Math 9 Midterm Review

Transcription

1 Class: Date: Math 9 Midterm Review Short Answer 1. Which graphs represent a linear relation? 2. Which expressions have negative values? È i) ( 4) 3 3 ÎÍ Ê ii) 4 3 ˆ 3 È iii) ( 4) 3 3 ÎÍ È iv) ( 4) 3 3 ÎÍ 3. Insert brackets to make each statement true. a) = 13 b) = Determine the length of the hypotenuse, h. 5. Evaluate:

2 6. Determine this product. Ê 3 ˆ Evaluate: 3 3 ( 4) 3 8. A submersible descends at an average rate of 6.7 m/min. Express the depth below the surface after 4.2 min as a rational number. 9. Which decimal has a square root between 14 and 15? i) ii) 169 iii) 14.5 iv) Complete the table of values. y = x Evaluate: ( 12) Evaluate: 3 3 ( 4 + 2) 2 6 ( 9) 0 ( 2) ( 7 4) Which numbers are rational numbers? 5.5, 5 4, 11, Which of the following expressions is a binomial with degree 2? i) x 2 12x + 5 ii) 3x 2 iii) 8x 2 2x 1 iv) 7 x 2 2

3 15. Evaluate Write 9 5 as repeated multiplication. 17. Identify the polynomials that can be represented by the same set of algebra tiles. i) 3x x ii) 3x 2 5x + 6 iii) 6 + 5x 3x 2 iv) 5x 6 + 3x Write 2643 using powers of Write the product of ( 7) 4 ( 7) 5 as a single power. 20. This pattern of unit squares continues. Determine an equation that relates the number of unit squares, n, to the figure number, f. 21. Evaluate: ( 3) 6 ( 3) 4 ( 3) A large white square represents an x 2 -tile, a large black square represents a x 2 -tile, a white rectangle represents an x-tile, a black rectangle represents a x-tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Write the simplified polynomial. 23. Evaluate: 4 4 3

4 24. Which fraction has a square root between 3 and 4? 52 i) 3 61 ii) 3 iii) 37 4 iv) This object is made from 7 centimetre cubes. Determine its surface area. 26. Determine this difference Ê 1 1 ˆ 3 È 27. Write ÎÍ ( 7) ( 8) 3 as a product of powers. 28. Which expressions have the same answer as ( 17)? i) ii) iii) iv)

5 29. Which of the following expressions are polynomials? 1 i) 5 x ii) 1 6.5n 2 iii) 5 t iv) This graph represents a linear relation. Determine the value of x when y = Express as a single power. 32. A student has $1773 in her savings account. She withdraws $95 each week. A formula for calculating the amount of money remaining in her account is A = T 95w, where T dollars is the original amount and w is the number of weeks she has been withdrawing money. Determine the amount of money remaining in her account after 18 weeks. 33. Calculate the number whose square root is This object is made from 9 centimetre cubes. Determine its surface area. 35. Determine the value of

6 36. A square has an area of 26.8 cm 2. Determine the side length of the square, to the nearest millimetre. 37. Write 1 as a power in three different ways. 38. Simplify, then evaluate. ( 2) 5 ( 2) 7 ( 2) The pattern in this table continues. Determine the expression that relates the number of triangles to the figure number. Figure, f Number of Triangles, t Estimate to determine which sum is greater than 0. i) ( 7.7) ii) ( 1.6) iii) iv) Simplify: 12x x + 2 7x 2 8x 42. Determine the value of This object is composed of a cylinder of diameter 6 cm and height 11 cm on top of another cylinder of diameter 12 cm and height 4 cm. Determine the surface area of the object, to the nearest square centimetre. 6

7 44. Here are the 6 views of an object made using centimetre cubes. Determine its surface area. 45. Which expressions have the same answer as ( 0.45) 0.68? i) 4.5 ( 6.8) ii) ( 45) (6.8) iii) 45 ( 0.068) iv) ( ) 46. Determine this quotient. Ê 7 ˆ 10 Ê 4 ˆ Name the coefficients, variable, degree, and constant term in the polynomial 5x 2 8x

