Math 9 Final Exam Review and Outline

Transcription

1 Math 9 Final Exam Review and Outline Your Final Examination in Mathematics 9 is a comprehensive final of all material covered in the course. It is broken down into the three sections: Number Sense, Patterns and Relations, and Shapes and Spaces. Format: Number Sense Unit: 35 Multiple Choice, Short Answer Patterns and Relations Unit: 0 Multiple Choice, 5 Short Answer Shapes and Space Unit: 3 Multiple Choice, 3 Short Answer Please use these review materials as an outline of what you are responsible for. Remember to use the study skills we have worked on all year while you are studying. Tips: Put away electronic devices while studying If you don t know how to do something, first look in your notes and textbook. Youtube is an excellent resource there are many videos explaining the material we have studied. Number Sense Review 1. Determine the value of.. Determine the value of. 3. Calculate the number whose square root is.. Identify the decimals that are perfect squares. 36, 3.6, 0.36, 0.036, Determine the value of. 6. Between which two whole numbers does lie? 7. A square garden has an area of 0.5 m. a) Determine the length of one side of the garden. b) Determine the perimeter of the garden. 8. To estimate the value of, determine the two whole number perfect squares closest to and their square roots. 9. Determine the value of, to the nearest tenth.

2 10. Approximate to the nearest tenth. 11. Name decimals that have square roots between.6 and Replace with a decimal to make this statement true. 13. Replace with a fraction to make this statement true. 1. A square has an area of 8.9 cm. Determine the side length of the square, to the nearest millimetre. 15. Write the number of unit cubes in the large cube as a power. 16. Write the base and the exponent of this power: 17. Write the base and the exponent of this power: 18. Write as a power, then evaluate the power. 19. Write as a power, then evaluate the power. 0. Which answers are positive? i) ii) iii) iv) 1. Write 7 and 3 as a power with base 3.

3 . Which power is greater, or? 3. Complete this table. Power Base Exponent Repeated Multiplication 7 3. Write these powers in order from least to greatest.,,, 5. Evaluate: 6. Write 865 using powers of Write 1 as a power in three different ways. 8. Write 1 as a power in three different ways. 9. Write in standard form. 30. Write using powers of Write in standard form. 3. Write the product of ten thousand times one thousand as a power of Write + in standard form. 3. Which number, or 00 00, is greater? 35. State which operation you would do first to evaluate. 36. State which operation you would do first to evaluate. 37. Evaluate: 38. Evaluate:

4 39. Identify, then correct, any errors in the work below. 0. Determine the first terms of this pattern: What is the 7 th term? 1. Insert brackets to make each statement true. a) b). Evaluate. a) b) c) What do you notice about the answers? 3. Evaluate:. Write the product of as a single power. 5. Write the product of as a single power. 6. Write the quotient of as a single power. 7. Write the quotient of as a single power. 8. Evaluate: 9. Evaluate: 50. Simplify, then evaluate. 51. Simplify, then evaluate.

5 5. Evaluate: 53. Write as a product of powers. 5. Write as a quotient of powers. 55. Write as a product of powers. 56. Simplify, then evaluate. 57. Evaluate: 58. Simplify, then evaluate. 59. Simplify, then evaluate. 60. Simplify, then evaluate. 61. Express as a single power of Is the value of positive or negative? Explain. 63. Write the rational number represented by the letter P on the number line, as a decimal. 5 P

6 6. Write the rational number represented by each letter on the number line, as a decimal. 0. R Q Write the rational number represented by each letter on the number line, as a fraction. 3 B 1 1 C Write 3 rational numbers between.3 and Which rational number is greater? 3.3, Which rational number is less?, Insert <, >, or = to make each expression true. a) b) Insert <, >, or = to make each expression true. a) b) Insert <, >, or = to make each expression true. a) 065 mm 0.65 cm b) 333 m 33.3 km c) 17 cm 1.7 m 7. Order these numbers from least to greatest.,,, 73. Order these numbers from greatest to least. 1 1, 1., 1 1,, Write the addition statement that this number line represents.

7 Write the addition statement that this number line represents Determine this sum. 77. Determine this sum. 78. Determine this sum. 79. Determine this sum. 80. Determine this sum Estimate whether this sum is greater than or less than Estimate whether this sum is greater than or less than Determine a number that makes this sentence true. 8. Determine this difference Determine this difference.

