4. If (x h)(x + k) = x 2 16, what is the value of h + k? (A) 8 (B) 4 (C) 0 (D) 4 (E) 8
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1 1. In the figure below, the graph of y = kx 2 intersects triangle C at. If = C and the area of triangle C is 6, what is the value of k? y = kx 2 4. If (x h)(x + k) = x 2 16, what is the value of h + k? () 8 () 4 (C) 0 (D) 4 (E) 8 ( 1,0) C (,0) For all n, let n be defined as n = n 2 n 2. If a and b are positive integers and a b, which of the following could be true? I. (a + b) is even. II. (a + b) is odd. III. (a b) is negative.. The graphs of two linear functions, f and g, are perpendicular. If f (2) = 4 and f ( 4) = 1, which of the following could define g? portion of the graph of the function h is shown in the xy-plane above. If h(4) h(s) = 4, which of the following could be the value of s? () 2 () 0 (C) 1 (D) 4 (E) 7 () g(x) = 1 2 x + 4 () g(x) = x + 1 (C) g(x) = 2x + 4 (D) g(x) = 2x (E) g(x) = x + 5 1
2 Q 9. The value of an investment increased by 20 percent to $800 by the end of the first week. To the nearest dollar, what was the value of the investment at the beginning of the week? O P In the figure above, three identical circles of radius 8 with centers O, P and Q are tangent to each other. What is the area of the shaded region bound by the circles? y = f (x) y = g(x) 7. The participants in a certain community service club come from all four grade levels in Smithville High School. There are equal numbers of sophomores and juniors. The number of seniors is twenty more than twice the number of sophomores and juniors combined, and there are 20 freshmen. If the number of sophomores, juniors and seniors combined accounts for 80 percent of the club s participants, how many seniors are there in the club? The figure above shows the graphs of the functions f and g. If g is defined in terms of a transformation of f such that g(x) = f (x+h)+k, what is the value of h k? 8. For integers a and b where a > 0 and b 0, let the operation be defined as a b = ab. Which of the a following could be the value of a b? I. a b a For all x and y, let the operation x y be equal to the whole number remainder obtained when finding 2x y. If s is an even integer and the value of 7 s = 2, what is a possible value of s? II. 0 III. 1 2
3 O 0º P S E R Q 12. In the figure above, OPQR is a square, and PS is the arc of a circle with center O. If the length of arc PS is π, the area of the shaded sector is what fraction of the area of OPQR? ( 1,0) D C () π 2 () π In the figure above, rectangle CD lies on the coordinate plane with point D located at the origin. If = E = ED, what is the area of quadrilateral CDE? (C) π 8 (D) (E) π 12 π Jack drove to work in the morning at an average speed of 45 miles per hour. He returned home in the evening along the same route and averaged 0 miles per hour. If Jack spent a total of one hour commuting to and from work, how many miles did he drive to work in the morning? 14. student is weighing large and small marbles. While weighing one large marble with 8 small marbles, the student discovers that the large marble s weight is 5 times the average (arithmetic mean) of the weight of the small marbles. The large marble s weight is what fraction of the total weight of the 9 marbles? 105º C 150º F Note: Figure not drawn to scale. 16. In the figure above, triangle C and parallelogram CDEF are constructed with, C, and F along the same line. If the ratio of CF : C = 1 : 2 and DE = 2, what is the area of triangle C? () 2 () 6 (C) 6 2 (D) 6 (E) D E
4 17. The function f is defined as f (x) = (x n)(x + m) for all values of x. If the function g is defined as g(x) = f (x) +, what is the y-intercept of the graph of g in terms of n and m? () n + m () n m (C) nm (D) nm (E) nm 20. Triangle C has side lengths, 8, and a. Triangle DEF has side lengths 7, 10, and d. If a and d are both integers, what is the smallest possible value of (d a)? () 10 () 8 (C) 6 (D) 0 (E) 5 a, b, b a, a, In the sequence above, each term after the first two is obtained by finding the difference between the two previous terms. If a = and b = 4, what is the sum of the first 200 terms of this sequence? 21. n antique coin collector has a number of coins and several display cases. If he puts one coin in each case, there are four coins left out of the cases. If instead he puts three coins in each case, all coins are placed, and there are six empty cases left over. How many coins does the collector have? g(x) = x 2 + c h(x) = g(x 5) + Start 19. The equations of two functions, g and h, are shown above, where c is a constant integer. If the graph of h has two solutions, what is the maximum possible value of c? xº () 5 () 4 (C) (D) 1 (E) Stop 22. small circle,, is rolled around the circumference of a larger circle,, as shown in the figure above. Circle starts at the position indicated Start and makes two complete rotations, coming to rest at the position marked Stop. If the ratio of the areas of to is 1 to 25, what is the value of x? 4
