2o o o o o o o o MATHEMATICS TEST 60 Minutes — 60 Questions Directions: Solve each of the following problems, select the correct answer, and then fill in the corresponding space on your answer sheet Don’t linger over problems that are too time-consuming Do as many as you can, then come back to the others in the time you have remaining Note: Unless otherwise noted, all of the following should be assumed Illustrative figures are not necessarily drawn to scale All geometric figures lie in a plane The term line indicates a straight line The term average indicates arithmetic mean If 5x + = –17, then x = ? A –25 –7 C D –4 E John wants to make fruit salad He has a recipe that serves people and uses oranges, pears, 10 apples, and dozen strawberries If he wants to serve 18 people, how many pears will John need? F G H J K DO YOUR FIGURING HERE B 10 15 20 25 What is the greatest integer that is a factor of both × 10 and × 10 ? A B C D E × × × × × 10 10 10 10 10 232 GO ON TO THE NEXT PAGE 2o o o o o o o o What is the area of the rectangle in the standard (x, y) coordinate plane shown in the figure below? y x F G H J K 5 10 12 14 A costume designer wants to put a white silk band around a cylindrical top hat If the radius of the cylindrical part of the top hat is inches, how long, in inches, should the white silk band be to just fit around the top hat? A B C D E DO YOUR FIGURING HERE 8π 25 π 50 π 100π 200π A large jar holds 48 olives while a small jar only holds 32 olives Which of the following expressions represents the number of olives needed to fill x large jars and y small jars? F G H J K 48x + 32y y x 48 + 32 xy 80 80xy 1536 xy 233 GO ON TO THE NEXT PAGE 2o o o o o o o o If f (x) = 3x2 + 4, f (x + 1) = ? A B C D E DO YOUR FIGURING HERE x+ 4 2x + 6x + 55 + 35 + 11 =? F G H J K 3x2 + 3x2 + 3x2 + 3x2 + 3x2 + 11 17 19 24 10 24 10 10 19 24 Jimmy's school is 10 miles from his house, on the same street If he walks down his street directly from the school to his house he passes a candy store and a grocery store The candy store is 2.35 miles from the school and the grocery store is 3.4 miles from the candy store How many miles is it from the grocery store to Jimmy's house? A B C D E 3.75 4.25 4.75 5.25 5.75 234 GO ON TO THE NEXT PAGE 2o o o o o o o o 10 Harry is a piano student who can learn new pieces in a week If his piano teacher gives him new pieces every week for weeks, how many weeks will it take Harry to learn all these pieces? C Exactly two sides are the same length D One angle measures 90° E One angle measures more than 90° DO YOUR FIGURING HERE F G 7.5 H J 12 K 15 11 In ∆ DEF below, the measure of ∠ EDF is 35° and the measure of ∠ DFE is 65° What is the measure of ∠ DEF ? F D A B C D E 12 35° 45° 75° 80° 100° Randy scored 150, 195, and 160 in bowling games What should she score on her next bowling game if she wants to have an average score of exactly 175 for the games? F G H J K 13 E 205 195 185 175 165 Which of the following best describes a triangle in the standard (x, y) coordinate plane with vertices having coordinates (0, 0), (3, 5), and (0, 2)? A All three angles measure less than 90° B All three sides are the same length 235 GO ON TO THE NEXT PAGE 2o o o o o o o o 14 What is the sum of the solutions of the equation 2y – 4y – = ? F – G –2 H –1 J K 15 Which of the following is the decimal equivalent of ? A B C D E 16 1.125 1.120 0.875 0.870 0.625 June, Maria, and Billy each have a collection of marbles June has 20 more marbles than Billy, and Maria has times as many marbles as Billy If all together they have 100 marbles, how many marbles does Billy have? F G H J K 17 DO YOUR FIGURING HERE 16 20 25 30 32 The equation 3x – 2y = can be graphed in the standard (x, y) coordinate plane What is the y–coordinate of a point on the graph whose x–coordinate is ? A 11 B C D E –11 236 GO ON TO THE NEXT PAGE 2o o o o o o o o 18 In the figure below, parallel lines r and s are cut by transversal t The measure of ∠ p is 20° less than three times the measure of ∠ q What is the value of p – q ? G H J K t 20 23 25 37 DO YOUR FIGURING HERE p r q s F 80° G 90° H 100° J 130° K 160° 19 Which of the following systems of equations does NOT have a solution? A x + y =19 3x + y = B x + y =19 x – 3y =13 C x – 3y = 3x – y = D x – 3y =19 3x + y = E x + y = 3x + y = 20 In the figure below, L, M, R, and S are collinear LS is 50 units long; MS is 38 units long; and MR is 13 units long How many units long is LR ? L M R S F 13 237 GO ON TO THE NEXT PAGE 2o o o o o o o o 21 If 33 % of t is 9, what is 133 % of t ? 