CERT Grade 11 Mathematics Test 2 60 Minutes 60 Questions

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Abigayle Tate
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1 DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer sheet. 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. You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, b CERT Grade 11 Mathematics Test 2 60 Minutes 60 Questions but some of the problems may be best done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed: 1. Illustrative figures are NOT necessarily drawn to scale. 2. Geometric figures lie in a plane. 3. The word line indicates a straight line. 4. The word average indicates arithmetic mean. 1. The sum of Jason s 5 quiz scores is 95. What is the average of Jason s quiz scores? A. 95 B. 45 C. 20 D. 19 E If a = 3, b = 1, and c = 1, what does (b + c) (c a) equal? F. 4 G. 3 H. 0 J. 2 K The digit 5 in the number 1, is in which of the following places? A. The hundreds place B. The units place C. The tenths place D. The hundredths place E. The thousandths place 4. If 7(p + 3) = 28, the p =? F. 4 G. 1 H. 1 J. 4 K. 7

2 5. A triangle has two congruent angles. The length of one side of the triangle is 16 cm and the length of another side is 32 cm. Which of the following is the length of the third side of the triangle? A. 64 cm B. 48 cm C. 32 cm D. 16 cm E. It cannot be determined based on the information provided. 6. Which of the following properly expresses the verbal statement The square root of a number, x, is 5 less than the sum of the number and 2? F. xx = 5 (x + 2) G. xx = (x + 2) 5 H. x 2 5 = 2x J. 5x 2 = 2x 5 K. xx 5 = (x + 2) 7. Calvin earns $10.00 per hour for up to 40 hours of work in a given week. For each hour Calvin works over 40 hours in a week, he earns 1.25 times his regular hourly rate. How much does Calvin earn for a week in which he works 48 hours? A. $ B. $ C. $ D. $ E. $ What is the distance between the point (2, 7) and the point ( 1, 3) in the xy-coordinate plane? F. 17 G. 4 2 H. 5 J. 5 2 K. 6

3 9. The price, P, of a sweater was discounted by 10% in February. Because the sweater did not sell by the end of the winter season, it was discounted by another 20% in March. In terms of P, what was the price of the sweater after the discount in March? A P B P C P D P E P 10. The expression (4a + b) 3(2a + b) is equivalent to: F. 2a + 4b G. 2a 2b H. 10a + 4b J. 10a 2b K. 10a 4b 11. log log 3 81 = A. 181 B. 127 C. 19 D. 14 E Ian wants to place 5 trophies in a row on a shelf in his bedroom. How many different arrangements of the 5 trophies are possible? F. 120 G. 80 H. 60 J. 14 K. 8

4 13. What is the sum of all of the single-digit factors of 60? A. 21 B. 17 C. 14 D. 11 E For two consecutive even integers, the result of subtracting the larger integer from 3 times the smaller integer is 14. Which of the following is the larger integer? F. 12 G. 10 H. 8 J. 6 K Mary poured 40,000 cm 3 of water into an aquarium that is shaped like a rectangular box. If the length and width of the aquarium are 40 cm and 80 cm, respectively, what is the height, in centimeters, of the water in the aquarium? A B C D E If x 3 = F. 125 G. 100 H. 75 J. 15 K , then 625x3 =? 17. If 4 + xx = 8, xx could equal which of the following? A. 4 only B. 4 only C. 4 or 4 D. 12 only E. 4 or 12

5 18. If xx + 2 = xx + 4, then xx could equal which of the following? F. 3 G. 2 H. 1 J. 0 K Circle O has a radius that is 10 units long. Chord AB is drawn on Circle O such that it is 4 units long. Chord CD is then drawn on Circle O such that it is 4.5 units long. Finally, Chord EF is drawn on Circle O such that it is 5 units long. Which chord is the closest to the center of Circle O? A. Chord AB B. Chord CD C. Chord EF D. They are all the same distance from the center. E. It cannot be determined based on the information provided. 20. The number of cars on a bridge on a given weekday can be estimated using the equation c = 800(0.9) t, where t represents time, in hours, after 7:00 am on any given weekday, and c represents the number of cars. According to this formula, approximately how many cars are on the bridge at 9:00 am on a given weekday? F. 800 G. 720 H. 648 J. 583 K A function g(x) is defined as g(x) = x 3 (x 2) 2. What is the value of g( 2)? A. 128 B. 24 C. 0 D. 24 E. 128

