MATHEMATICS TEST 60 Minutes 60 Questions

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1 MTHEMTICS TEST 60 Minutes 60 Questions DIRECTINS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on our answer document. Do not linger over problems that take too much time. Solve as man as ou can; then return to the others in the time ou have left for this test. You are permitted to use a calculator on this test. You ma use our calculator for an problems ou choose, but some of the problems ma best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed.. Illustrative figures are NT necessaril drawn to scale.. Geometric figures lie in a plane.. The word line indicates a straight line. 4. The word average indicates arithmetic mean.. The blood tpes of 0 people were determined for a stud as shown in the figure below. If person from this stud is randoml selected, what is the probabilit that this person has either Tpe or Tpe blood?.. C. D. E. number of people blood tpe 6. n a particular road map, _ inch represents 8 miles. bout how man miles apart are towns that are inches apart on this map?. 8. C. 6 D. 4 E Given f = cd, f = 40, and d = 0, what is c? If f() = ( + 7), then f() =? C. 08 D. 079 E. 00. The monthl fees for single rooms at colleges are $70, $0, $80, $40, and $0, respectivel. What is the mean of these monthl fees? $0 $40 $4 $0 $80 6. Jorge s current hourl wage for working at Denti Smiles is $.00. Jorge was told that at the beginning of net month, his new hourl wage will be an increase of 6% of his current hourl wage. What will be Jorge s new hourl wage? $.06 $.60 $.7 $8.00 $9.0 CT-7CPRE 4

2 7. The first term is in the geometric sequence,, 9, 7,. What is the SEVENTH term of the geometric sequence? C. 0 D. 89 E The shipping rate for customers of Ship Quick consists of a fee per bo and a price per pound for each bo. The table below gives the fee and the price per pound for customers shipping boes of various weights. Gregg wants Ship Quick to ship bo that weighs pounds. What is the shipping rate for this bo? $09.7 $6.0 $9.7 $0.00 $ computer chip 0. cm thick is made up of laers of silicon. If the top and bottom laers are each 0.0 cm thick and the inner laers are each 0.0 cm thick, how man inner laers are there?.. C. 6 D. E The table below shows the number of cars Jing sold each month last ear. What is the median of the data in the table? Month Number of cars sold CT-7CPRE Weight of bo (pounds) Fee Price per pound Less than 0 0 More than $0.00 $0.00 $0.00 $.00 $0.6 $0.0 Januar Februar March pril 9 Ma 6 June Jul 9 ugust September 6 ctober 7 November 8 December 9 } 0. cm. Students studing motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at -second intervals from t = 0 seconds to t = seconds. Which of the following equations represents this relationship between d and t?. d = 00t + 4. d = 06t + 08 C. d = 06t + 4 D. d = 4t + 06 E. d = 4t. The length of a rectangle with area 4 square centimeters is 9 centimeters. What is the perimeter of the rectangle, in centimeters? In the figure below, C is the intersection of D and E. If it can be determined, what is the measure of C? D 4 C E C D. E. Cannot be determined from the given information 4. ntwan drew the circle graph below describing his time spent at school in da. His teacher said that the numbers of hours listed were correct, but that the central angle measures for the sectors were not correct. What should be the central angle measure for the Core subjects sector? t d Electives hours Core subjects 4 hours Lunch and passing time hour Choir hour

3 . This month, Kami sold 70 figurines in sizes. The large figurines sold for $ each, and the small figurines sold for $8 each. The amount of mone he received from the sales of the large figurines was equal to the amount of mone he received from the sales of the small figurines. How man large figurines did Kami sell this month? C. D. 4 E car accelerated from 88 feet per second (fps) to 0 fps in eactl seconds. ssuming the acceleration was constant, what was the car s acceleration, in feet per second per second, from 88 fps to 0 fps? _ 7. In a plane, the distinct lines and CD intersect at, where is between C and D. The measure of C is 47. What is the measure of D? C. 094 D. E In which of the following are _,, and arranged in 6 8 ascending order? < _ 8 6 < _ < _ In scientific notation, 670,000, ,000,000 =? C D E For trapezoid CD shown below, i DC, the measures of the interior angles are distinct, and the measure of D is. What is the degree measure of in terms of? (80 ) (80 0.) ( ) (80 + ) D C. To get a driver s license, an applicant must pass a written test and a driving test. 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. ased on these figures, how man applicants in a random group of,000 applicants would ou epect to get driver s licenses? C. 600 D. 70 E If a, b, and c are positive integers such that a b = and c b =, then =? ac b ac b (ac) b (ac) b (ac) b. Which of the following epressions is equivalent to _ (6 + + )? C. 0 + D. 09 E n artist makes a profit of (00p p ) dollars from selling p paintings. What is the fewest number of paintings the artist can sell to make a profit of at least $60,000? CT-7CPRE 6