5 2. When the positive integer w is divided by 6, the remainder is. When the positive integer x is divided by 7, the remainder is 5. How many possible values of wx are there such that wx < 500? 24. For their senior class trip, all seniors at Smithville High School chose between going to an amusement park and seeing a theater performance. If 20 more than 40 percent of the seniors chose to go to the amusement park and the remaining 160 students chose to go to the theme park, how many total seniors went on the senior class trip? 25. Mr. Halyard has forgotten two of the numbers in the 5-digit zip code of his son s mailing address. He remembers that the digits -8-7 appear together, in that order, somewhere within the zip code, and that a zero does not appear in the remaining digits. If he guesses at random, what is the probability that Mr. Halyard will write the correct zip code on a package he is mailing to his son? 26. Let the operation j k be defined as good if the set of all prime factors of j includes all numbers in the set of prime factors of k. Which of the following is NOT good? 27. In a store, the list price of one item is x dollars, and the list price of another is y dollars. If a discount of p percent is offered for the first item and a discount of q percent is offered for the second item, which of the following gives the total percent discount off of the original total price when both items are purchased at their respective discounted prices? () x + y (p + q) % ( ) (1 p)x + (1 q)y () x + y % 100 x + y ( p + q ) (C) 100 % 100 (D) px + qy x + y % (E) xy pq 100 % 28. In Marksville Elementary School, 40 classrooms do not have computers, and 25 percent of all rooms with computers do not have a white board. If rooms with computers represent two-thirds of all classrooms in the school, and if 50 of the classrooms do not have a white board, how many classrooms with a white board do not have computers? () () (C) 12 4 (D) (E)
6 2. If 40x + 7y = 66 and x and y are positive integers, which of the following is a possible value of xy? y = h(x) () 500 () 620 (C) 70 (D) 810 (E) In the graph of the function h shown above, h(0) = 2. If r and s are integers and h(r) = 2h(s), which of the following are possible values of s? I. 0 II. 1 III. 5 () I only () II only (C) III only (D) I and II only (E) I, II, and III x ay = 11 x + 4y = 6 D Note: Figure not drawn to scale.. In the figure above, points and D lie on the circumference of the circle with center O, circumference c and radius r. If the area of triangle O is equal to the area of the circle, then in terms of c and r, what is the area of triangle D? O 0. For which of the following values of a will the system of equations above have no solution? () 12 () 6 (C) 0 (D) 6 (E) oth a and b are positive integers less than 0. If the sum of a and b is even, what is the smallest possible () 1 4 cr () 1 2 cr (C) cr (D) 2cr (E) 4cr value of a b? 6
7 4. For a certain exam, the base score is calculated as the difference between the number of questions answered correctly, c, and one-third the number of questions answered incorrectly. If there are q questions on an exam and Lynn left b questions unanswered, which of the following expressions gives the base score for Lynn s exam? () c 1 (q b) () c 1 (q b c) (C) c + b 1 (q c) (D) c + b 1 (q + b c) (E) c 1 (c + b q) 6. The warehouse at Paper Supply Unlimited must keep an inventory that ranges between 5000 and 7500 reams of paper. If r is the number of reams of paper in the warehouse, which of the following must be true? () r () r (C) r (D) r (E) r drawer contains only blue pens. When red pens are added, the fraction of blue pens in the drawer decreases to 4. How many red pens must be added 5 to the drawer so that blue pens account for one-third the final number of all pens in the drawer? O m C 5. The graph above shows circle O with center at (1, 2). Line m has equation y = x + 6, and is 2 tangent to the circle at point. If point is directly across from and has coordinates (x, y), what is the 8. In the figure above, three-fourths of a circle s arc is drawn from and C, and right triangle C is isosceles. If C = 10 2, what is the perimeter of the figure outlined by the solid line? value of y x? 7
8 C D 42. What is the maximum number of intersection points of a circle with radius r and a square with side length 2r? () 2 () 4 (C) 5 (D) 6 (E) 8 9. The figure above shows a small square with diagonal C within a large square with diagonal D, and,, C, and D are collinear. If the ratio of : C : CD is 1 : 2 : 1, what is the ratio of the area of the small square to the area of the shaded region? x y = y 2 x > 0 y > If the statements above are true and y is a prime integer, what is the smallest possible integer value of x? 41. The quadratic function h is given by h(x) = ax 2, where a is a positive constant. If h(m) = h(n) for some values of m and n, which of the following could be true? I. m = n II. m = n III. h(m) = h( n) () I only () II only (C) III only (D) I and II only (E) I and III only 4. If 4s 6w = 2t + 18 and w 2s = 5 + t, what is the value of t? () 7 () (C) 0 (D) 4 (E) The average of a set of five positive integers is a. When the number 9 is added to the set, the average of the numbers increases by 1. What is the value of a? () 12 () 9 (C) 8 (D) (E) cylindrical tank with a base radius of feet and height of 12 feet is filled with water to two-thirds of its capacity. The water is then transferred to a larger cylindrical container with a base radius of 2 feet. What is the height of the water, in feet, in the the larger container? 8