6 22. ABC and DEF are similar. The length of the smallest side of ABC is 2 units and the length of the smallest side of DEF is 5 units. The area of ABC is 4 units squared. What is the area, in units squared, of DEF? F. 8 G. 10 H. 15 J. 18 K Given the right triangle with sides as labeled below, what is the value of tan θ? A B C D θ E Given the pattern of H s and T s below, how many T s are there between the 15 th H and the 17 th H? H T H T T H T T T H T T T T H T T T T T H... F. 48 G. 31 H. 28 J. 22 K. 16

7 25. Lines m and n lie in the standard (x, y) coordinate plane. Line m includes the points (5, 3) and (5, 7). If line n is perpendicular to line m, which of the following could be the equation of line n? A. x = 5 B. x = 1 C. y = 8 D. y = x E. y = x In triangle ABD below, AD = BD and m A = 40. What is the measure, in degrees, of BDC? F. 140 G. 120 H. 100 J. 80 K. 60 A D B C 27. The expression (x + 5) 2 (2x 3) is equivalent to: A. x 2 + 8x + 28 B. x 2 2x + 22 C. x 2 2x + 28 D. x 2 + 8x + 22 E. x 2 8x The inequality 4( ) < 3(3 x) is equivalent to which of the following inequalities? F. x < 9 G. x > 3 H. x < 9 J. x > 9 K. x < The graph of f (x) = x includes the point ( 1, 2n) in the standard (x, y) coordinate plane. What is the value of n? A. 5 B. 4 C. 0 D. 4 E. 5

8 30. Which of the following equations properly models the data in the table below? x h(x) F. h(x) = x 3 G. h(x) = x H. h(x) = 2x 2 J. h(x) = x 2 K. h(x) = The center of a circle is at (3, 4) in the standard (x, y) coordinate plane. The point (8, 4) is on the circumference of the circle. Which of the following points is NOT also on the circumference of the circle? A. (3, 9) B. (8, 3) C. ( 2, 4) D. (3, 1) E. (8, 4) 32. Each dot ( d ) in the Venn diagram below represents 2 people. According to the Venn diagram, how many people own both a laptop and a tablet? F. 1 Ownership of Electronic Devices G. 2 H. 3 J. 4 laptop phone K. 6 tablet 33. What is the period of the function f (xx) = 2 sin 1 xx? 2 A. 5π B. 4π C. 2π D. π E. π

9 34. A bucket contains 4 tennis balls, 7 baseballs, and 11 golf balls. What is the least number of tennis balls that need to be added to the bucket so that the probability of randomly choosing a tennis ball is 1 4? F. 1 G. 2 H. 3 J. 4 K What are the quadrants of the standard (x, y) coordinate plane shown below that contain the points on the graph of the equation x + 41 = 0? II I III IV A. I and II B. II and III C. III and IV D. I and IV E. I, II, and III 36. Abigail, Bart, and Carson shared a box of mints after school. Abigail ate 1 5 of the mints, Bart ate 1 of the 3 mints, and Carson ate the rest. What is the ratio of numbers of mints eaten by Abigail, Bart, and Carson? F. 5:3:8 G. 8:5:3 H. 3:7:5 J. 7:5:8 K. 3:5:7 37. What is the volume of a cube with total surface area equal to 294 in 2? A. 49 in 3 B. 64 in 3 C. 128 in 3 D. 146 in 3 E. 343 in 3

10 38. Which of the following is the equation for a circle in the standard (x, y) coordinate plane that has a radius of length 6 and its center at (4, 3)? F. (x + 4) 2 + (y 3) 2 = 6 G. (x + 4) 2 (y 3) 2 = 6 H. (x 4) 2 (y + 3) 2 = 36 J. (x 4) 2 + (y + 3) 2 = 36 K. (x + 3) 2 + (y 4) 2 = The figure below consists of an equilateral triangle with perimeter 24 and three semicircles. What is the total area, in square inches, of the three shaded semicircles? A. 12π B. 16π C. 24π D. 48π E. 96π 40. The figure below is a rectangle that has been divided into 5 separate regions. Three of the regions are shaded and two are unshaded as shown. What is the ratio of the total shaded area to the unshaded area? F. 3:2 G. 1:1 H. 3:5 J. 1:2 K. 2:5 41. The endpoints of PQ in the standard (x, y) coordinate plane are (0, 5) and (8, 15). What is the y-coordinate of the midpoint of PQ? A. 4 B. 5 C. 10 D E. 15.5

