Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 08 Mathematics Mathematics Exam 3 Description: Paper-Based: 8th Grade Comprehensive Mathematics Assessment Form: 201 1. Which of the following statements is correct? Select all that apply. 22 3.14 is rational, and is rational. 7 22 3.14 is irrational, and is rational. 7 π is irrational, and 3.14 is irrational. π is rational, and 3.14 is irrational. E. 22 7 F. 22 7 is rational, and π is irrational. is irrational, and π is irrational. 2. Which fraction is equal to 0.57? 52 99 19 33 26 45 19 30
3. Which value is closest to 2.25 2.5 2.75 3.5
4. Three irrational numbers are given below. Select the option that correctly plots the approximate value of each number on the number line.
5. Which of these expressions are equivalent to 2 2 28? Select all that apply. 2 4 2 6 ( 1 2) 6 ( 1 2) 4 E. 1 64 F. 16 6. Mrs. Jones asked her students to write an equivalent numerical expression to Which of these responses is correct?
7. What is x 3 = 64? 2 4 8 16 8. Tim bought 128 sandbags to completely fill a cube-shaped sandbox. Each bag fills a cubic foot in the sandbox. What is the length, in feet, of one of the sides of the sandbox? 9. The diameter of a speck of dust is about 0.00002 in. Which of these is an appropriate estimate for the diameter of the speck of dust? 2 10 5 in. 2 10 4 in. 2 10 4 in. 2 10 5 in.
10. The populations of two towns, town A and town B, are being compared. The population of town A is and the population of B is How many times greater is the population of town B than town A? 0.2 0.5 2 5 11. Which expression is equivalent to (9.5 10 5 ) (2.3 10 4 )? 7.2 10 9.27 10 7.2 10 5 9.27 10 5
12. Tyler s math class found that it would take dollar bills to cover a square mile area. The surface area of the United States is about square miles. About how many dollar bills are needed to cover the United States? 13. Select all relations that represent a function. {( 7, 5), (3, 2), ( 6, 4), ( 1, 9), ( 7, 3)} {(6, 8), ( 5, 8), (4, 1), ( 9, 7), ( 3, 3)} {( 2, 6), (0, 8), ( 4, 5), (9, 0), (7, 2)} {(9, 9), ( 8, 1), (0, 0), ( 5, 6), (2, 5)}
14. Which statement is true of table A and table B shown below? Table A represents a function because there is only one output for each input value. Table B represents a function because there is only one output for each input value. Table A represents a function because there is only one input for each output value. Table B represents a function because there is only one input for each output value.
15. Sarah has been keeping track of how many hours she practices basketball each week and thinks that the percentage of free throws she makes during practice improves the more she practices. To check this, she makes a graph comparing the number of hours she practices each week with the percentage of free throws she makes each week. Based on what she learned in her Algebra class, she realizes that her graph represents a function. Which of these could be Sarah's graph?
16. Look at the table shown below. x y 5 150 3 94 1 38 Which situation(s) could be modeled by the table shown? Select all that apply. A driver already drove 10 miles. Now she is driving at a rate of 28 miles per hour. A driver already drove 38 miles. Now she is driving at a rate of 56 miles per hour. A shopper needs to buy shelves for $56 each. He will also purchase $28 in other merchandise. A shopper needs to buy shelves for $28 each. He will also purchase $10 in other merchandise. E. A student read 10 pages in her book already and is currently reading at a rate of 56 pages per hour. F. A student read 38 pages in her book already and is currently reading at a rate of 28 pages per hour.
17. Hector purchased a used car and the graph below shows the number of miles on the car since he bought it. Which of these is a correct statement based on the graph? Hector is driving the car 2000 miles per month. Hector is driving the car 3000 miles per month. The car had 2000 miles on it when Hector bought it. The car had 3000 miles on it when Hector bought it. 18. The table of values below shows the number of minutes since Raul got online at an Internet cafe and the total amount he paid up until that point. If x is the number of minutes since Raul got online and y is the total amount he paid in dollars, which of these equations models this situation? Number of Minutes Since Raul Got Online Total Amount Paid 0 $4.00 2 $4.12 4 $4.24 6 $4.36 8 $4.48 x = 0.06y + 4 x = 0.12y + 4 y = 0.06x + 4 y = 0.12x + 4
19. Damon is playing with his remote controlled car. He increases its speed for 15 seconds. He stays approximately the same speed for the next 15 seconds. He increases its speed again for 10 seconds. He then slows it down to a stop for the last 20 seconds. Select the graph that best represents Damon's remote controlled car speed over time.