8 86. Determine this difference. 87. Determine this difference Determine this difference Which expressions have negative answers? Determine these negative answers. i) ii) iii) 90. Evaluate this expression Evaluate this expression Determine a rational number that makes this statement true. 93. Determine this product. ( 8) Determine this product Which products are less than 0? i) ii) iii) iv) v)

9 96. Determine this product. ( 17.5)( 19.) 97. a) Multiply: b) Use the result in part a to determine these products. i) ii) iii) iv) 98. Determine this product Determine this product Write 3 different products equal to Determine this product. ( 3.8)(5.1)(.) 10. Determine this product Given that ( 50) 50 = 85, determine this quotient. (.5) Determine this quotient Which quotients are less than 0? i) ii) ( ) 5 9 iii) 1 7 ( ) 8 9 iv) ( ) 9 5

10 106. Determine this quotient. ( 1.35) ( 3.5) 107. Determine this quotient Determine this quotient a) Determine this quotient. b) Use the result in part a to determine these quotients. i) ii) iii) iv) a) Write a division expression with the same answer as. 3 3 b) Write two multiplication expressions with the same answer as Suppose each rational number below is divided by 0.6. Evaluate the quotients that are less than ,.7, 5.3, 3.66, Which operation would you do first to evaluate this expression? 113. Evaluate. 11. Evaluate Evaluate Evaluate.

11 117. Evaluate: 118. Evaluate Evaluate. Give your answer to the nearest hundredth. Patterns and Relations Review 1. In the equation, determine the value of R when w = 13.. The pattern in this table continues. Write an equation that relates the number of squares to the figure number. Figure Number, f Number of Squares, s The cost of a taxi ride is the sum of a fixed cost of $.50 for the first kilometre, plus $1.75 for each additional kilometre. a) Write an equation that relates the cost of a taxi ride, F dollars, to the distance travelled, n. b) Determine the cost of a 8-km taxi ride.. Here is a pattern made with toothpicks. The pattern continues. Figure 1 Figure Figure 3 a) Write an equation that relates the number of toothpicks, N, to the figure number, n. b) How many toothpicks are needed for figure 80? 5. Which graphs represent a linear relation?

12 5 3 1 y Q P x 1 R Which equations represent a linear relation? i) ii) iii) iv) 7. a) Which table of values represents a linear relation? i) ii) iii) x 1 3 y x 1 3 y x 1 3 y b) Write an equation that represents the linear relation. 8. a) Create a table of values for the linear relation. Use,, 0,, for values of x.. x 0 y 9. Create a table of values for the linear relation, then graph the relation. Use values of x from 0 to 6.

13 x y y x A helicopter is at a height of 1600 m when it starts descending to land. The helicopter s height changes at an average rate of 10 m/min. a) Write an equation that relates the height of the helicopter, H metres, to the time since the helicopter began its descent, t minutes. b) What is the height of the helicopter 9 min after it began its descent? 11. Graph the equation.

14 y 0 x 1. Graph the following lines on the same grid. Label the lines. i) ii) y 0 6 x 13. Graph these equations on the same grid. What shape is formed by the lines? i) ii) iii) iv)

15 y x 6 1. Graph the following lines on the same grid. What shape do they form? i) ii) iii) 1 y x 15. a) Graph the straight line that passes through the points (0, 10), (3, 7), and (10, 0).

16 y x b) Write an equation to describe the line. 16. Match each equation with a graph on the grid below. i) ii) iii) Graph A 6 y Graph B Graph C x Match each equation with a graph on the grid below. i) ii) iii) iv)

17 10 y 8 Graph D Graph C 6 Graph A Graph B x Which graph on this grid has the equation x + y = 3? 8 y 6 Graph A Graph B Graph C x 19. Match each equation with a graph on the grid below. i) ii) iii)

18 1 8 y B A x C This graph represents a linear relation. a) Estimate the value of y when x = 7. b) Estimate the value of x when y = 5. 8 y x This graph represents a linear relation. a) Estimate the value of y when. b) Estimate the value of x when.

19 Consumption (L) y x This graph shows the gas consumption rate of a car. a) Estimate the volume of gas required to travel 630 km. b) Estimate the distance the car can travel on 60 L of gas. 70 Gas Consumption Distance (km) 3. A large white square represents an x -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?

