22 MATHEMATICS TEST 60 Minutes—60 Questions DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test. 1. 2. 3. 4. You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, 3. On a particular road map, _1_ inch represents 18 miles. number of people 1. The blood types of 150 people were determined for a study as shown in the figure below. 70 60 50 40 30 20 10 0 62 Illustrative figures are NOT necessarily drawn to scale. Geometric figures lie in a plane. The word line indicates a straight line. The word average indicates arithmetic mean. 2 About how many miles apart are 2 towns that are 67 2 _12_ inches apart on this map? A. 18 B. 22 _12_ 15 O B A blood type C. 36 6 D. 45 AB E. 90 If 1 person from this study is randomly selected, what is the probability that this person has either Type A or Type AB blood? 4. Given f = cd 3, f = 450, and d = 10, what is c ? F. 000.45 G. 004.5 H. 015 J. 045 K. 150 62_ A. ___ 150 66_ B. ___ 150 68_ C. ___ 150 5. If f (x) = (3x + 7)2, then f (1) = ? A. 010 B. 016 C. 058 D. 079 E. 100 73_ D. ___ 150 84_ E. ___ 150 6. Jorge’s current hourly wage for working at Denti Smiles is $12.00. Jorge was told that at the beginning of next month, his new hourly wage will be an increase of 6% of his current hourly wage. What will be Jorge’s new hourly wage? F. $12.06 G. $12.60 H. $12.72 J. $18.00 K. $19.20 2. The monthly fees for single rooms at 5 colleges are $370, $310, $380, $340, and $310, respectively. What is the mean of these monthly fees? F. $310 G. $340 H. $342 J. $350 K. $380 ACT-1572CPRE 24 GO ON TO THE NEXT PAGE. 00 $20. What is the perimeter of the rectangle.00 $1. C. What is the median of the data in the table? Month Number of cars sold January February March April May June July August September October November December 45° 35° Core subjects 4 hours 25 15 22 19 16 13 19 25 26 27 28 29 F. B. …. E. His teacher said that the numbers of hours listed were correct. 24 K.65 $0. −3. The table below gives the fee and the price per pound for customers shipping boxes of various weights. but that the central angle measures for the sectors were not correct. d = 34t Weight of box (pounds) Fee Price per pound Less than 10 10−25 More than 25 $05. K.03 cm thick and the inner layers are each 0. 13 15 16 52 64 F. K.2 2 7. Antwan drew the circle graph below describing his time spent at school in 1 day. J. $16. −27.00 K. 06 G. In ___the figure below. 0−30 C.50 H. d = 06t + 08 C. the cart was from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds. $09. 8. The length of a rectangle with area 54 square centimeters is 9 centimeters. A computer chip 0. D.32 cm thick is made up of layers of silicon. What should be the central angle measure for the Core subjects sector? 10.02 cm thick. E. Students studying motion observed a cart rolling at a constant rate along a straight line. 30 ___ 13. The table below gives the distance. . What is the SEVENTH term of the geometric sequence? A.00 $10. C. d = 14t + 06 E. J. in centimeters? F. 9.32 cm B A.00 $0. d = 06t + 14 D. 13 16 19 20. $24. 15 J. 081 D. If it can be determined. The table below shows the number of cars Jing sold each month last year. The first term is 1 in the geometric sequence 1.75 G.5 23. A.50 9. 12 H. D. $19. 189 E.5 ACT-1572CPRE 35° C E 080° 100° A 110° 115° Cannot be determined from the given information 14. 