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CRCT Review

Practice solving algebraic equations and geometry problems. Includes questions on equations, transformations, shapes, and constructions.

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CRCT Review

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  1. CRCT Review Ms. Jennifer Heins

  2. Geometry Algebra Data Analysis Number Sense

  3. Algebra #1 • Which of the following statements describes a correct method for solving the equation below? 20 + 2w = 50 A. Add 20 to both sides of the equation and then divide both sides by 2 B. Subtract 20 from both sides of the equation, and then divide both sides by 2 C. Divide both sides of the equation by 2, and then add 20 to both sides. D. Divide both sides of the equation by 2, and then subtract -20 from both sides.

  4. Algebra #2 • Ashley studied one hour less than twice as many hours as Melissa studied. Let m stand for the number of hours Melissa studied. Which of the following expressions represents the number of hours Ashley studied? A. ½m – 1 B. 1 – ½m C. 1 – 2m D. 2m - 1

  5. Algebra #3 • Simplify: (12x – 4) – (8x + 4) A. 4x B. 4x – 8 C. 20x – 8 D. 20x

  6. Algebra #4 • The cost per person to rent an event space varies indirectly with the number of people who participate. If the cost per person is $72 when 3 people participate, what is the cost per person if 8 people participate? A. $9 B. $24 C. $27 D. $72

  7. Algebra #5 • If x = -3, find 3x² - 5x A. 12 B. -6 C. 42 D. 3

  8. Algebra #6 • Today, Emily has driven 180 miles in 4 hours. Tomorrow, she wants to drive 275 miles. Approximately how many hours should Emily plan to drive tomorrow if she drives at the same rate? A. 2 B. 5 ½ C. 6 D. 7

  9. Algebra #7 • Solve the equation for x: 5x – 1.2 = 6.8 A. 1.6 B. 16 C. 1.12 D. 8

  10. Algebra #8 • Solve for x: 2(x + 5) = -14 A. x = 2 B. x = 7 C. x = -2 D. x = -12

  11. The table shows how many scoops of hot chocolate mix are needed in order to make different numbers of cups of hot chocolate. For the data in the table, which of the following equations can be used to calculate s, the number of scoops of hot chocolate mix needed to make c cups of hot chocolate? A. s = 2 + c B. s = 2c C. s = c/2 D. s = 2/c Algebra #9

  12. Algebra #10 • The cost of renting a boat is $10. There is also a charge of $2 for each person. Which expression represents the total cost for renting the boat for p persons? A. 10 + 2p B. 10 – 2p C. 2 + 10p D. 2 – 10p

  13. Algebra #11 • Aaron has 5 fewer than 3 times the number of baseball cards that Sam has. Aaron has 31 baseball cards. The equation below represents the situation. 3x – 5 = 31 What does x represent in this equation? A. the number of cards Sam has B. the number of cards Aaron has C. how many more cards Aaron has than Sam D. how many cards Sam and Aaron have together.

  14. Algebra #12 • Look at the function table. • What happens to y when x increases by 2? A. y decreases by 3 B. y decreases by 6 C. y increases by 3 D. y increases by 6

  15. Algebra #13 • The number of hours, h, it takes to wash c cars at a school fundraiser is inversely proportional to the number of students, s, who come to help at the car wash. Which expression represents this relationship?

  16. Algebra #14 • Which statement about the graph is true? A. y stays the same as x decreases. B. y decreases as x decreases C. y increases as x increases D. y decreases as x increases

  17. Algebra #15 • The distance a spring is stretched directly varies with the amount of force applied. A force of 15 pounds stretches a spring 7 inches. How many pounds of force are needed to stretch the spring 21 inches? A. 5 pounds B. 30 pounds C. 45 pounds D. 60 pounds

  18. Kurt made this construction with a compass and a straight edge. Which construction did Kurt make? A. copying a line segment B. bisecting a line segment C. drawing a line parallel to a given line through a point not on the line D. drawing a line perpendicular to a given line through a point not on the line Geometry #1

  19. In this figure, A’B’C’D’ is a transformation of ABCD. What type of transformation is A’B’C’D’? A. dilation B. rotation C. reflection D. translation Geometry #2

  20. Geometry #3 • If the cylinder is sliced in half vertically as shown by the dotted line what shape is the cross section that is formed? A. circle B. cone C. rectangle D. sphere

  21. Max drew a triangle on the coordinate plane. He want to translate the triangle 3 units right and 5 units down. Which of the following represents the coordinates of the triangle after the translation? A. (1,0), (4, -4), (0, -4) B. (1, 10), (4, 6), (0, 6) C. (-5, 0), (-2, -4), (-6, -4) D. (-2, 5), (1, 1), (-3, 1) Geometry #4