20 . What algebra tiles would you use to model the polynomial? 5. Which of the following expressions are polynomials? i) ii) iii) iv) 6. Is each expression a monomial, binomial, or trinomial? a) b) x c) d) e) 7. Name the coefficients, variable, degree, and constant term in the polynomial. 8. Identify the degree of each polynomial. a) b) c) d) e) 9. Write a polynomial that matches this description: variable: p; degree: ; binomial; constant: Identify the polynomials that can be represented by the same set of algebra tiles. i) ii) iii) iv) v)

21 31. A large white square represents an x -tile, a large black square represents a x -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. Match each polynomial with its corresponding algebra tile model. i) ii) iii) iv) v) vi) Model A Model B Model C Model D Model E Model F 3. A large white square represents an x -tile, a large black square represents a x -tile, a white rectangle represents an x-tile, and a black rectangle represents a x-tile. Write the simplified polynomial.

22 33. Combine like terms. Sketch algebra tiles if it helps. 3. Group like terms. 35. Simplify: 36. 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 polynomial sum modelled by this set of tiles A large white square represents an x -tile, a large black square represents a x -tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Write the polynomial sum modelled by this set of tiles Add: 39. Add: 0. Add:. 1. Write the perimeter of this equilateral triangle as a polynomial in simplest form. 9x + 5

23 . Subtract: 3. Subtract:. Subtract: 5. Subtract: 6. Subtract: 7. Subtract: 8. A white rectangle represents an x-tile and a small white square represents a 1-tile. Write the multiplication sentence modelled by this set of algebra tiles. Determine the product. 9. Multiply: 50. Divide: 51. Here is a student s solution for this question: Identify the errors in the solution. 5. A large white square represents an x -tile, a white rectangle represents an x-tile, and a small white square represents a 1-tile. Write a division sentence that is modelled by these algebra tiles.

24 53. Divide: 5. Multiply: 55. Divide: 56. Here is a student s solution for this question: Divide: Identify any errors in the solution. 57. Here is a student s solution for this question: Multiply: Identify any errors in the solution. 58. Determine the product: 59. Determine the quotient: 60. Solve: 61. Solve: 6. Solve:

25 63. Solve: 6. Here is a student s solution for this question: Solve: Identify any errors in the solution. 65. Solve:, c Forty-four divided by a number is 11. Write, then solve an equation to determine the number. 67. Solve: 68. Solve: 69. Solve: 70. Write numbers that are solutions of this inequality: 71. Write an inequality whose solution is graphed on the number line x 7. Which of these numbers is a solution of?.5,.7,.1,.3, Graph the solution of on a number line w 7. Graph the solution of m 3 1 on a number line.

26 m 75. Which operation will you perform on each side of the inequality to isolate the variable? 76. Which operation will you perform on each side of the inequality to isolate the variable? 77. Solve: 78. Solve: 79. Solve, then graph this inequality: x 80. Solve, then graph this inequality: y 81. Solve, then graph this inequality: x 8. Claire has $18. She wants to buy a book and a magazine. The book costs $13.8. How much can Claire spend on a magazine? a) Choose a variable, then write an inequality that can be used to solve this problem. b) Solve the problem. 83. State whether you would reverse the inequality sign to solve each inequality. a) b) c) d) 8. Solve: 85. Write, then solve an inequality to show how many magazines you would have to sell at $6 each to raise at least $70.

27 86. Solve. Graph the solution Solve: 88. Solve: 89. Solve: 90. When 3 times a number is subtracted from 15, the result is less than 9. Write and solve an inequality to determine the number. Shapes and Space Review 1. This object is composed of a cube on top of a right rectangular prism. Determine the surface area of the object. 10 cm 15 cm 30 cm 15 cm. This is the floor plan of a building that is 30 m tall with a flat roof. Determine the surface area of the building, including its roof. 0 m 0 m 3. Three identical right rectangular prisms are glued together to make this composite object. Determine the surface area of the object.

28 18 cm cm 0 cm 0 cm. Determine the surface area of this composite object, to the nearest square centimetre. The cylinder has diameter 3 cm and height cm. The prism has length 10 cm, width 9 cm, and height 9 cm. 3 cm cm 9 cm 10 cm 9 cm 5. This object is composed of two identical cylinders connected by a right rectangular prism. Each cylinder has diameter 18 cm and height cm. The rectangular prism has length 8 cm and square ends of side length cm. Determine the surface area of the object. Give your answer to the nearest whole number. cm 18 cm cm 8 cm 6. A two-layer cake is composed of a cylinder on top of a rectangular prism. The rectangular prism has length 30 cm, width 30 cm, and height 7 cm. The cylinder has diameter 0 cm and height 6 cm. The surface of the cake is frosted. What area of cake is frosted? 7. Determine the scale factor for this scale drawing.