8 48. Which equation describes the graph below? i) y = 1 2 x + 2 ii) y = 1 2 x 2 iii) y = 2x 2 iv) y = 2x This graph represents a linear relation. Determine the value of x when y = Simplify, then evaluate. Ê ˆ 2 Ê ˆ 2 8

9 51. At a harbour, the effect of the tide changed the water level by 9.9 m in 4.5 h. What was the mean change in water level per hour? 52. This object is composed of a cube on top of a right rectangular prism. Determine the surface area of the object. 53. Write ( ) + ( ) + ( ) + ( ) in standard form. 54. Describe the graph of the equation x + 9 = Name the two whole numbers whose squares are closest to State which operation you would do first to evaluate A 3-cm cube is attached to the top of a right triangular prism as shown. Determine the surface area of the composite object, to the nearest square centimetre. 9

10 58. This object is composed of three identical cylinders and a right rectangular prism. Each cylinder has diameter 12 cm and height 5 cm. The rectangular prism has length 31 cm and square ends of side length 12 cm. Determine the surface area of the object, to the nearest square centimetre. 59. A large white square represents an x 2 -tile, a black rectangle represents a x-tile, and a small white square represents a 1-tile. Write the polynomial represented by this set of algebra tiles. 60. Evaluate: ( ) 0 ( ) 61. Determine the value of Which of these numbers are between 2 4 and 5 3? 3 4, 1 3, 5 6, This composite object is made using centimetre cubes. Determine its surface area. È 7 Ê 64. Evaluate: 15 5 ˆ Ê 7 ˆ 9 ÎÍ 12 10

11 65. A large white square represents an x 2 -tile, a large black square represents a x 2 -tile, a white rectangle represents an x-tile, a black rectangle represents a x-tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Write the simplified polynomial. 66. A large white square represents an x 2 -tile, a black rectangle represents a x-tile, and a small white square represents a 1-tile. What polynomial does this collection of algebra tiles represent? 67. Write Ê 9 7 ˆ 3 as a quotient of powers. 68. Yesterday, the temperature of a freezer was 6.9 C. When the technician checked the freezer today, its temperature had decreased by 8.8 C. Determine the temperature of the freezer today. 69. Dorina is having a party. She estimates that she will need 5 sandwiches for each guest, and 9 extra sandwiches for unexpected guests. a) Write an equation that relates the total number of sandwiches, T, to the number of guests, p. b) How many sandwiches will Dorina need for 16 guests? 11

12 70. This graph represents a linear relation. a) Estimate the value of y when x = 4. b) Estimate the value of x when y = Group like terms, then simplify x 7 + 7x 2 + 3x 7x x 72. Write as a power of Identify the greatest rational number. 2 3, 3 4, 5 6, A student first borrowed $44.75, then borrowed another $17.75 from his father. He then paid back $ How much does he still owe his father? 75. Evaluate The lengths of the two legs of a right triangle are 6.9 cm and 3.4 cm. Determine the length of the hypotenuse to 1 decimal place. 12

13 77. Name the two whole numbers whose squares are closest to Write the quotient of as a single power. 79. Which tables of values represent a linear relation? i) ii) iii) iv) x y x y x y x y A square garden has an area of m 2. a) Determine the length of one side of the garden. b) Determine the perimeter of the garden. 81. A barn is built in the shape of a right rectangular prism with a semi-circular roof. Determine the surface area of the barn. Give your answer to the nearest whole number. 13

14 82. Which equation describes the graph? i) x + y = 4 ii) x y = 4 iii) y x = 4 iv) x + y = This composite object is made of a 5-cm cube on top of a 10-cm cube. Determine its surface area. 84. List all the whole numbers between 63 and 101 that are perfect squares. 14