  22. Geometry #5 Which must be true?

  23. Geometry #6 • To construct a line segment which is congruent to a segment that is given, you need to use A. a compass and straightedge B. a protractor and straightedge C. a compass and a protractor D. tracing paper

  24. Geometry #7 • If the circle below is rotated about the line through its diameter, what solid figure would be formed? A. cylinder B. cone C. sphere D. cube

  25. Geometry #8 • What figure does a horizontal cross section of the cylinder below create? A. rectangle B. circle C. sphere D. oval

  26. Geometry #9 • Mrs. Micelli placed a picture of an equilateral triangle on an overhead projector in her math class. The overhead projector dilated the triangle’s image on the screen by a scale factor of 3.5. If the length of each side of the actual triangle is 5 cm, what is the length of each side of the dilated triangle on the screen? A. 175 cm B. 17.5 cm C. 8.5 cm D. 3 cm

  27. Geometry #10

  28. Geometry #11 The graph shows that rectangle P’Q’R’S’ is a dilation of rectangle PQRS centered on the origin. What is the scale factor used to create rectangle P’Q’R’S’?

  29. Geometry #12 • In the diagram below, line DE is the perpendicular bisector of line segment AB. • Which statement is NOT true? B. C is the midpoint of line segment AB C. AE = EB D. AE = AC

  30. Geometry #13 • John wants to construct line segment PQ, a copy of line segment RS. What should he do first? A. Draw a point P above line segment RS. B. Draw a line through point R. C. Draw a line through point S. D. Draw a ray.

  31. Geometry #14 • Which is NOT a step for constructing line segment CD congruent to line segment B? A. Draw a ray with endpoint C. B. Open a compass so one end is on point A. C. Draw an arc AC. D. Open a compass so one end is on point B.

  32. Geometry #15 • What is being constructed in the diagram? A. a line through point Q perpendicular to line segment RS. B. a line through point Q parallel to line segment RS C. a line through point R parallel to line segment QR D. A line through point S perpendicular to line segment QR

  33. Number Sense #1 Mrs. Blackwell has been on a diet for the last six weeks and goes to a support group every Monday night to weigh in & make plans for the next week. The changes in her weight for each of the six weeks are listed below, with negative numbers denoting a loss in weight and positive numbers denoting a gain in weight from the previous week. Place the data in order from the smallest number to the largest number.

  34. Number Sense #2 • What is the value of the expression below? A. -10 B. -4 C. 4 D. 10

  35. Number Sense #3 • Use the number line to complete the sentence. A. negative because both y and z are negative B. positive because both y and z are negative C. negative because z is farther from 0 than y D. positive because y is closer to 0 than z

  36. Number Sense #4 A dolphin is 30 ft below the surface of the water. She rises 23 feet, sinks 17 ft, and finally rises another 27 ft. If there are no other changes, the dolphin is _______. A. 3 ft above the surface of the water B. 3 ft below the surface of the water C. 63 ft above the surface of the water D. 63 ft below the surface of the water

  37. Number Sense #5 • Simplify. A. 4 B. 14 C. 17 D. 26

  38. Number Sense #6 • Which of these sets of numbers is ordered from least to greatest?

  39. Number Sense #7 8 – (-10) A. 2 B. -2 C. 18 D. -18

  40. Number Sense #8

  41. Number Sense #9 • One cold winter morning, the temperature was -3°F. Jacob was not able to start his car until the temperature had risen 8 degrees. What was the temperature when he finally started his car? A. 5°F B. -5°F C. 11°F D. -11°F

  42. Number Sense #10 • Which expression has the greatest value?

  43. Number Sense #11

  44. Number Sense #12

  45. Number Sense #13

  46. Number Sense #14 -2 – (-8) A. -6 B. 6 C. -10 D. 10

  47. Number Sense #15 • Which integer makes this inequality true? -19 < ? < -13 A. -20 B. -15 C. -10 D. 14

  48. Data Analysis #1 • Below is a list of the ages of your friend’s aunts and uncles. 23, 33, 35, 27, 38, 25, 24, 19 What is the median age? A. 25 B. 26 C. 27 D. 28

  49. Data Analysis #2 • At lunch, the Grade 7 teacher were talking about the high price of gasoline. They compared the gas mileage of their vehicles by making the data set below, and graphing it as a box-and-whisker plot. Which graph shows the box-and-whisker plot the teachers made? 31, 27, 12, 23, 45, 24, 48, 19, 34, 17, 29, 22, 29, 24, 39

  50. Data Analysis #3 • Which measure has the greatest value for the data listed? 18 24 18 23 19 24 23 18 A. mode B. mean C. range D. median

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