Name: Class: Date: Math 8 Performance Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1) Which of the following is an irrational number? 300 a. 5 c. 2 b. 0.6 d. 49 2) Kelly is learning about rational and irrational numbers. What conclusion can she draw about the number 0.01011011101111011111...? a. It is rational because it repeats. b. It is rational because it terminates. c. It is irrational because it neither repeats nor terminates. d. It is irrational because it repeats. 3) Which of the following is equivalent to 0.13? a. 1 13 c. 8 100 b. 13 1 d. 99 3 4) Which of these expressions is true? a. 11.5 < 165 < 12 c. 12.5 < 165 < 13 b. 12 < 165 < 12.5 d. 13 < 165 < 13.5 5) A square box lid has an area of 40 square inches. Which is the best estimate of the length of one side? a. 6.0 inches c. 6.5 inches b. 6.3 inches d. 7.0 inches 6) Which of the following is equivalent to 2 3? 1 a. ( 2)( 2)( 2) c. (2)(2)(2) 1 b. (2)(2)(2) d. (2)(2)(2) 1
7) How could you write 8 27 as a product of powers? a. Multiply two powers, both with a base of 8. The sum of the exponents should be 27. b. A power with a base of 64 and 729 as the exponent. c. Multiply two powers, both with exponents of 27. The product of the bases should be 8. d. Multiply two powers, both with a base of 8. The product of the exponents should be 27. 8) Describe and give the value of 100. a. Irrational, 50 c. Irrational, 10 b. Not a real number d. Rational, 10 9) Find a rational number between 144 and ( 4) 2. a. 150 c. 11 1 2 b. 150 d. 16.253 10) Which of the following is not a solution to the equation x 2 = 64? a. 8 c. -8 b. 32 d. These are all solutions. 11) The mass of an electron is approximately 9.1 10 31 kilograms. The mass of a proton is approximately 1.7 10 27 kilograms. Approximately how many times greater is the mass of a proton than the mass of an electron? a. 1,900 c. 5,500 b. 19,000 d. 55,000 12) Which is the product of Ê 8.22 10 12 Ë Á ˆ Ê 9.5 10 2 Ë Á ˆ in scientific notation? a. 7.809 10 13 c. 7.809 10 15 b. 7.809 10 14 d. 7.809 10 24 13) Which is the quotient of (8.6 10 9 ) (2 10 3 )? a. 10.6 10 12 c. 4.3 10 3 b. 6.6 10 6 d. 4.3 10 6 2
14) The graph shows the relationship between the number of hours h Greg has been driving and the total distance d he has traveled, in miles. Which statement is true? a. Greg is traveling at 90 miles per hour. b. Greg is traveling at 30 miles per hour. c. To find Greg s rate of speed, multiply the total number of hours driven by the total distance. d. To find Greg s rate of speed, divide the total number of hours driven by the total distance. 15) Which of the following statements is NOT true concerning the graph below? a. The simplified ratio of the vertical side length to the horizontal side length of each triangle is 1. b. The slope of the line is 1. c. The slope of the line is -1. d. The smaller triangle and the larger triangle shown are similar. 3
16) Which of the following equations has NO solution? a. a + 2 = a + 2 c. a + 2 = a 2 b. a = a + 2 d. a + a = 2 17) Which of the following equations has infinitely many solutions? a. b + 2 = b + 2 c. b + 2 = b 2 b. b = b + 2 d. b + b = 2 18) Solve 2y + 1 = y 5. a. y = 6 c. y = 2 b. y = 2 d. y = 6 19) Solve 2(m + 5) = 8. a. m = 1 c. m = 9 b. m = 4 d. m = 6.5 20) Giovani solves a system of equations algebraically. He concludes that the lines are parallel. Which could be the final line of his solution? a. 5 = 5 c. 11 = 11 b. 5 = 5 + 1 d. 5 = 5 21) Cara graphs a system of linear equations and identifies a point as the solution. Where is the point located? a. the origin c. the y-intercept b. the x-intercept d. the intersection of the two lines 22) Solve the system of equations. x + y = 3 x y = 5 a. (4, 2) c. ( 4, 1) b. ( 5, 2) d. ( 5, 4) 4
23) Chloe, Tarina, and Lizette solved the system of equations shown. 2 x + 3y = 26 3 2x + 1 2 y = 27 Chloe claims the solution is (3, 8). Tarina claims the solution is ( 6, 10). Lizette claims the solution is (12, 6). Which statement is true? a. Chloe s solution is correct. b. Tarina s solution is correct. c. Lizette s solution is correct. d. None of the solutions are correct. 24) Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 a month plus $0.01 per copy. For which number of copies do the two companies charge the same amount? a. 5000 copies c. 7000 copies b. 6000 copies d. 7500 copies 25) The data in the table below form a function. What values in the table would change the relation to NOT be a function? x y 4 9 6 1 0 2 2 7 8 10 a. (1, 9) c. (9, 4) b. ( 3, 7) d. (6, 5) 26) Which function has the least rate of change. a. y = 3x 16 b. x 0 1 2 3 4 y 3 4 5 6 7 c. Helga earns $12 per hour working at a restaurant. d. {( 2, 4), (0, 0), (2,4),(4,8),(6, 12)} 5