729 11. what is the measure of ∠BAC ? D Gregg wants Ship Quick to ship 1 box that weighs 15 pounds. Which of the following equations represents this relationship between d and t ? A. H. If the top and bottom layers are each 0. G. G. What is the shipping rate for this box? F.30 t 00 01 02 03 04 05 d 14 20 26 32 38 44 12. H.75 J. −243 B. d = 00t + 14 B. 25 072° 080° 160° 200° 288° Electives 3 hours Lunch and passing time 1 hour Choir 1 hour GO ON TO THE NEXT PAGE. how many inner layers are there? } 0. d feet. B. The shipping rate for customers of Ship Quick consists of a fee per box and a price per pound for each box. $20. C is the intersection of AD and BE . 5_ 8 F.000. 480 C. 5_ 6 _ J. Past records show that 80% of the applicants pass the written test and 60% of those who have passed the written test pass the driving test. an applicant must pass a written test and a driving test. To get a driver’s license. A car accelerated from 88 feet per second (fps) to 220 fps in exactly 3 seconds. b. 300 K. 6 _5_ 8 _1_ 2 _5_ 6 _1_ 2 1. In scientific notation. C. E.000. 20 B. 133° E. 047° C. What is the fewest number of paintings the artist can sell to make a profit of at least $60. where A is between C and D. H. from 88 fps to 220 fps ? F. Kami sold 70 figurines in 2 sizes.37 × 108 1. J. (180 − x)° G. 100 G.000 applicants would you expect to get driver’s licenses? A. 750 E. then xy = ? ↔ ↔ 17. and _5_ arranged in ascending order? _1_ 2 _ G. 600 19. B. K. 075 _13_ K. x° D C 15. 1_ 00 __ 44 G. the distinct lines AB and CD intersect at A. 094° D. An artist makes a profit of (500p − p 2 ) dollars from selling p paintings. 029 _13_ H. 28 C. acb ac2b (ac)b (ac)2b 2 (ac)b 26 GO ON TO THE NEXT PAGE. . Based on these figures. 35 D. how many applicants in a random group of 1.37 × 109 137 × 1015 ACT-1572CPRE 09xy2 18xy 03xy2 + 12x 09xy2 − 2y3 03xy2 + 12x − y3 − 2y 24.37 × 107 1. and the measure of ∠D is x°. 043° B. How many large figurines did Kami sell this month? A. C. _5_ . B.000 ? F. (180 − 0. In a plane. The measure of ∠BAC is 47°. In which of the following are _1_ . 137° F. 670. (180 + x)° K. 800 16. For trapezoid ABCD shown below. What is the measure of ∠BAD ? A.2 2 ___ ____ 20. 150 H. what was the car’s acceleration. in feet per second per second. 2 6 23. If a. What is the degree measure of ∠A in terms of x ? A B F.5x)° x° J.5x)° H. G.000 + 700. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. AB i DC . 50 21. The large figurines sold for $12 each. This month. 5_ 8 _ K. the measures of the interior angles are distinct. 600 D. D. 5_ 6 _ H. Assuming the acceleration was constant.37 × 10−9 1. and the small figurines sold for $8 each. Which of the following expressions is equivalent to 8 _1_ y2(6x + 2y + 12x − 2y) ? 2 < _5_ < _5_ < < < < 8 _1_ 2 _5_ 8 _1_ 2 _5_ 6 < < < < A. D. (180 + 0.000 = ? A. 200 B. 200 J. and c are positive integers such that ab = x and cb = y. 102 _23_ 22. 044 J. 42 E. E. 18. Solving which of the following equations gives the measure. and c. break the seal on the box. which of the following best describes the solutions for x ? y 755 5_ E. B. H. Last month. D. H. θ = _5_ 7 J. of the angle formed by a slant height of the cone and a radius? $219 entertainment F. to the nearest 1% ? clothes gas $254 $120 A. 07 + 24i 25. Lucie had total expenditures of $900. E. 7 G.2 2 29. ___ 750 5_ D. C. _5_ 6 7_ H. θ = _5_ 08 08 + 08√•2 08 + 16√•2 16 16 + 08√•2 A. What fraction lies exactly halfway between _2_ and _3_ ? 