9 r t 49. To make a cran-apple juice, parts of cranberry juice are mixed with 2 parts of apple juice. To make an apple-pomegranate juice, 2 parts of pomegranate juice are mixed with 1 part of apple juice. If equal amounts of cran-apple and apple-pomegranate juice are mixed, what fraction of the new mixture is apple juice? () 16 Note: Figure not drawn to scale. 46. In the figure above, a circular track is shown. The outside of the track is a distance r meters from the center, and the inside of the track is t meters from the center. If the area of the shaded portion of the track shown is 28π square meters and t = r, what 4 is the value of t? () 1 4 (C) 11 0 (D) 8 (E) Of 5 members of a high school club, are to be assigned to the finance committee and 2 are to be assigned to the activities committee. If of the members are seniors and 2 are juniors, and if those assigned to the finance committee are to be chosen at random, what is the probability that the finance committee assignments will be given to 2 of the seniors and 1 of the juniors? () 1 () For a poll, 72 people were asked about two models of a car, and. Of the people polled, 8 have owned model, 42 have owned model, and 10 have owned neither model. How many of the people polled have owned both models? 51. In choosing a color scheme for her living room, Julia must pick 2 colors from a list of 6 available paint colors. How many different two-color schemes are available for Julia to use for painting her living room? (C) 1 2 (D) 5 (E) If x 2 = y 6 and x 8 = y t, what is the value of t? 9
10 O xº P 20º m P Q 52. In the figure above, the circle has center O and radius r, and triangle OPQ is equilateral. If the area of the shaded region is 120π and PQ = r, what is 2 the area of triangle OPQ? 5. There are blue and red shirts on a clothing display. If 15 of the shirts are blue and x of the shirts are red 7 where x is an integer, what is the minimum number of shirts that could be on display? () 17 () 18 (C) 19 (D) 20 (E) 21 Note: Figure not drawn to scale. 54. In the figure above, line m is tangent to a vertex of a regular octagon at point P. What is the value of x? 55. If the function g is defined as g(x) = 2x 2 x and g(t + 1) = 0, what is the value of g(t + 1.5) if t > 0? 56. If a is inversely proportional to the square of b, and a = 4 when b = 8, what is the value of b when a = 16? () 2 () 4 (C) 8 (D) 16 (E) If x, y, and z are positive integers and x z y z = 225, what is the value of xyz? () 90 () 60 (C) 45 (D) 0 (E) 15 10
11 C 60. Some of William s friends arranged to contribute $6 each to buy him a birthday cake. Two of the friends then decided to use their money to buy a different present, and the remaining friends had to contribute an extra $ each to make up the difference for the cost of the cake. How many friends were originally going to contribute to the cost of the cake? 58. The cube above has a side length of x. Point is at the center of the top face of the cube, and points and C are midpoints of the bottom edges of the cube. In terms of x, what is the perimeter of C? () x + x 2 () x + x (C) x + x 5 (D) x + 2x 2 (E) x 61. On his first day reading a book, Henrik reads 1 4 of the book s pages. On the second day, he reads 1 4 of the pages that remain, leaving 189 pages left to read. What is the total number of pages in Henrik s book? 62. On the xy-coordinate plane, lines l and m are perpendicular and intersect at ( 2, 0). If b is the y- intercept of line l and c is the y-intercept of line m, what is the value of bc? 4π () 4 () 2 (C) 1 (D) 1 120º O (E) 4 2, 4, 8, 16, In the figure above, O is inscribed in the circle with center O. If measures 4π and O = 120, what is the length of? 6. In the sequence above, every term after the first is obtained by multiplying the preceding term by 2. The sum of which pair of terms in the sequence is equal to 2 49? () 24 th and 25 th () 25 th and 26 th (C) 48 th and 49 th (D) 49 th and 50 th (E) 50 th and 51 st 11
12 C D x y semicircular window is divided into four equal panes, as shown in the figure above. straight line drawn between points and D (not shown) is 16 feet long. What is the perimeter of one of the panes? () 16 () 2 (C) (16 + 2π) 2 (D) 48 (E) (2 + 2π) 2 F E 67. Given the table of x and y values above, y could be inversely proportional to which of the following? () x () x (C) x 2 (D) x 2 (E) 2 x 65. When the square of a number is raised to 10 times the number, the result is equal to 4 raised to 5 times the number. What is the square of the number? Q (0, b) P (, 2) O 66. In the figure above, OPQ is shown on the xy-plane. What is the value of b? ll problems c Evan Wessler and Method Test Prep, No part of this document may be reproduced, distributed, or otherwise replicated in any form. 12
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