11 42. In the system of equations below, a and b are integers. ax + by + 7 = 0 ax = b 7 Which of the following describes the graph of at least 1 such system of equations in the standard (x, y) coordinate plane? I. A single line II. 2 intersecting lines III. 2 parallel lines F. I only G. II only H. III only J. II or III only K. I, II, or III 43. The circle graph below shows the distribution of flowers, by type, for sale at a florist. If a flower other than a rose is randomly chosen, what is the probability that the flower will be a tulip? Distribution of Flowers by Type 30% 10% 20% 22% tulip lily rose iris orchid A B C D E % 44. If x, y, and z are positive real numbers such that x is even, y is odd, and 2z is even, then which of the following must be true? F. xyz is odd G. x + y + z is odd H. x + y + z is even J. x + (y + 2z) 2 is odd K. x + 2y + 2z is odd

12 Use the following information to answer questions The figure below is composed of a circle and 4 small congruent equilateral triangles (3 shaded and 1 unshaded) that are arranged to form a larger equilateral triangle that is inscribed in the circle. The circle has radius What is the distance between the center of the circle and any one of the vertices of the small unshaded triangle? A. 2 3 B. 2 2 C. 2 D. 3 E The figure has how many lines of symmetry in the plane in which it lies? F. 1 G. 3 H. 6 J. 12 K. Infinitely many 47. If the design in the figure above were replicated with a circle having area 4 times that of the circle in the figure and triangles having area 4 times that of the triangles in the figure, which of the following would be the length of the radius of the new, larger circle? A. 4 B. 8 C. 12 D. 16 E. 20

13 48. For which value of c would the following equation have only one real solution? x 2 6 x + c = 0 F. 12 G. 9 H. 6 J. 0 K In the circle shown below, BD and CE are diameters and EB is a chord. If minor arc CD measures 58, what is the degree measure of EBD? E B A D C 58 A. 58 B. 59 C. 60 D. 61 E. Cannot be determined from the given information aa bb 50. The determinant of matrix equals aaaa bbbb. cc dd Which of the following must be the value of xx, given that the determinant of the matrix xx 4 equals 36? 16 xx F. 10 G. H J. 2 5 K. 20

14 Use the following information to answer questions The bar graph below displays information regarding balloons sold by a party-supply store on a given day. The x-axis shows the color of the balloon sold and the y- axis shows the number of balloons sold. number sold red blue green white color 51. If the data in the bar graph above were translated to a circle graph, which of the following circle graphs would best represent the data? A. B. C. D. E.

15 52. According to the bar graph, what percent of the balloons sold were green? F. 20% G. 25% H. 30% J. 40% K. 45% 53. If the cost of a blue balloon is 25 cents and the cost of a white balloon is 20 cents, how much money, in dollars, was collected from the sale of blue balloons and white balloons on the day represented in the bar graph? A B C D E If the value of cos θ = 3, which of the following could 2 be true? F. 2π θθ < 5π 2 G. 3π θθ < 7π 2 H. 4π θθ < 9π 2 J. 11π 2 θθ < 6π K. 6π θθ < 13π If i 2 = 1, then (i)(1 + 2i)(2 3i) 2 =? A i B i C. 10 5i D i E i

16 56. How many seconds total are there in 4 hours, 18 minutes and x seconds? F. 15, x G. 15,480 + x H x J x K. 14, x 57. The average price of a gallon of gasoline varies from year to year. The table below displays the average price of one gallon of regular gasoline over a five-year period. Which of the following is equal to the average of the mode and the median of the five average-price values in the table below? Year Average Price of One Gallon of Regular Gasoline 2009 $ $ $ $ $3.40 A. $3.50 B. $3.45 C. $3.40 D. $3.35 E. $ Right triangle XYZ is shown below. If m Y = 60 and YZ = 10, what is the length of XZ? F G H J K X 60 Y 10 Z

17 59. Set A consists of all prime numbers between 0 and 17. If a number is randomly selected from Set A, what is the probability that the number is odd? A. B. C. D. E What is the altitude of the graph of the function f (x) = 5 cos (x + 2) 5? F. 5 G. 5 H. 10 J K. 15 END OF TEST

MATHEMATICS TEST 60 Minutes 60 Questions

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. Do not linger over problems that take