3 A B C D E 22 12 18 27 36 42 DO YOUR FIGURING HERE In ∆ DEF below, DE = and DF = What is the value of tan x ? D x F F E 2 G H J K 23 A circle with center at the origin and radius is graphed in the standard (x, y) coordinate plane Which of the following is NOT a point on the circumference of the circle? A B C D E (7, 0) (–3, 10 ) ( , 3) (0, –7) (– 26 , – 23 ) 238 GO ON TO THE NEXT PAGE 2o o o o o o o o 24 Points A and B have integral coordinates in the standard (x, y) coordinate plane below What is the product of the y–coordinates of A and B ? y G H J K –10 –5 15 33 DO YOUR FIGURING HERE -5 –4 –3 –2 –1 –1 –2 –3 B –4 –5 A x F 12 G H –2 J –6 K –12 25 In the figure below, line m is parallel to line n, point A lies on line m, and points B and C lie on line n If ∠ BAC is a right angle, what is the measure of ∠ y? A m 46° B C n y A 54° B 90° C 124° D 136° E 154° 26 If s = –3, then s3 + 2s2 + 2s = ? F –15 239 GO ON TO THE NEXT PAGE 2o o o o o o o o 27 For all r, s, t, and u, r(t + u) – s(t + u) = ? A B C D E 28 (r + s)(t + u) (r – s)(t – u) (r + s)(t – u) (r – s)(t + u) DO YOUR FIGURING HERE In the figure below, ∠ ABC is a right angle and DF is parallel to AC If AB is units long, BC is units long and DB is units long, what is the area in square units of ∆ DBF ? A D B F G H J K 29 F C 12 16 24 48 What is the value of cos 225° ? A − 22 B − 33 C − D E 22 240 GO ON TO THE NEXT PAGE 2o o o o o o o o 30 In triangle ∆ XYZ below, XS and SZ are and 12 units long, respectively If the area of ∆ XYZ is 45 square units, how many units long is altitude YS ? Y X K A = π r(r + s) DO YOUR FIGURING HERE 12 Z S F G H J 12 K 15 31 In the figure below, O is the center of the circle, C and D are points on the circle, and C, O, and D are collinear If the length of CD is 10 units, what is the circumference, in units, of the circle? C D O A 10π B 20π C 25π D 40π E 100π 32 The formula for the surface area of a right circular cone, including the base, is A = π rs + π r2, where A is the surface area, r is the radius, and s is the length from the vertex to the edge of the cone Which of the following represents an equivalent formula for A ? F G H J A = π rs A = π r2s A = π r(1 + s) A = π r2(1 + s) 241 GO ON TO THE NEXT PAGE 2o o o o o o o o 33 What is the slope of the line determined by the equation 5x + 3y = 13 ? DO YOUR FIGURING HERE A –15 B − C − D 5 E 34 Given any two real numbers a and b, which of the following is true about the quantity a−b+ b− a? F G H J K 35 It is always equal to an integer It is positive if b > a It is always positive It is negative if a = b It is always real One of the solutions of the equation x2 – 7x + = is x = – 17 What is the other solution? A − – 17 B –7 –2 17 C –7 +2 17 D – 17 + 17 E 36 How many units long is one of the sides of a square that has a diagonal 20 units long? F G H J K 10 10 15 20 15 242 GO ON TO THE NEXT PAGE 2o o o o o o o o 37 For all a, (3a – 4)(a + 2) = ? A B C D E 38 F G H J K 3a2 – 3a2 + 7a – 3a2 + 2a – 3a2 – 2a – 3a2 + 5a – 40° 50° 60° 70° 80° DO YOUR FIGURING HERE The midpoint of line segment AC in the standard (x, y) coordinate plane has coordinates (4, 8) The (x, y) coordinates of A and C are (4, 2) and (4, s), respectively What is the value of s ? F G H 10 J 12 K 14 39 In a group of numbers, the second number is less than times the first number, and the third number is more than twice the first If s represents the first number, which of the following expressions represents the sum of the three numbers in terms of s ? A B C D E 40 5s 5s + 6s + 7s – 7s + In the figure below, line PQ intersects ∆ ABC at points E and D ∠ B measures 80°, ∠ SAB measures 130° , and ∠ CDQ measures 110° What is the measure of ∠ DEC? B P 80° E 130° S A D 110° C Q 243 GO ON TO THE NEXT PAGE 2o o o o o o o o 41 Jack bought a painting for $200 A year later a friend bought it from him for $170 What percent of the original price did Jack lose in the overall transaction? A B C D E 42 DO YOUR FIGURING HERE 10% 12% 15% 22% 25% Which of the following is the set of all values of x such that ≤ x ≤ π and cos x = − ? π 5π F { , } 6 π 5π G { , } π 3π H { , } 2 2π 4π J { , } 3 2π 5π K { , } 3 43 The roots of the equation 5x2 + 2x – = are x = and x = ? A –7 B − C –1 D E 244 GO ON TO THE NEXT PAGE 2o o o o o o o o 44 H m is positive and b is negative J Either m or b must equal K m and b are both negative In the figure