MATH 9 - Midterm Practice - Chapters 1-5

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1 Period: Date: MATH 9 - Midterm Practice - Chapters 1-5 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What type of symmetry is shown by the figure? a. horizontal line symmetry only c. many types of line symmetry b. oblique line symmetry only d. vertical line symmetry only 2. The symmetry shown by the flag of the Bahamas is a. vertical line symmetry c. oblique line symmetry b. rotation symmetry d. horizontal line symmetry 5

2 3. In the figure shown, the order of rotation is a. 1 c. 6 b. 3 d What is the angle of rotation of the figure? a. 15 c. 45 b. 30 d. 60 2

3 5. Each of the 12 identical cubes in the object has dimensions of 2 cm. What is the exposed surface area of the object, excluding the base? a. 47 cm 2 c. 414 cm 2 b. 94 cm 2 d. 188 cm 2 6. Compare the surface area of Block B to that of Block C. Which statement is correct? a. The surface area of Block B is equal to that of Block C b. The surface area of Block B is greater than that of Block C c. The surface area of Block C is greater than that of Block B d. The surface area of Blocks B and C cannot be determined 7. Which decimal number is equivalent to 3 8? a c b d

4 8. Stocks can gain or lose money over time. Changes in the price of stocks are shown using decimal numbers. The following stocks are listed along with the price changes over a one-week period. Stock A Stock B 5.18 Stock C Stock D 1.25 Stock E 0.48 Which choice lists the stocks in order, from the stock with the greatest gain to the stock with the greatest loss? a. A, B, C, D, E c. B, A, D, C, E b. A, C, E, D, B d. B, D, E, C, A 9. Evaluate ( 5.2) a c. 2.0 b. 3.2 d What is ? a. 3 2 b. 4 3 c. d Evaluate a. 5 9 b Which diagram represents the power 3 3? c. d a. c. b. d. 4

5 13. Which powers are equal in value? 32 2, 4 6, ( 5) 4, 2 10 a. 4 6 and ( 5) 4 c and 2 10 b. ( 5) 4 and 2 10 d and Express as a single power. a. 7 2 c. 7 6 b. 7 4 d Evaluate a c. 125 b. 625 d Express ( 4) 3 ( 4) 9 as a single power. a. ( 4) 3 c. ( 4) 12 b. ( 4) 6 d. ( 4) What is 9 3 (9 6)? a. 27 c. 81 b. 75 d What is ( ) 2 3 4? a. 0 c. 12 b. 2 d Which of the following expressions represents the surface area of this rectangular prism? a c. (2 4 2 ) + (6 4 2 ) b (4 6) d (4 6) 5

6 20. Determine which expression represents the volume of the cube. a c. 5 6 b d Calculate the volume of the cube. a units 3 c units 3 b units 3 d units If a colony of 1000 bacteria doubles in size every 2 h, what is the size of the colony after 6 h? a c b d A scale factor greater than 1 indicates a. that the image is an enlargement of the actual object b. that the image is a reduction of the actual object c. that the image is the same size as the actual object d. that the image is a different shape than the actual object 6

7 24. The scale factor used to draw the letter on the right is a. equal to 0 c. greater than 1 b. equal to 1 d. less than A digital picture on a computer screen is 8.2 mm wide. When the picture is printed, the image enlarged by a scale of 1:3.5. What is the width of the printed picture? a mm c mm b. 3.5 mm d mm 26. An image with a scale of 8:1 means a. there are 8 units of the actual object for every unit of the image b. there is 1 unit of the actual object for 8 units of the image c. there are 8 units of the image for every unit of actual size d. there is 1 unit of the image for every 8 units of actual size 27. In the two triangles shown, A and D are a. complimentary angles c. exterior angles b. corresponding angles d. inscribed angles 7

8 28. How would you describe the two triangles below? a. complimentary triangles c. equal triangles b. equilateral triangles d. similar triangles 29. What scale must be applied to make JKL from RST? a. 1:5 c. 2:1 b. 1:4 d. 4:1 8