3 O F. What is the product of the complex numbers (−3i + 4) and (3i + 4) ? A. tan. The category in which Lucie’s expenditures were greatest is what percent of her total expenditures. 07 C. The radius of the base of the right circular cone shown below is 5 inches. 25 D. 9_ __ 16 17_ K. b. G. What is the measure of ∠CAD ? B C F.y) coordinate plane below for real values of a. E. H. G. B. whose hypotenuse is 8√•2 inches long? A. . −7 + 24i E. a puzzle company includes 5 extra pieces in the box along with the 750 pieces. C. J. 4 J.θ = _7_ 5 D A 31. The equation y = ax + bx + c is graphed in the standard (x. ___ 750 32. ___ 755 1_ C. When y = 0. __ 12 2 distinct positive real solutions 2 distinct negative real solutions 1 positive real solution and 1 negative real solution 2 real solutions that are not distinct 2 distinct solutions that are not real ACT-1572CPRE F. θ = _7_ 5 26. D. θ. K. and immediately select 1 piece at random. of the isosceles right triangle shown below. K. tan. J. in inches. sin. cos. θ = _7_ 5 7 θ 5 K. 01 B. 24% 28% 32% 34% 39% $182 food $125 insurance 30. the measure of ∠BAC is (x + 20)° and the measure of ∠BAD is 90°. To make a 750-piece jigsaw puzzle more challenging. If you buy such a puzzle box. __ 24 27 GO ON TO THE NEXT PAGE. and those 5 extra pieces do not fit anywhere in the puzzle. In the figure shown below. What is the perimeter. ___ 2 28. and the height of the cone is 7 inches. what is the probability that it will be 1 of the extra pieces? 27. The pie chart below breaks down these expenditures by category. 0(x − 70)° 0(70 − x)° 0(70 + x)° (160 − x)° (160 + x)° sin. _1_ 5 1_ B. x _3_ 5 G. 450. J. . F. $2. −1 −2 2 x 37.00 for building and installing the cabinets. of the portion of the floor that will NOT be covered by cabinets? F. The scale drawing shown below displays the location of the cabinets in the craft room (0. 15 ft wall Cabinets will be installed along one of the 12-foot walls from floor to ceiling.375 E. 3 D. 1. 164 between the functions f (x) = (x − 3) 2 + 2 and g(x) = _1_ x + 1 graphed below in the standard (x.300. Use the following information to answer questions 33–35.00 ACT-1572CPRE 1 O F. 15} ? A. A 15-foot wall is how many inches long in the scale drawing? A.00 B. 3. H.5 B.00 charge for labor.y) coordinate plane? y y J. door y K.25 inch represents 2 feet). 12 33. What is the difference between the mean and the median of the set {3. plus a fixed charge per cabinet. Which of the following describes a true relationship 34. and each of them will be 2 feet wide and 2 feet deep. Gianna will install tile herself but will have CC Installations build and install the cabinets. Gianna will install tile on the portion of the floor that will NOT be covered by cabinets.00 D.650. CC Installations has given Gianna an estimate of $2. 8. −2 2 1 −1 2 1 x 1 2 x 2 x 2 ft deep window cabinets cabinets y G. 3.75 38.875 C. 00 B. 09 E. in square feet. CC Installations would give Gianna what estimate if the craft room were to have twice as many cabinets as Gianna is planning to have? A. G. Which of the following is the graph of the region 1 < x + y < 2 in the standard (x. $3. 10. CC Installations’ estimate consists of a $650. and 4 cabinets that are each 3 feet tall will be installed in the middle of the room. 072 G. 04 D. $3. $3. 140 J.000.2 2 36.00 E.y) 2 coordinate plane? y 35. −2 12 ft wall 2 2 1 −1 x −1 −1 y H. K. 01 C.150. $4. 