27) Tan tracks the height of a ball in a game. He records the results in a table. Time (s) Height (ft) 1 0 2 0 3 0 4 7 5 3 6 0 Tanya also tracks the height of a ball during a game. She shows the results on a graph. Comparing these two functions, which statement is true? a. One ball leaves the ground, while the other remains on the ground the entire time. b. The two balls bounce the same height. c. One ball bounces repeatedly, while the other could bounce or could be on the ground for most of the time. d. The ball shown on the graph never touches the ground, while the other ball remains on the ground. 6
28) Which graph is NOT that of a function? a. c. b. d. 29) Which of these functions is not a linear function? a. f(x) = x c. f(x) = 3x b. f(x) = 3 x d. f(x) = 3x 2 30) Use the graph of f(x) and the function g(x) = 1 x + 2. Which best compares the slopes and 2 y-intercepts of the linear functions f and g? a. The slope of f is greater than the slope of g. The y-intercept of f is greater than the slope of g. b. The slope of f is less than the slope of g. The y-intercept of f is less than the y-intercept of g. c. The slope of f is greater than the slope of g. The y-intercept of f is less than the y-intercept of g. d. The slope of f is the same as the slope of g. The y-intercept of f is greater than the y-intercept of g. 7
31) Which best compares the slopes and y -intercepts of the linear functions f and g, where f = 2x 2 and g is shown in the table? a. The slope of f is greater than the slope of g. The y-intercept of f is greater than the y -intercept of g. b. The slope of f is less than the slope of g. The y-intercept of f is less than the y -intercept of g. c. The slope of f is the same as the slope of g. The y-intercept of f is the same as the y -intercept of g. d. The slope of f is less than the slope of g. The y -intercept of f is greater than the y -intercept of g. 32) Maya sketches a graph of a linear function. Which graph might she have sketched? a. c. b. d. 33) What equation could be written for this table? a. y = 4x c. y = 2x 1 b. y = 4x 1 d. y = 1 + 6x 8
34) Which equation is graphed? a. y = x + 1 c. y = x + 1 b. y = x 1 d. y = x 1 9
35) Gloria drives her daughter to school in the morning and then comes back home. She stays home until she has to go to pick up her daughter from school, and then they both return home again. Which graph best shows the situation? a. b. c. d. 10
36) Which situation is best represented by the graph? a. A swimmer starts at a steady pace, slows down to a stop, and then starts up swimming again, but at a slower pace than when she first started. b. After a ball is thrown into the air, it falls back to the ground and bounces. c. An airplane starts slowly on the runway, and then quickly takes off before finding a nice cruising speed. d. A car starts on flat ground and drives quickly up a hill, and then it keeps driving. 11
37) As an airplane starts to land, it gradually slows down until it reaches its landing speed. It stays at this speed until it touches the ground. After touching the ground, the plane quickly slows to a complete stop. Which graph best shows the situation? a. b. c. d. 12
38) The translation (x 10, y + 17) is applied to a triangle. Maryanne makes a conjecture about the perimeter of the image of the triangle, tests the conjecture, and finds that it is true. What could have been her conjecture? a. The perimeter of the image is 10 times the perimeter of the original triangle. b. The perimeter of the image is the same as the perimeter of the original triangle. c. The perimeter of the image is 10 units shorter than the perimeter of the original triangle. d. The perimeter of the image is 17 units longer than the perimeter of the original triangle. 39) What can be concluded from observing a 45-degree angle reflected across the y-axis three times? a. The measure of the angle doubles with each reflection. b. The measure of the angle increases 45 degrees with each reflection. c. The measure of the angle decreases by one-third with each reflection. d. The measure of the angle remains the same with each reflection. 40) Predict the result when parallel lines are rotated 90 clockwise. a. The lines become perpendicular lines. b. The lines remain parallel lines. c. The lines intersect, but not at 90 degrees. d. The lines become parallel rays. 13