9 30. This polygon has sides that are 1.5 cm each. If a similar polygon was created using a scale factor of 3, determine the side length of the similar polygon. a. 0.5 cm c. 3.5 cm b. 1.5 cm d. 4.5 cm 31. Compare hexagon A to hexagon B. Hexagon A has a. angles that are smaller than the angles in hexagon B b. angles that are proportional to the angles in hexagon B c. angles that are larger than the angles in hexagon B d. angles that are equal to the angles in hexagon B 32. A scale diagram of the polygon below was created using a scale factor of 4. The interior angles of the new polygon would be a. 1 times the size of the angles of the original polygon 4 b. the same size as the angles of the original polygon c. 2 times the size of the original polygon d. 4 times the size of the original polygon 9

10 33. The term 5x 3 y 2 z represents the a. sum of 5 and x 3 and y 2 and z c. 10 times the sum of x and y and z b. product of 5 and x 3 and y 2 and z d. 5 times the sum of x 3 and y 2 and z 34. How many terms are there in the polynomial 4x 2 + 3x 5? a. 2 b. 3 c. 4 d How many terms are there in the polynomial 2c 2 + 3cd 2d 2 + 5? a. 2 b. 3 c. 4 d Identify the like terms in the following list of terms. 2g 2, 3gh, 2h 2, 4g 2, 5g 2 h 2 a. 2g 2 and 4g 2 c. 2h 2 and 5g 2 h 2 b. 2g 2 and 2h 2 d. 3gh and 5g 2 h When you combine the like terms in 3a 2 2a 4a a, the result is a. 3a 2 3a + 2 c. a 2 7a + 2 b. a 2 5a + 2 d. 7a 2 5a When the following model is simplified, it produces the expression a. 3x 2 + 5x + 2 c. x 2 3x 4 b. 2x 2 + 2x 2 d. 3x 2 5x The opposite expression for 2x 2 4x + 3 is a. 2x 2 + 4x 3 c. 2x 2 4x 3 b. 2x 2 + 4x + 3 d. 2x 2 4x Subtract the following polynomials. (7j 2 2j) (4j + 5) a. 7j 2 2j 5 c. 7j 2 6j 5 b. 7j 2 6j + 5 d. 7j 2 + 2j Simplify (4z 2 + 2z + 2) (3z 2z 2 3) + (2 + 5z + 3z 2 ). The answer is a. 3z 2 + 4z + 1 c. 9z 2 + 6z + 7 b. 6z 2 + 4z + 5 d. 9z 2 + 4z

11 Short Answer Write your answer in the space provided. 42. Draw all lines of symmetry for the figure. Label each line with the type of symmetry. 43. Complete the rotation of the figure. 11

12 44. What is the surface area of the object? 45. The object below is made of 0.5-m cubes. There is one cube completely hidden from view under the stack on the left. There is a total of 10 cubes in the object. Calculate the surface area of the object, excluding the bottom. 46. Complete the expression with the symbols <, >, or =. a) 5 14 b) c) d) Jerry s bedroom is square. He has a square desk in his bedroom which has an area of cm 2. The area of the bedroom is sixteen times the area of the desk. What is the side length of the bedroom? 48. Calculate the dimensions of a square that has the same area as a circle with a radius of 5.7 cm. Round your answer to the nearest tenth of a centimetre. 12

13 49. Denise evaluated the following expression as shown: ( ) ( 8.4 2) = = Did she evaluate the expression correctly? If not, show all the steps to correctly evaluate the expression and show the correct solution. Explain where Denise went wrong. 50. Tia travels from her home in Kelowna to visit a friend in Edmonton. The cost of a taxi from her home to the airport is $15.00 each way. The cost of her round-trip flight is $ She stays at a hotel for three nights, at a cost of $87.20 per night. How much does Tia spend, in total, on her trip? 51. Evaluate each expression. Write your answer in lowest terms. a) b) c) Evaluate each expression. a) 64 as a power of 2 c) 1296 as a power of 6 b) 243 as a power of 3 d) 4096 as a power of Write each power as repeated multiplication, and evaluate. a) 7 4 c) 12 3 b) 11 3 d) Given the side lengths below, calculate the volume of each cube. a) 8 cm c) 50 mm b) 14 m d) 0.6 km 55. Evaluate a) Ê ˆ 19 Ë Á Ê b) ( 82 2) ˆ 5 Ë Á Ê ˆ c) Ë Á Ê 9 3 ˆ Ê ˆ 36 d) Ë Á Ë Á Write an expression using exponents, and determine the total area of a pair of squares, given their side lengths. a) 6 cm, 7 cm b) 4 cm, 9 cm c) 8 cm, 11 cm 13