20. Todd's teacher asked him to construct a graph with the following specifications. y is decreasing when x is between 5 and 0 y is increasing when x is between 0 and 5 the relationship between x and y is non linear from x = 5 to x = 0 the relationship between x and y is linear from x = 0 to x = 5 Todd constructed the graph below. What did he do wrong? Select all that apply. He has y increasing when x is between 5 and 0 instead of decreasing. He has y decreasing when x is between 0 and 5 instead of increasing. He has a linear relationship from x = 5 to x = 0 instead of a non linear relationship. He has a non linear relationship from x = 0 to x = 5 instead of a linear relationship. 21. Which of these statements are correct about an angle measuring 78 in a coordinate plane? Select all that apply. If it is reflected across the line y = x, it will still measure 78. If it is translated 22 units down, it will no longer measure 78. If it is rotated 180 about the origin, it will no longer measure 78. If it is reflected across the y axis, it will no longer measure 78. E. If it is translated 26 units to the left, it will still measure 78. F. If it is rotated 90 about the origin, it will still measure 78.
22. Suppose a rectangle will undergo a rotation about the origin of a coordinate plane and a translation of 6 units down. Which of these is a true statement? The resulting rectangle will be congruent to the original rectangle only if the rotation occurs before the translation. The resulting rectangle will be congruent to the original rectangle only if the translation occurs before the rotation. The resulting rectangle will be congruent to the original rectangle regardless of the order of the rotation and the translation. The resulting rectangle will not be congruent to the original rectangle regardless of the order of the rotation and the translation. 23. Which transformation could NOT be used to prove that two circles are congruent to one another? a dilation with a scale factor of 2 a dilation with a scale factor of 1 a reflection a rotation
24. Figure JKLM is shown below. Figure JKLM is dilated by a scale factor of with the center of dilation at the origin. What are the coordinates for the vertices of the new image?
25. Triangle ABC is shown on the coordinate plane below. Which of these represents the rotation of triangle ABC by 90º counterclockwise about the origin?
26. Rectangle PQRS is graphed on a coordinate plane with vertices P( 2, 1), Q( 2, 4), R( 4, 4), and S( 4, 1), as shown below. Rectangle PQRS is reflected over the y axis and then translated 2 units to the left resulting in Rectangle P'Q'R'S'. What are the coordinates of P'? ( 4, 1) (0, 1) (1, 0) (4, 1) 27. Miguel claims that if a trapezoid is rotated, reflected, or translated to produce another trapezoid, the two trapezoids are similar. However, he says that if a trapezoid is dilated to produce another trapezoid, the two trapezoids are not similar. Which of these statements are correct? Select all that apply. Miguel is right in saying that if a trapezoid is rotated to produce another trapezoid, the two trapezoids are similar. Miguel is right in saying that if a trapezoid is reflected to produce another trapezoid, the two trapezoids are similar. Miguel is right in saying that if a trapezoid is translated to produce another trapezoid, the two trapezoids are similar. Miguel is right in saying that if a trapezoid is dilated to produce another trapezoid, the two trapezoids are not similar.
28. Suppose a pentagon graphed on a coordinate plane will undergo a dilation. Which of these is a true statement? The resulting pentagon will be similar to the original pentagon only if the center of the dilation is the origin. The resulting pentagon will be similar to the original pentagon only if the center of the dilation is a vertex of the original pentagon. The resulting pentagon will be similar to the original pentagon regardless of the center of the dilation. The resulting pentagon will not be similar to the original pentagon regardless of the center of the dilation. 29. Samantha is studying the geometric design of roads. She uses a surveying tool to measure the angles at the intersections of the roads near to her school, which are shown in the picture below (NOT to scale). Samantha noted that Smith Street is parallel to Abbey Road. Which of the following statements are true about the picture? Select three that apply. The value of x is 8. The value of x is 21. The measure of angle A is 42. The measure of angle B is 42. E. Angles A and B are same side interior angles.
30. Triangle Triangle is similar to triangle is a right triangle. Which angle measure is closest to the smallest angle in triangle
31. Given: ΔABC is a right triangle There are 3 shaded squares with sides a, b, and c, respectively. a, b, and c are also the lengths of the sides of the right triangle, such that the area of the square with side a is a 2 and the area of the square with side b is b 2 and the area of the square with side c is c 2. Prove: a 2 + b 2 = c 2 (Pythagorean Theorem) Proving which of the following will prove the Pythagorean Theorem? When you subtract the area of the smallest square from the medium square the difference equals the area of the largest square. The sides of a right triangle are also the sides of squares. m A + m B = m C The area of the two smaller squares will add up to the area of the largest square.
