = 0.56, then sin4 x = (A) 0.531 (B) 0.692 (C) 0.784 (D) 2.125 (E) 2.240 9. If �(�)= � −32, what is the value of f(9)? (A) 0.0007 (B) 0.0370 (C) 0.2311 (D) 4.3267 (E) 6.8587 10. In the xy -coordinate system shown above, for what values of x are the corresponding values of y on the graph of the line greater than the corresponding values of y on the graph of the parabola? (A) –2 < x < 2 (B) 0 < x < 3 (C) x < 0 and x > 3 (D) x < 1 and x > 2 (E) x > y

# 22 4 11. If 71−= 21+, what is the value of x? (A) –0.60 (B) –0.26 (C) 0.47 (D) 0.73 (E) 2.25 12. What negative integer is 42 less than its square? (A) –8 (B) –7 (C) –6 (D) –5 (E) –3 13. If f(x) = x2 + 1 for x ≥ 0, then f(√�) = (A) x (B) x + 1 (C) �+ √� (D) �+ √�+ 1 (E) √�2+ 1 14. The product of x2 and its reciprocal when x ≠ 0 is (A) less than –1 (B) equal to –1 (C) equal to 0 (D) equal to 1 (E) greater than 1 15 . If �(�)= 5�2− 2�− 2, then �(�+ ℎ)− �(�)= (A) 3ℎ (B) 5ℎ2− 2ℎ (C) 10 �ℎ− 4�+ 2 (D) 10 �ℎ− 2�− 2 (E) 10 �ℎ+ 5ℎ2− 2ℎ

# 22 5 16. In the xy -plane, a straight line ℓ contains the points (0,0) and (3,4). What is the cosine of the acute angle that makes with ℓ the x-axis? (A) 3 5 (B) 3 4 (C) 4 5 (D) 4 3 (E) 5 3 17. Th e cube in the figure above has edge of leng th 10 centimeters. If △BST is formed by connecting the centers of the top , bott om, and lateral face as shown, what is the perimeter in centimeters of △BST ? (A) 20 (B) 21.21 (C) 24.14 (D) 30 (E) 42.43

# 22 6 18. The figure above shows one cycle of the graph of y = 1 + sin x for 0 ≤ x ≤ 2. If the maximum value of y occurs at U, what are the coordinates of U? (A) ( 4,1) (B) ( 4,2) (C) ( 2,1) (D) ( 2,2) (E) ( 2+ 1,1) 19. If g(x) = x + 1 and f(g(x)) = +1 +3, what is f(x) ? (A) 1 +2 (B) +2 (C) +1 +2 (D) +1 +3+ 1 (E) 1+ 2 20. In the coordinate plane, the circle whose equation is (�− 3)2+ (�+ 1)2= 25 is to be translated 5 units to the right and 2 units down. What is the equation of the translated circle? (A) (�− 3)2+ (�+ 1)2= 74 (B) (�+ 2)2+ (�− 1)2= 25 (C) (�+ 2)2+ (�− 1)2= 74 (D) (�− 8)2+ (�+ 3)2= 25 (E) (�− 8)2+ (�+ 3)2= 74

# 22 7 21. The graphs below sho w the scores on a test for five classes. In which graph does the set of scores have a standard deviation of 0? (A) (B) (C) (D) (E)

# 22 8 22. If sin x = 0.85 and 0 < x < 2, then tan x = (A) 0.53 (B) 0.62 (C) 0.65 (D) 1.18 (E) 1.61 23. For which of the following values of a and c does the equation � 2+ 3�+ = 0 have no real roots? (A) = 1,= 2 (B) = 1,= −2 (C) = −1,= 2 (D) = −3,= 1 (E) = −3,= −1 24. Let 1= {1,2,8}, 2= {−3,0,6}, and 3= {−1,−2,0}. If 1denotes the largest number in �, then the smallest number in set {1,2,3} is (A) –3 (B) –2 (C) 0 (D) 1 (E) 8

# 22 9 25. The figure above shows two buildings. From the top of the municipal building, the angle of elevation to the top of the office building is 40º. If the office building is 380 feet tall and the municipal building is 60 feet tall, what is the distance between the two buildings, to the nearest foot? (A) 498 ft (B) 453 ft (C) 418 ft (D) 381 ft (E) 286 ft 26. Which of the following is NOT in the domain of f(x) = ln(4−3) 5+2 ? (A) − 5 2 (B) –2 (C) 2 5 (D) 3 4 (E) 3

# 22 10 Questions 27 -28 refer to the following situation. In a certain situation, if a piece of cheese is put in a refrigerator to cool, the temperature of the cheese, in degrees Fahrenheit, after t minutes can be modeled by the function C, where �(�)= 55 + 20 �−0.0231 . 27. According to the model, how many minutes after placing the cheese in the refrigerator is the temperature of the cheese 65ºF? (A) 13.03 (B) 30.01 (C) 43.79 (D) 51.02 (E) 59.46 28. Which of the following statements are true according to the model? I. The temperature of the cheese will approach 55ºF over a long period of time. II. The temperature of the cheese is 75ºF when it is first placed in the refrigerator. III. The temperature of the cheese is 50 ºF at some time. (A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III 29. How many distinct four -digit numbers contain the digits 1, 2, 3, and 4 without repetition if the digit 2 is always immediately followed by the digit 3? (A) Four (B) Six (C) Twelve (D) Eighteen (E) Twenty -four