090 H. 156 K. 1. These are the only cabinets that will be installed. The labor charge and the charge per cabinet remain the same for any number of cabinets built and installed.00 C. Gianna is converting a 12-foot-by-15-foot room in her house to a craft room.800. What is the area. 28 x f (x) = g(x) for exactly 2 values of x f (x) = g(x) for exactly 1 value of x f (x) < g(x) for all x f (x) > g(x) for all x f (x) is the inverse of g(x) GO ON TO THE NEXT PAGE. what are the coordinates of D′ ? F.y) coordinate plane below. ( 12.5 D.5 B. A formula to estimate the monthly payment. After 10 cups of water 8 are added. 1 5_ D. H. The points E(6.0−1) H. in cups? −3 F. the container is _3_ full. x = 2.12) ___ 39.0 1) G. what is x + z ? A. (−12. 15 J. and y years is the length of the loan.1) O C(9.1) x A.4) A(2. A container is _1_ full of water.08) (12. what is the effect on p ? A. 13 _12_ H. pis divided by 2 C. G. what is f g _1_ x x 2 F. Which of the following vertical lines cuts ABCD into 2 trapezoids with equal areas? A. What is the slope of CD ? C. − 2_ 3 13 _13_ G.12) lie in the standard (x.0−1) J. Point D___lies on EF between E and F such that the length of EF is 4 times ___ the length of DE . x = 5. x = 3. −1 F(14. on a short-term loan is Use the following information to answer questions 39–41. J. Given that a 21 64 = xy 27 z for some real number a. where a dollars is the amount of the loan.4) x O 3 4 3 4 45.08) (10. What is the volume 4 1 1 22 ? 42.10) E(6. pis divided by 6 B. of the container. pdoes not change D.05) (08.2 2 43. G. 48 46.5 C. x = 4.5 _4_ 3 27_ __ 2 C.4) D(12. _3_ 2 K. ( 01. K. _1_ ary + a 2 _ p = ________ 12y Trapezoid ABCD is graphed in the standard (x.y) ___ coordinate plane shown below. __ E.06) (08. 0 J. K. − _3_ 2 _ H. 27 E. 40 ACT-1572CPRE 29 16 GO ON TO THE NEXT PAGE.4) and F(14. r is the annual interest rate expressed as a decimal. 26 D. . B. ( 01. pis multiplied by 2 E. What are the coordinates of D ? y B. F. −3 44. 41. When a is multiplied by 2. pis multiplied by 4 y B(3. p dollars. Given f (x) = x − _1_ and g(x) = _1_ .5 E. When ABCD is reflected over the y-axis to A′B′C′D′. 21 _3_ 2 40. (−12.−12) (07. x = 6. 12) K. By doubling each of the dimensions (l. 7 + 3 F. −5 < x < 10 G. ___ √•6 49. 03:1 B.2 2 47. Twelfth D. E. and the water level goes up 0. and the ratio of eleventh graders to the school’s total student population is 18:51. the surface area will be multiplied by what factor? −x (x − 1)2 + (y − 2)2 = 9 + 2 A. The shaded region in the graph below represents the solution set to which of the following systems of inequalities? y y= 53. −2 < x < 3 K. E. what is the ratio of x:z ? A. of the object? F. w. 7 + __ 3 7d_ __ K. E. All grades are equally likely. x A. ___________ √•5 4√•3 + 2√•2_ G. 150 K. . Eleventh C. −3 < x H. Which of the following is the solution statement for the inequality shown below? −5 < 1 − 3x < 10 F. how many cans of food does the dog eat in 3 + d days? <9 _7_ + d 3 d G. The ratio of tenth graders to the school’s total student population is 86:255. 240 H. 15:4 √•3 4√•3 + 2√•2_ F. + 3 3d d J. Tenth B. D. which grade is that student most likely to be in? A. height. If x:y = 5:2 and y:z = 3:2. ___________ √•6 6 H. −3 < x < 2 J. The object sinks to the bottom. 08:4 E. width.25 centimeters. _________ J. 05:3 D. 52. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters by 30 centimeters and is filled with water to a depth of 20 centimeters. x < −3 or x > 2 √•2 + √•3 6_ ___ √•5 8_ K. D. Cannot be determined from the given information 50. B. ___ + 2_ = ? √•2 51. 300 G. and h. C. _7_ + __ 3 3 7_ __ 7_ _ H. B. 5 (xy <−−x1) ++2( y − 2) 5 (xy >−−x1) ++2( y − 2) 5 (xy >−−x1) ++2( y − 2) 5 (xy <−−x1) ++2( y − 2) 5 (( xy −− 2)1) <> 33 ACT-1572CPRE 2 2 2 2 <9 2 2 >9 2 2 >9 02 04 06 08 12 h l w 54. Only tenth-. 075 4 _ ___ 48. A dog eats 7 cans of food in 3 days. 200 J. If 1 student is chosen at random from the entire school. C. 30 GO ON TO THE NEXT PAGE. 03:5 C. and h). w. What is the volume. At this rate. in cubic centimeters. You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. and twelfth-grade students attend Washington High School. A formula for the surface area (A) of the rectangular solid shown below is A = 2lw + 2lh + 2wh where l represents length. eleventh-. 47 D. and 20 cm. Which of the following equations. 73 B. there are 3 possible answers. Which of the following number line graphs shows the solution set to the inequality ⎪x − 5⎪ < −1 ? Yes No F. x J. __ B. D. How many of the students polled indicated that they had skied both cross-country and downhill? A. B. 31 . sin. the 4 regions have equal areas. E. 65 C. Kelly wondered how many of the students polled had skied both cross-country and downhill. In the top row. the region labeled A has the same area as the region labeled B. 20 56. One of the following statements about the values of a and b is true. 3_ 9 H. In the bottom row.θ K. For each question. DO NOT RETURN TO THE PREVIOUS TEST. In the middle row. 37 After completing the poll. a < 0 and b = 0 a < 0 and b > 0 a = 0 and b > 0 a > 0 and b < 0 a > 0 and b > 0 ACT-1572CPRE END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. Kelly asked 120 students questions about skiing. for constants a and b. gives the measure of the smallest angle of the triangle? D (Note: For any triangle with sides of length a.2 2 55. B. What fraction of the square’s area is in a region labeled A ? A 6 H. D.) a b c sin. 08 F. _1_ 9 _ G. 1. 2. 12 13_ K. E. If Elliott randomly and independently answers each question. The sides of an acute triangle measure 14 cm. The functions have the same maximum value.θ A. As part of a probability experiment. ____ = __ 20 14 F. and c 57. _6_ 9 13_ __ J.θ_ 1_ H.θ_ 1_ ____ = __ 14 18 sin. 142 = 182 + 202 − 2(18)(20)cos. The square below is divided into 3 rows of equal area. 202 = 142 + 182 − 2(14)(18)cos. Have you skied either cross-country or downhill? 65 55 G. 18 E.A sin. did you ski cross-country? 45 Question A B C x 4 6 x 4 6 x x 59. only 1 of which is correct. Which statement is it? y O 6 6 4 (empty set) C B 4 K.B sin. 18 cm.θ_ 1_ G.C. If you answered Yes to Question 1. are graphed in the standard (x. the 3 regions have equal areas. did you ski downhill? 28 3. B A x J.C _____ = _____ = _____ and c2 = a2 + b2 − 2ab cos. 58. The results of the poll are shown in the table below. Elliott is to answer 4 multiple-choice questions. ____ = __ 14 20 sin. when solved for θ. b. respectively. respectively. The functions y = sin. C.x and y = sin(x + a) + b. If you answered Yes to Question 1. and C. C.y) coordinate plane below. 81 12_ __ 81 4_ __ 81 3_ __ 81 1_ __ 81 60. what is the probability that he will answer the 4 questions correctly? 27_ A. __ 36 4 that are opposite angles A. 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