29 Original diagram Scale diagram 8. Which of trapezoids A, B, C, and D are scale diagrams of trapezoid O? O A B C D 9. A square has side length.3 cm. The square is enlarged by a scale factor of 3.. Determine the side length of the enlargement. 10. Is PQR a scale diagram of ABC? If yes, state the scale factor. 8 6 y Q B P A C R x 11. Determine the scale factor of this reduction as a fraction and as a decimal.

30 Original Reduction 1. A building is 10 m tall. A scale model is built using a scale factor of Determine the height of the model to the nearest centimetre, if necessary. 13. A hockey rink measures 5 m by 3 m. A scale diagram is drawn using a scale factor of. Determine the dimensions of the rink in the scale diagram to the nearest centimetre. 1. Determine the value of y in this proportion: 15. These polygons are similar. Determine the values of x and y. 17 x y A rectangular garden measures 15 m by 9 m. A similar rectangular garden is 7.5 m long. Calculate the width of the garden. 17. Rectangle ABCD is similar to rectangle PQRS. If AB = 7. cm, BC = 5.7 cm, and PQ =.8 cm, determine the length of QR. 18. Any two of which shape will always be similar? Give two examples. 19. Triangle ABC is similar to PQR. The ratios of the corresponding sides are: State the corresponding angles.

31 0. Triangle KLM is similar to RST. The corresponding angles are: K = R, L = S, M = T State the ratios of the corresponding sides. 1. Determine the length of BD in these similar triangles. A B C D E. Determine the length of RS in these similar triangles. P 1 m T 19 m Q m R S 3. State the number of lines of symmetry in each design. a) b). This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by drawing its other half.

32 5 3 1 y x 5. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by drawing its other half. y x 6. Identify the pentagons that are related to the black pentagon by a line of reflection. Describe the position of each line of symmetry y P Q R S x 7. What is the order of rotational symmetry for this design?

33 8. Draw the rotation image after rotating the shape 90 clockwise about P. P 9. What is the order of rotational symmetry and angle of rotation symmetry for this design? 30. Describe two different rotations that will result in this square coinciding with itself.

34 31. Describe the rotational symmetry and line symmetry of this design. 3. Describe three different transformations that would make rhombus B the image of rhombus A. y 3 A 1 B x Triangle A'B'C' is the image of ABC after a 180 rotation about the origin. Identify any symmetry.

35 C' A 3 1 y A' B x B' C 3 3. Marleesa says these digits do not have line symmetry or rotational symmetry. Is she correct? If not, explain her mistake. 35. O is the centre of this circle. Which line is a tangent? A B C D O E 36. O is the centre of this circle. Point T is a point of tangency. What is the value of e? T e O

36 37. Is the line that passes through points U and V a tangent to the circle? U V O 38. O is the centre of this circle and point B is a point of tangency. Determine the values of v and w. O v 55 w C A 5 B 39. O is the centre of this circle and point Q is a point of tangency. Determine the values of s and t. If necessary, give your answers to the nearest tenth. L s M 3 N 8 19 t O 0. O is the centre of this circle.

37 Which line segment is a diameter? C E D O F G 1. O is the centre of the circle. What can you say about the lengths of WX and XY? W X O Y. O is the centre of the circle. What can you say about the measure of? A B C O 3. Point O is the centre of this circle. Determine the values of x and y. y R O x S 9 T. Point O is the centre of this circle. Determine the values of c and d.

38 c d O 3 5. Point O is the centre of this circle. Without solving for a, sketch and label the length of any extra line segments you need to draw to determine the value of a. 1 O 6 a K H J 6. Point O is the centre of this circle. Without solving for s, sketch and label the lengths of any extra line segments you need to draw to determine the value of s. W O s 6 X Y 7. Point O is the centre of this circle. Determine the value of n to the nearest tenth, if necessary.

39 H 10 O 3 n K J 8. O is the centre of this circle. Is a central angle or an inscribed angle? A O C B 9. O is the centre of this circle. What is the relationship between the measures of and? D E O F 50. What is the relationship between the measures of and? W X Z Y 51. Point O is the centre of the circle. Arc AB is a semicircle. What is the measure of?

40 A O B 5. Point O is the centre of the circle. Determine the values of y and z. A z 76 y C O B