41) Which describes the transformation from the original to the image, and tells whether the two figures are similar or congruent? a. translation, similar c. reflection, congruent b. translation, congruent d. dilation, similar 42) Which of the following is the correct description of the graph shown? a. Figure A B C D is the image of figure ABCD under a rotation of 90 clockwise about the origin. b. Figure A B C D is the image of figure ABCD under a rotation of 90 counterclockwise about the origin. c. Figure A B C D is the image of figure ABCD under a rotation of 180 about the origin. d. Figure A B C D is the image of figure ABCD under a rotation of 45 counterclockwise about the origin. 14
43) What are the coordinates of the image of ABCD after a reflection over the y-axis? a. A (2,2),B (5, 2), C (5,5),D (2, 5) b. A ( 5,5),B ( 2,5), C ( 2,2),D ( 5, 2) c. A (2, 2),B (5, 2), C (5, 5),D (2, 5) d. A (5, 2),B (2, 2), C (2, 5),D (5, 5) 44) A square has vertices T(1, 2), U(4, 2), V(4, 5), W(1, 5). If the square is rotated clockwise 90 degrees around (0, 0), what are the coordinates of W? a. Ê Ë Á 5, 1 ˆ c. Ê Ë Á 2, 4 ˆ b. Ê Ë Á 5, 4 ˆ d. Ê Ë Á 2, 1 ˆ 15
45) Describe a combination of two transformations that would move the design from its starting position to its final position. a. a reflection over the y-axis followed by a reflection over the x-axis b. a clockwise rotation of 90 about the origin followed by a clockwise rotation of 180 about the origin c. a counterclockwise rotation of 90 about the origin followed by a counterclockwise rotation of 180 about the origin d. a reflection across the y-axis followed by a downward translation 46) Triangle ABC is similar to triangle DEF. What is the value of x? a. 15 c. 30 b. 20 d. 60 16
47) If line m Ä line n and 4 measures 135, what is the measure of 3? a. 45 c. 135 b. 90 d. 180 48) If x = 40, what is the value of y? a. 40 c. 90 b. 50 d. 180 49) ABC EDF. Find f. a. 29 c. 58 b. 35 d. 87 17
50) Carlos records a proof of the Pythagorean Theorem. What is the area of the dark gray figure in Step 3? a. b 2 a 2 b. c 2 2 c. a 2 + b 2 a b d. c 2 (a 2 + b 2 ) 51) What is the value of x? a. 10 c. 306 b. 12 d. 13 18
52) Which expression represents the distance between the points in the graph? a. [ 3 2 + 5 2 ] 2 c. 7 2 + 9 2 b. [7 2 + 9 2 ] 2 d. 3 2 + 5 2 53) A rainwater collection tank is shaped like a cylinder with a diameter of 4 ft and a height of 6 ft. What is its volume? Use 3.14 for π. a. 15 units 2 c. 30 units 2 b. 20 units 2 d. 62 units 2 54) A beach ball is shaped like a sphere with a diameter of 12 feet. What is its volume? Use 3.14 for π. a. 150.72 units 3 c. 904.32 units 3 b. 50.24 units 3 d. 7, 234.56 units 3 55) Which of the statements is true about the data displayed in the scatter plot? a. It shows a positive correlation. b. It shows a negative correlation. c. It shows no correlation. d. As speed increases, cost decreases. 19
56) Which pair of data sets has a negative correlation? a. the total distance driven and the amount of tread on the tires b. the number of miles driven and the amount of gas used c. the number of passengers in a car and the number of driver s licenses d. the speed of the car and the rotation rate of its tires 20
57) Karen receives tips for some of her sales. Items Sold Tips Collected ($) 5 9 10 25 15 26 20 46 25 51 Which graph shows the best model for the data? a. d. b. c. 21
58) Write an equation for the trend line on the scatter plot. What is a reasonable interpretation for the slope in this context? a. y = x + 80; The number of students decreases by 1 student per year. b. y = 10x + 80; The number of students decreases by 1 student per year. c. y = 10x + 80; The number of students decreases by 10 students per year. d. y = x + 80; The number of students decreases by 10 students per year. 59) People at a movie theater were surveyed about whether they bought a popcorn or soda. The table below shows the results. What is the relative frequency of people who bought soda? a. 0.375 c. 0.425 b. 0.625 d. 0.25 60) Using the two-way table from #57, determine the relative frequency of buying a soda among those who bought popcorn. Round to the nearest hundredth as necessary. a. 0.60 c. 0.58 b. 0.23 d. 0.65 22