Gr.9 Math Final Exam Review (Ch.1-9) Name:

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1 Gr.9 Math Final Exam Review (Ch.1-9) Name: Unit 1 Review: Square Roots and Surface Area 1. Use each diagram to determine the value of the square root Which numbers below are perfect squares? How do you know? c) 2 50 d) Calculate the number whose square root is: c) 0.92 d) Determine the value of each square root c) d) Determine the value of each square root c) d) The area of a square garden is m 2. Determine the perimeter of the garden. The owner decides to put a gravel pathway around the garden. This reduces the area of the garden by 4.96 m 2. What is the new side length of the garden? 7. Which numbers below are perfect squares? How do you know? c) d) Use benchmarks to approximate each square root to the nearest tenth c) d) Suppose the key on your calculator is broken. Explain how you could use your calculator to estimate 58.6 to the nearest tenth. 10. In each triangle, determine the unknown length to the nearest tenth of a unit where necessary.

2 11. Each cube has edge length 1 unit. Determine the surface area of each object. 12. Determine the surface area of this composite object to the nearest square unit. Unit 2 Review: Powers and Exponent Laws 1. Identify the base of each power c) ( 5) 4 d) Use repeated multiplication to show why 3 5 is not the same as Complete this table. Power Base Exponent Repeated Multiplication Standard Form 4 4 ( 10) Write each product as a power, then evaluate c) d) (8 8 8) e) ( 8)( 8)( 8) f) ( 8)( 8)( 8) 5. Write each power as repeated multiplication, then evaluate c) 9 3 d) ( 5) 5 6. Evaluate each power. For each power: Are the brackets needed? If your answer is yes, what purpose do the brackets serve? ( 6) 5 (6) 5 c) ( 6) 5 d) ( 6 5 ) 7. Predict whether each answer is positive or negative, then evaluate. ( 3) 2 ( 3) 3 c) 3 2 d) ( 3) 3 8. Is the value of 2 4 different from the value of ( 2) 4? Explain. 9. Evaluate each power c) ( 6) 0 d) 1 0 e) 1 0 f) ( 1) 0

3 10. Evaluate. ( ) ( ) c) ( ) 0 2[( 3) 3 ] d) (7 5) 3 (8 + 2) 4 e) ( ) 2 f) [( 3) 4 ( 2) 3 ] 0 [( 4) 3 ( 3) 2 ] Insert brackets to make each statement true = = Tom, Julie and Paul got different answers when they evaluated this expression: ( 4) 2 3[( 9) 3] 2 Tom s answer was 97, Julie s answer was 43, and Paul s answer was 19. Who was correct? Explain the mistakes. Show the correct solution. 13. Write each product as a single power c) ( 2) 2 ( 2) 4 d) e) ( 7) 0 ( 7) 2 f) ( 9) 6 ( 9) Write each quotient as a single power c) ( 1) 6 ( 1) 3 3 d) e) Express as a single power ( 5) 8 ( 5) 4 ( 5) c) Simplify, then evaluate ( 2) 6 ( 2) 5 ( 2) 5 ( 2) 3 c) 2 2 ( ) Simplify, then evaluate c) Identify, then correct any errors in these answers. Explain how you think the errors occurred = = 8 5 c) ( 3) 8 ( 3) 4 = ( 3) 4 d) = 1 3 e) Write each expression as a product of powers or a quotient of powers. (3 2) 4 [( 4) 3] 2 c) [( 2) ( 4)] 3 d) (7 11) 0 e) (10 5) 3 f) [( 12 ) ( 6)] 2 g) Write as a single power. h) (3 4 ) 2 (5 0 ) 3 c) (7 2 ) 2 d) [( 3) 3 ] Why is the value of [( 3) 3 ] 2 positive and the value of [( 3) 3 ] 3 negative? 6 f)

4 22. Simplify, then evaluate. ( ) 2 ( ) 2 c) [( 3) 0 ( 3) 3 ] 2 d) (10 2 ) 4 (10 3 ) Simplify, then evaluate each expression. ( ) 2 ( ) 2 ( ) 3 + ( ) 0 c) [( 1) 3 ] 4 [( 1) 4 ( 1) 3 ] 2 d) ( ) 0 (3 2 ) 2 e) ( ) 3 + ( ) 3 f) ( ) 2 + ( ) Find and correct any errors in each solution. ( ) 2 = (8 5 ) 2 [( 10) 3 ] 4 = ( 10) 7 c) ( ) 2 = (2 5 ) 2 = 8 10 = = = 2 10 = 1024 Unit 3 Review: Rational Numbers 1. Which of the following numbers are equal to ,,,, ? 5 2. Write the rational number represented by each letter as a decimal. 3. Write the rational number represented by each letter as a fraction. 4. Sketch a number line and mark each rational number on it. Order the numbers from greatest to least ,, 1.5, 1, Diver A is 2.3 m below sea level. Diver B is 1.7 m below sea level. Diver C is 3.2 m below sea level. Draw a vertical number line to show the location of the divers. Which diver is farthest from the surface? Explain your thinking. 6. In each pair, which rational number is greater? Explain how you know. 7.3, 7.2 4, c) 1.2, 1.3 d) 10 10, 13 11