14 Write your answer in the space provided. 57. Use the grid provided to draw an enlargement of the letter using a scale factor of In a drafting class, students must create reductions of actual objects for technical diagrams. Barry wants to use a scale factor of 0.25 to draw a machine part. If the actual object has a width of 100 cm, what should the width of Barry s drawing be? 59. Examine the object below. Using a ruler, create an enlargement of the object, using a scale factor of Laura uses a map to determine the distance between her hometown and the closest campground. On the map, this distance is 2.5 cm. The actual distance is 15 km. What is the scale used on the map? 61. The scale diagram of a basketball court uses a scale of 1:280. The length of the court measures 10 cm in the diagram. What is the actual length of the court, in metres? 14

15 62. Draw a triangle similar to KLM using a scale factor of Label the length of each side. 63. You want to draw a triangle similar to the one shown. You are going to use a scale factor of 2. What should the length of the sides of the new triangle be? 64. Replace the question mark with an algebra tile model to make a true statement. 15

16 65. Simplify. Show the answer as an expression. 66. Create a model to represent the answer to the following subtraction. (5x 2 4x + 5) (3x 2 2x + 4) 67. Draw a diagram to show the opposite expression for the model shown. 68. Gail charges a flat rate per hour for babysitting for a family. In addition, she charges an hourly fee for each child she is looking after. Her flat rate per hour is twice the square of what she charges per hour for each child. Create an expression and an algebra tile model to show her hourly rate for babysitting 3 children. 16

17 MATH 9 - Midterm Practice - Chapters 1-5 Answer Section MULTIPLE CHOICE 1. C 2. D 3. C 4. B 5. D 6. A 7. C 8. B 9. C 10. B 11. A 12. B 13. C 14. C 15. B 16. C 17. D 18. B 19. C 20. C 21. B 22. C 23. A 24. D 25. D 26. C 27. B 28. D 29. B 30. D 31. D 32. B 33. B 34. B 35. C 36. A 37. B 38. B 39. A 40. C 1

18 41. D SHORT ANSWER area of top:25 35 = 875 cm 2 area of front: = 875 cm 2 area of side:25 25 = 625 cm 2 total surface area: 2( ) = 4750 cm 2 The cutout piece does not affect the surface area of the object. The totalsurface area of the object is 4750 cm There are 38 faces exposed. Each face is 0.5 m by 0.5 m or 0.25 m = 9.5 m 2. The total surface area exposed is 9.5 m 2. 2

19 46. a) 5 14 < 0.4 c) 0. 6 = b) > 2 3 d) = Area of bedroom = 16 area of desk = = cm 2 Side length of bedroom = = 400 cm The side length of the square bedroom is 400 cm. 48. Area of circle = πr 2 = π(5.7) 2 = Side length of square = The square is approximately 10.1 cm by 10.1 cm. 49. ( ) ( 8.4 2) = ( 3.3) 4.2 = No, Denise did not evaluate the expression correctly. She made a mistake subtracting 7.8 from 4.5. The answer should be negative, not positive. 50. cost of airfare + cost of taxi + 3(cost of hotel night) = = = Tia spends a total of $ on her trip. 3

20 51. a) = = 15 2 = b) = = = 5 12 c) = = = a) 2 6 c) 6 4 b) 3 5 d) a) = 2401 c) = 1728 b) = 1331 d) = a) 512 cm 3 c) mm 3 b) 2744 m 3 d) km a) 1 c) 17.6 b) d) a) = 85 cm 2 b) = 97 cm 2 c) = 185 cm

21 cm 0.25 = 25 cm The width of Barry s drawing should be 25 cm. 59. Check that the enlargement has the measurements shown on the labels in the diagram below = 6 The scale used on the map is 1 cm:6 km = 10 x x = 2800 cm 1m= 100 cm 2800 cm = 28 m The length of the actual basketball court is 28 m. 62. Multiply each side of KLM by = 2 units = 1.9 units = 2.5 units Draw a triangle with the corresponding side lengths. 63. HJ = 2 5 cm = 10 cm HI = 2 4 cm = 8 cm IJ = 2 7 cm = 14 cm HJ would be 10 cm long, HI would be 8 cm long, and IJ would be 14 cm long. 5

22 p 2 p c 2 + 3c 6

Math 9 Final Exam Review and Outline

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