15 85. Write the number of unit cubes in the large cube as a power. 86. Combine like terms. Sketch algebra tiles if it helps. 9x 2 6x + 2x 7x Write a polynomial that simplifies to 6x 2 5x Which graph on this grid has the equation y = 2x + 2? 89. Write these powers in order from least to greatest. 2 5, 4 3, 3 4, In the equation P = 7n + 4, determine the value of P when n =

16 91. Determine an equation that relates the number of circles, C, to the figure number, n. 92. The cost to print stickers is $7.55, plus $0.65 per sticker. Determine an equation that relates the total cost, C dollars, to the number of stickers, s. 93. This object is composed of two identical cubes joined by a right rectangular prism. The edge length of each cube is 10 cm. The rectangular prism is 7 cm long and has square ends of side length 2 cm. Determine the surface area of the object. 94. Estimate the value of 5, to the nearest tenth Which graph on this grid has the equation y = 5? 16

17 96. This object is composed of a right triangular prism on top of a right rectangular prism. Determine the surface area of the object. 97. Write the base and the exponent of this power: ( 6) Evaluate ( ) È Ê 99. Express 7 4 ˆ ÎÍ 6 5 as a single power of Which rational number is greater? 1.8, Write the quotient of 6 6 as a single power Which fraction is a perfect square? 121 i) ii) iii) 400 iv)

18 103. Write an equation that describes the line Which graph on this grid has the equation y = x + 2? 105. Insert <, >, or = to make each expression true. a) b) Write the base of ( 3) 5. 18

19 107. A large white square represents an x 2 -tile, a large black square represents a x 2 -tile, a white rectangle represents an x-tile, a black rectangle represents a x-tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Sketch algebra tiles to model the polynomial 5 5v 2 + v Determine this product. Ê 4 ˆ Ê 5 ˆ Ê ˆ This object is made of a right rectangular prism of length 13 cm, width 6 cm, and height 4 cm. A cube of side length 2 cm has been removed from one corner. Determine the surface area of the object A large white square represents an x 2 -tile, a large black square represents a x 2 -tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. How would you model the polynomial 3x 2 4 with algebra tiles? Problem 111. Evaluate: 5(3) 5 3( 4) 5 Show your steps Blocks A, B, and C are joined together to form the composite object shown. Block A is a cube with side length 14 cm, Block B is a cube with side length 7 cm, and Block C is a right rectangular prism with length 28 cm, width 14 cm, and height 14 cm. Determine the total surface area of the composite object. Justify your answer. 19

20 113. Write a polynomial to represent the perimeter of each shape. a) b) 114. Marsha has 50 shares in an oil company and 180 shares in a gas company. On Monday, the value of her oil shares was $ and the value of her gas shares was $ On Friday, the value of her oil shares was $ and the value of her gas shares was $ Determine the change in price of a single share in each company. Show your steps Evaluate: (4) 2 + ( 3) 2 (3) 2 Show your steps. 20

21 116. Geoffrey has $130 in his savings account. Each week he withdraws $20. a) Write an equation that relates the amount of money in his account, A dollars, after t weeks. b) Create a table of values for the relation, then graph the relation. Use values of t from 0 to 6. Will you join the points on the graph? Explain. t A c) At what point will Geoffrey have $70.00 in his account? 117. The sum of two rational numbers, p and q, is 1.5. a) Make a table to show 5 possible pairs of numbers that satisfy this relation. Include p = 1.5 and q = 1.5 in your table. p q b) Graph the data. Describe your graph. c) Write an equation for the relation. 21

22 118. Evaluate this expression. Show your work ( ) A phone company charges a fixed cost of $2.95 per month, plus $0.55 per minute for local calls and $1.09 per minute for long distance calls. a) Write an equation that relates the total monthly cost, B dollars, to the local calls, p minutes, and long distance calls, q minutes. b) Determine the phone bill for a month in which 55 min of local calls and 31 min of long distance calls were made Determine the values of s and h. Show your work. 22