4 . Last month, Lucie had total ependitures of $900. The pie chart below breaks down these ependitures b categor. The categor in which Lucie s ependitures were greatest is what percent of her total ependitures, to the nearest %? clothes. 4%. 8% C. % D. 4% E. 9% 6. In the figure shown below, the measure of C is ( + 0) and the measure of D is 90. What is the measure of CD? C 0( 70) 0(70 ) 0(70 + ) (60 ) (60 + ) 7. What is the perimeter, in inches, of the isosceles right triangle shown below, whose hpotenuse is 8 inches long? C D. 6 E gas insurance 8. The equation = a + b + c is graphed in the standard (,) coordinate plane below for real values of a, b, and c. When = 0, which of the following best describes the solutions for? $0 $8 $4 $ entertainment $9 D food 9. What is the product of the comple numbers ( i + 4) and (i + 4)? C. D i E i 0. The radius of the base of the right circular cone shown below is inches, and the height of the cone is 7 inches. Solving which of the following equations gives the measure, θ, of the angle formed b a slant height of the cone and a radius? tan, θ= tan, θ= sin, θ= sin, θ= cos,θ =. To make a 70-piece jigsaw puzzle more challenging, a puzzle compan includes etra pieces in the bo along with the 70 pieces, and those etra pieces do not fit anwhere in the puzzle. If ou bu such a puzzle bo, break the seal on the bo, and immediatel select piece at random, what is the probabilit that it will be of the etra pieces?.. C. D. E.. What fraction lies eactl halfwa between _ and _? θ distinct positive real solutions distinct negative real solutions positive real solution and negative real solution real solutions that are not distinct distinct solutions that are not real CT-7CPRE 7

5 Use the following information to answer questions. 6. Which of the following is the graph of the region < + < in the standard (,) coordinate plane? Gianna is converting a -foot-b--foot room in her house to a craft room. Gianna will install tile herself but will have CC Installations build and install the cabinets. The scale drawing shown below displas the location of the cabinets in the craft room (0. inch represents feet). window ft deep cabinets cabinets ft wall CT-7CPRE door ft wall Cabinets will be installed along one of the -foot walls from floor to ceiling, and 4 cabinets that are each feet tall will be installed in the middle of the room. These are the onl cabinets that will be installed, and each of them will be feet wide and feet deep. CC Installations has given Gianna an estimate of $,0.00 for building and installing the cabinets.. -foot wall is how man inches long in the scale drawing? C. D..7 E Gianna will install tile on the portion of the floor that will NT be covered b cabinets. What is the area, in square feet, of the portion of the floor that will NT be covered b cabinets? CC Installations estimate consists of a $60.00 charge for labor, plus a fied charge per cabinet. The labor charge and the charge per cabinet remain the same for an number of cabinets built and installed. CC Installations would give Gianna what estimate if the craft room were to have twice as man cabinets as Gianna is planning to have?. $, $, C. $,40.00 D. $,60.00 E. $4, What is the difference between the mean and the median of the set {, 8, 0, }? C. 04 D. 09 E. 8. Which of the following describes a true relationship between the functions f () = ( ) + and g() = _ + graphed below in the standard (,) coordinate plane? f() = g() for eactl values of f() = g() for eactl value of f() < g() for all f() > g() for all f() is the inverse of g()