below, PS is parallel to QR , and PR intersects SQ at T If the measure of ∠ PST is 65° and the measure of ∠ QRT is 35° , then what is the measure of ∠ PTQ ? P DO YOUR FIGURING HERE Q T R S F G H J K 45 Ms Rodriguez leaves her office and drives east At the same time, Ms Green leaves the same office and drives west at a rate of speed which is 15 miles per hour faster than Ms Rodriguez At the end of hours, the two cars are 475 miles apart How many miles were traveled by the faster car? A B C D E 46 35° 75° 90° 100° 115° 200 250 275 300 350 Line l is graphed in the standard (x, y) coordinate plane as shown below If the equation for line l is written in the form y = mx + b, which of the following is true about m and b ? y l x F m and b are both positive G m is negative and b is positive 245 GO ON TO THE NEXT PAGE 2o o o o o o o o 47 Which of the following must be true of the fraction x if y < x , and xy ≠ ? y2 DO YOUR FIGURING HERE A B C D E 48 x y2 x2 y2 x2 y2 x2 y2 x2 y2 must be greater than or equal to must be greater than could equal must be less than cannot equal What is the value of a2 – 2ab + b2 if a – b = 12 ? F G 24 H 48 J 144 K 288 49 In ∆ DEF, x represents the measure of ∠ EDF The measure of ∠ DEF is 30° greater than the measure of ∠ EDF, and the measure of ∠ EFD is 15° less than the sum of the measures of ∠ EDF and ∠ DEF Which of the following expressions represents the measure of ∠ EFD ? A –2x + 15° B –x + 15° C x + 15° D 2x – 15° E 2x + 15° 246 GO ON TO THE NEXT PAGE 2o o o o o o o o 50 In the figure below, CD is parallel to AB , and PQ intersects CD at R and AB at T If the measure of ∠ CRP = 110° , then what is the measure of ∠ ATQ? B D DO YOUR FIGURING HERE P R 110° T Q A C F 30° G 50° H 70° J 90° K 110° 51 If x = sin q, y = cos q, and z = tan q, then x2 + y = ? A B C D E 52 z2 (x + y)2 2y Line T in the standard (x, y) coordinate plane has y– intercept –3 and is parallel to the line determined by the equation 3x – 5y = Which of the following is an equation for line T ? F y = − x + G y = − x – 3 H y = x + J y = x + 3 K y = x – 247 GO ON TO THE NEXT PAGE 2o o o o o o o o 53 On the number line below, what is the distance from A to B ? A B x DO YOUR FIGURING HERE -5 -4 -3 -2 -1 A B C D E 18 54 In the standard (x, y) coordinate plane shown in the figure below, points A and B lie on line m, and point C lies below it The coordinates of points A, B, and C are (0, 5), (5, 5), and (3, 3), respectively What is the shortest distance from point C to line m ? y A B m C x F G H J K 55 2 13 Which of the following inequalities is equivalent to –2 – 4x ≤ –6x ? A B C D E x ≥ –2 x≥ x≥ x ≤ –1 x≤ 248 GO ON TO THE NEXT PAGE 2o o o o o o o o 56 In the figure below, each corner of the polygon is a right angle What is the area of the polygon? H 20% J 25% K 30% DO YOUR FIGURING HERE 10 F G H J K 57 50 56 62 72 80 In the standard (x, y) coordinate plane shown below, two circles of the same radius r are enclosed by rectangle ABCD Which of the following expressions is equal to a – b ? y D (0,b) C (a,b) r A A B C D E 58 (0, 0) r r B (a,0) x –r r 2r 4r Each one of the 60 teenagers in an after school club is 14, 15, 16, 17 or 18 years old 20 teenagers are 15 years old, are 18 years old, and 20% are 14 years old There are twice as many 16 year–olds as there are 18 year–olds What percent of the teenagers are either 17 or 18 years old? F 10% G 15% 249 GO ON TO THE NEXT PAGE 2o o o o o o o o 59 Darryl has blue t–shirts and orange t–shirts If he picks one t–shirt at random, what is the probability that it will NOT be blue? A B C D E 60 DO YOUR FIGURING HERE 12 12 What is the equation of the ellipse graphed in the standard (x, y) coordinate plane below? y (0,2) (–5,0) (5,0) x (0,–2) F G H J K x2 25 x2 25 x2 25 x2 25 x2 20 y2 + =1 y2 – y2 – y2 + y2 + =1 =1 =1 =1 250 STOP! END OF SECTION 2! DO NOT TURN TO ANY OTHER SECTION! ... What is the measure of ∠ DEF ? F D A B C D E 12 35° 45° 75° 80° 100° Randy scored 150, 195, and 160 in bowling games What should she score on her next bowling game if she wants to have an average... value of p – q ? G H J K t 20 23 25 37 DO YOUR FIGURING HERE p r q s F 80° G 90° H 100° J 130° K 160? ? 19 Which of the following systems of equations does NOT have a solution? A x + y =19 3x + y... 4)(a + 2) = ? A B C D E 38 F G H J K 3a2 – 3a2 + 7a – 3a2 + 2a – 3a2 – 2a – 3a2 + 5a – 40° 50° 60? ? 70° 80° DO YOUR FIGURING HERE The midpoint of line segment AC in the standard (x, y) coordinate