# 22 11 30. The graph of which of the following functions has exactly three distinct x-intercepts? (A) �(�)= (�2− 4)(�+ 2) (B) �(�)= (�2+ 4)(�+ 2) (C) �(�)= (�2+ 4)(�+ 2)2 (D) �(�)= (�2+ 4�+ 4)(�+ 2) (E) �(�)= (�2+ 4�− 4)(�+ 2) 31. One method for finding a given number that is in an ordered list of numbers requires a computer to repeatedly split the list in half until the number is found. For a list of n numbers, the maximum number of splits is the least integer greater than or equa l to �� � 2. What is the maximum number of splits needed to find a given number in a list of 300,000 numbers? (A) 3 (B) 6 (C) 15 (D) 18 (E) 19 32. In the xy -plane, which of the following points lies on the graph of the inequality |�|+ |�|≤ 2? (A) (0,2√2) (B) (−2,1) (C) (1,2) (D) (−1,√2) (E) (1,− √2 2)

# 22 12 33. A right circular cone has a base radius r that is one half the length of its height h. Which of the following gives the volume of the cone in terms of its height? (A) 1 24 ℎ3 (B) 1 12 ℎ3 (C) 1 6ℎ3 (D) 1 4ℎ3 (E) 1 3ℎ3 34. John had a pa ck of cards numbered 1 -50. He shuffled them and drew two cars at random The first card he drew was number 10. He looked at the second card observed that if he drew a third card, the probability was 1 2 that its number would be between the two he had. What was the number of the second card? (A) 25 (B) 30 (C) 34 (D) 35 (E) 40

# 22 13 35. Rectangle ABCD is inscribed in the parabola with equation � = 16 − �2, as shown above. What is the area of ABCD if the coordinates of point D are (2.3, 0)? (A) 114.7 (B) 49.3 (C) 24.6 (D) 12.3 (E) 10.7 36. In which of the following is y a function of x? I. x y –2 –10 0 –1 1 0 –1 1 0 2 II. x y –10 –2 –1 0 0 1 1 –1 2 0 III. x y –2 1 2 –1 1 2 0 1 2 1 1 2 2 1 2 (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III

# 22 14 37. Point C is 6 inches from plane M. To the nearest integer, what is the area, in square inches, of the portion of M that contains all points that are not more than 12 inches from C? (A) 33 (B) 113 (C) 339 (D) 452 (E) 565

# 22 15 38. A portion of the graph of y = f(x) is shown above. Which of the following is the graph of y = –|f(x)|? (A) (B) (C) (D) (E)

# 22 16 39. If �(�)= �−1(�) for all x, which of the following functions could equal f(x)? (A) –x (B) 2 (C) x + 2 (D) lnx (E) 1 +1 40. In the figure above, which of the following could NOT be pol ar coordinates of points P, Q, or R? (A) (0,0) (B) (1,− 4) (C) (1,7 4) (D) (2, 2) (E) (2,3 2) 41. If �(�)= 3�+ 9 and �(�)= �2, what are all values of k such that f(g(3)) = g(f(k))? (A) –1 only (B) 1 only (C) –1 and 1 (D) –5 and –1 (E) 1 and 5

# 22 17 {19.3, 18.5, 29.0, 7.31, 16.1, 22.8, 20.3} 42. The highest elevation of each of the continents, in thousands of feet, is given in the data set above. The interquartile range of the data set is what percent of the range of the data set? (Interquartile range = upper quartile minus lower quartile. Upper/lower quartile is the median of the upper/lower half of the data set, and the median of the data set is not included in either half ). (A) 8% (B) 15% (C) 23% (D) 31% (E) 50% 43. The measure of which of the following sides would be needed to use the law of cosines to calculate the measure of ∠ABC in the triangle above? (A) �� ̅̅̅̅̅only (B) ��̅̅̅̅ and �� ̅̅̅̅̅ only (C) ��̅̅̅̅ and ��̅̅̅̅ only (D) �� ̅̅̅̅̅ and ��̅̅̅̅ only (E) ��̅̅̅̅, ��̅̅̅̅, and �� ̅̅̅̅̅ 44. The number n can be expressed as the product of four prime numbers, exactly three of which are the same. How many different positive divisors does n have, including n and 1? (A) Four (B) Five (C) Six (D) Eight (E) Sixteen

# 22 18 �(�)= cos (2�)+ �� � 45. The function f is defined above. What is the difference between the maximum and minimum values of f? (A) 0.875 (B) 2 (C) 2.5 (D) 3 (E) 3.125 46. A fire alarm system consists of two independent alarms whose probabilities of operating correctly in an emergency are 0.92 and 0.96, respectively. What is the probability that at least one alarm operates correctly in an emergency? (A) 0.997 (B) 0.94 (C) 0.92 (D) 0.883 (E) 0.117 47. If �2− �2= 1 and the value of x – y is between –1 and 0, then the value of x + y must be (A) less than –1 (B) between –1 and 0 (C) between 0 and 1 (D) between 1 and 2 (E) greater than 2 48. If �� 2 �+ �� 2 �+ �� 2 �= 1.716 , what does ��� 2 �+ ��� 2 �+ ��� 2 � equal? (A) –0.716 (B) 0.716 (C) 1.133 (D) 1.284 (E) 4.716

# 22 19 49. In the figure above, f and g are graphed in the xy -coordinate plane. Both functions are defined and increasing on the interval 0 < x ≤ 5. If a > 0, then all of the following statements are true, where x + a ≤ 5, EXCEPT (A) �(�)> 0 (B) �(�)> �(�) (C) �(�+ )> �(�) (D) �(�+ )> �(�) (E) �(�+ )− �(�)> �(�+ )− �(�) 50. The population of doves within a certain forest can be modeled by the equation (�)= 445 − 112 �� (12) where t is the number of months since January 1990. When is the population at its maximum? (A) January of every year (B) January of every even -numbered year (C) January of every odd -numbered year (D) July of every even -numbered year (E) July of every year

# 22 20

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