6 Use the following information to answer questions 9 4. Trapezoid CD is graphed in the standard (,) coordinate plane below. 9. What is the slope of CD?.. (,4) (,) C(9,4) D(,) 4. formula to estimate the monthl pament, p dollars, on a short-term loan is p = ar + a where a dollars is the amount of the loan, r is the annual interest rate epressed as a decimal, and ears is the length of the loan. When a is multiplied b, what is the effect on p?. pis divided b 6. pis divided b C. pdoes not change D. pis multiplied b E. pis multiplied b The points E(6,4) and F(4,) lie in the standard (,) coordinate plane shown below. Point D lies on EF between E and F such that the length of EF is 4 times the length of DE. What are the coordinates of D? F(4,) C. D. E. 40. When CD is reflected over the -ais to C D, what are the coordinates of D? (,0 ) (,0 ) (,0 ) ( 0, ) ( 0, ) 4. Which of the following vertical lines cuts CD into trapezoids with equal areas?. =.. =. C. = 4. D. =. E. = Given f() = and g() =, what is f g? _ _ 0 CT-7CPRE _ 9 (07,0) (08,06) (08,08) (0,08) (,0) 6 4. Given that a 4 = what is + z? C. 6 D. 7 E. 48 for some real number a, 46. container is _ full of water. fter 0 cups of water 8 are added, the container is full. What is the volume 4 of the container, in cups? 6 40 z E(6,4)

7 47. nl tenth-, eleventh-, and twelfth-grade students attend Washington High School. The ratio of tenth graders to the school s total student population is 86:, and the ratio of eleventh graders to the school s total student population is 8:. If student is chosen at random from the entire school, which grade is that student most likel to be in?. Tenth. Eleventh C. Twelfth D. ll grades are equall likel. E. Cannot be determined from the given information =? The shaded region in the graph below represents the solution set to which of the following sstems of inequalities? = + ( ) + ( ) = 9 0. You can find the volume of an irregularl shaped solid object b completel submerging it in water and calculating the volume of water the object displaces. You completel submerge a solid object in a rectangular tank that has a base 40 centimeters b 0 centimeters and is filled with water to a depth of 0 centimeters. The object sinks to the bottom, and the water level goes up 0. centimeters. What is the volume, in cubic centimeters, of the object? If : = : and :z = :, what is the ratio of :z?. 0:. 0: C. 0: D. 08:4 E. :4. Which of the following is the solution statement for the inequalit shown below? < < 0 < < 0 < < < < < < or >. formula for the surface area () of the rectangular solid shown below is = lw + lh + wh where l represents length; w, width; and h, height. doubling each of the dimensions (l, w, and h), the surface area will be multiplied b what factor? C. 06 D. 08 E. h w l. < + ( ) + ( ) < 9. > + ( ) + ( ) < 9 C. > + ( ) + ( ) > 9 D. < + ( ) + ( ) > 9 ( ) < E. ( ) > CT-7CPRE 0 4. dog eats 7 cans of food in das. t this rate, how man cans of food does the dog eat in + d das? 7 + d 7 + d d 7 + d 7d 7 +

8 . Kell asked 0 students questions about skiing. The results of the poll are shown in the table below. fter completing the poll, Kell wondered how man of the students polled had skied both cross-countr and downhill. How man of the students polled indicated that the had skied both cross-countr and downhill? C. 47 D. 8 E The square below is divided into rows of equal area. In the top row, the region labeled has the same area as the region labeled. In the middle row, the regions have equal areas. In the bottom row, the 4 regions have equal areas. What fraction of the square s area is in a region labeled? Question Yes No. Have ou skied either cross-countr or downhill? 6. If ou answered Yes to Question, did ou ski downhill? 8 7. If ou answered Yes to Question, did ou ski cross-countr? _ 9 6_ The functions = sin, and = sin( + a) + b, for constants a and b, are graphed in the standard (,) coordinate plane below. The functions have the same maimum value. ne of the following statements about the values of a and b is true. Which statement is it? C C D 8. Which of the following number line graphs shows the solution set to the inequalit <? 9. s part of a probabilit eperiment, Elliott is to answer 4 multiple-choice questions. For each question, there are possible answers, onl of which is correct. If Elliott randoml and independentl answers each question, what is the probabilit that he will answer the 4 questions correctl?.. C. D. E (empt set) 60. The sides of an acute triangle measure 4 cm, 8 cm, and 0 cm, respectivel. Which of the following equations, when solved for θ, gives the measure of the smallest angle of the triangle? (Note: For an triangle with sides of length a, b, and c that are opposite angles,, and C, respectivel, sin, = sin, = sin,c and c = a + b ab cos,c.) a b c sin,θ = 4 8 sin,θ = 4 0 sin,θ = = (8)(0)cos,θ 0 = (4)(8)cos,θ. a < 0 and b = 0. a < 0 and b > 0 C. a = 0 and b > 0 D. a > 0 and b < 0 E. a > 0 and b > 0 CT-7CPRE END F TEST STP! D NT TURN THE PGE UNTIL TLD T D S. D NT RETURN T THE PREVIUS TEST.