32. Which set of measurements identify the length, width, and diagonal of a rectangle? 5 ft, 7 ft, 8 ft 6 in., 7 in., 12 in. 8 cm, 9 cm, 10 cm 9 m, 12 m, 15 m 33. A ladder that has a length of 13 m leans against a wall with the base of the ladder 5 m away from the bottom of the wall. Use this information to find how high above the ground the ladder meets the wall. 194 m 13 m 12 m 8 m
34. Jenny s pencil case is 24 cm long, 11 cm wide, and 4 cm high. What is the longest length, in cm, of a pencil that can fit in Jenny s pencil case? 21.7 24.3 26.4 26.7 35. What is the distance between the points (4, 2) and ( 1, 10)? 5 units 6 units 12 units 13 units
36. What is the distance between the two points plotted below? 5 units 9 units 12 units 15 units 37. Two cars are traveling along the same highway. The distance, d, in miles, from San Francisco after h hours spent driving is described for each car below. Car A: d = 60h + 20 Car B: h d 0 60 2 160 4 260 Select all the statements that are true. Car A is traveling at the same rate, in miles per hour, as Car Car A is traveling at a faster rate, in miles per hour, than Car Car A is traveling at a slower rate, in miles per hour, than Car Car A is originally closer to San Francisco than Car E. Car A is originally at the same distance from San Francisco as Car F. Car A and Car B are at the same distance away from San Francisco after 4 hours.
38. Consider the functions represented by the graph and table shown below. Which statement is true of these functions? The rate of change of the function in the graph is more than that of the function in the table by 2 units. The rate of change of the function in the graph is less than that of the function in the table by 2 units. The rate of change of the function in the graph is more than that of the function in the table by 1 unit. The rate of change of the function in the graph is less than that of the function in the table by 1 unit.
39. Consider the linear function y = 10x + 2 and the linear function with a slope of 2 and a y intercept of 10. Which of these statements are correct? Select two that apply. The function y = 10x + 2 has the greater y intercept The function with a slope of 2 and a y intercept of 10 has the greater y intercept. The two functions have the same y intercept. The function y = 10x + 2 has the greater rate of change. E. The function with a slope of 2 and a y intercept of 10 has the greater rate of change. F. The two functions have the same rate of change. 40. Which function is nonlinear? x y 1 5 0 4 1 3 3 1 x y 4 7 2 6 2 4 4 3 {( 2, 10), (0, 4), (2, 2), (4, 8)} {(1, 1), (4, 2), (9, 3), (16, 4)}
41. Select the three linear functions. y = y = y = x 8 4 6 x 2 x 2 y = 2x E. y = 4x 3 F. y = 8 4 6
42. Which functions are nonlinear? Select two that apply. y = 5 y = x 3 + 1 E.
F. 43. The table below shows the proportional relationship between the time in hours (h) Sara babysits and the amount in dollars (a) Sara earns babysitting. h a 2 8 3 12 4 16 5 20 The equation a = 5h shows the relationship between the amount in dollars (a) Abbey earns babysitting and the time in hours (h) Abbey babysits. Which statement correctly identifies who earns more and how much more she earns? Sara earns $1 more per hour than Abbey. Sara earns $4 more per hour than Abbey. Abbey earns $1 more per hour than Sara. Abbey earns $5 more per hour than Sara.
44. Zoe and Lara are both traveling to an out-of-town soccer tournament with their parents. The distance traveled by Zoe and her family during their trip can be modeled by the equation where x represents the number of hours traveled and D represents the distance traveled in miles. The graph below models the distance, y, traveled by Lara's family after x hours. Which statement correctly compares the speeds at which Zoe's and Lara's families traveled? Zoe's family traveled at a speed 5 mph faster than Lara's family. Zoe's family traveled at a speed 35 mph faster than Lara's family. Zoe's family traveled at a speed 5 times as fast as Lara's family. Zoe's family traveled at a speed about 2 times as fast as Lara's family.
45. What is the equation of the line shown in the coordinate plane below?
46. Select the equation that represents the graph of the line below. y = x 1 y = y = 1 2 x 1 1 2 x + 2 y = x + 2
47. What is the value of x in the graph below? 4 8 10 18 48. Select all equations that have infinitely many solutions. 5x + 10 = 5x + 20 4(2x 5) = 8x 20 5x + 8 x = 20 + 4x 12 15x (10 + 5x) = 20x 10
49. Which statement correctly describes the solution(s) of the equation below? The equation has one solution, which is The equation has one solution, which is The equation has infinitely many solutions. The equation has no solution. 50. Which value of x satisfies the equation
51. What is the solution to the equation shown below? 52. What is the solution to the system of equations shown in the graph? ( 5, 2) (2, 5) No solution All real numbers
53. Select all the statements that correctly describe the solutions to this system of equations. 2x y = 0 x + y = 9 There is exactly one solution to the system of equations. There is more than one solution to the system of equations. The coordinates (3, 6) are the solution to the system of equations. The coordinates (6, 3) are the solution to the system of equations. E. The coordinates ( 3, 6) are the solution to the system of equations. 54. How many solutions does the system of equations shown below have? no solution one solution two solutions infinite solutions 55. Two families are saving up for a summer trip. The Smith family originally has $1000 and will save $50 every week. The Jones family originally has $500 and will save $75 every week. After how many weeks will the two families have saved up the same amount of money? 4 12 20 60