5 7. Determine each sum c) d) Sarah borrowed $40.25 from her parents for a new sweater. She earns $17.50 for a night of babysitting and gives this to her parents. Write an addition statement to represent this situation. How much does Sarah now owe? 9. Determine each sum Use integers to estimate each sum. Then, determine each sum c) d) Determine each difference. Describe the strategies you used Two climbers leave base camp at the same time. Climber A ascends 20.4 m, while climber B descends 35.4 m. How far apart are the climbers? Write a subtraction statement using rational numbers to solve the problem. 13. Predict whether each difference is positive or negative. Determine each difference Use integers to estimate each difference. Then, determine each difference c) Predict the sign of each product. Determine each product. ( 1.2) ( 0.5) c) ( 0.6) ( 0.15) d) 0.9 ( 1.2)

6 16. Predict the sign of each product. Determine each product c) From November 12th to November 21st, the temperature in Burnaby, B.C. dropped an average of 1.7 C each day. Suppose the temperature on the morning of November 12th was 11.4 C. What was the temperature on the morning of November 21st? 18. Use integers to estimate each product then calculate each product. (1.19)( 13.2) ( 8.65)( 1.6) 19. Determine each product Determine each quotient. i) 16 2 ii) ( 1.6) 0.2 i) 60 3 ii) ( 0.6) ( 3) 21. Predict the sign of each quotient, then calculate each quotient c) d) A diver descends 3.2 m in 5 min. What was his average rate of descent in metres per minute? 23. Use a calculator to determine each quotient. Round each answer to the nearest hundredth ( 5.5) ( 0.98) Determine each quotient Evaluate. Do not use a calculator Evaluate. Do not use a calculator Evaluate

7 Unit 4 Review: Linear Relations 1. In each equation, determine the value of A when n is 3. A = 2n + 1 A = 3n 2 c) A = 4n + 3 d) A = 30 2n 2. The pattern in this table continues. Which equation below relates the figure number n, to the perimeter of the figure P? Figure Number, n Perimeter, P P = 3n + 7 P = 7n + 3 c) P = 3n + 4 d) n = 3P The pattern in each table below continues. For each table: i) Describe the pattern that relates v to t. ii) Write an equation that relates v to t. iii) Verify your equation by substituting values from the table. Term Number, t Term Value, v Term Number, t Term Value, v Rachel takes care of homes during the summer while their owners are away on vacation. She charges $8, plus $2.50 a day. Create a table that shows the charges when the owners are away for up to 5 days. Write an equation that relates the charge, C dollars, to the number of days, n, that the owners are away. c) What will the charge be when the owners are away for 14 days? d) How many days were the owners away when the charge was $33? 5. For each table of values below: i) Does it represent a linear relation? ii) If the relation is not linear, explain how you know. iii) If the relation is linear, describe it. x y x y c) x y d) x y

8 6. Each table of values represents a linear relation. Complete each table. Explain your reasoning. x y x y c) x y Create a table of values for each linear relation and then graph the relation. Use values of x from 2 to 2. y = x + 4 y = 2x + 1 c) y = 5 2x 8. A computer repair company charges $80 for a service call, plus $50 an hour for labour. Create a table to show the relation between the time in hours for the service call and the total cost. Is this relation linear? Justify your answer. c) Let n represent the time in hours for the service call and C represent the total cost in dollars. Write an equation that relates C and n. d) How much will a 7-h service call cost? 9. Does each equation describe a vertical, a horizontal, or an oblique line? Describe each vertical or horizontal line. y = 4 2x + 5 = 7 c) 2x y = 6 d) 3y + 9 = Which equation below describes each graph? i) x = 2 ii) x = 2 iii) y = 2 iv) y = The sum of two numbers is 8. Let x and y represent the two numbers. Create a table for 5 different values of x. Graph the data. Should you join the points? c) Write an equation that relates x and y. 12. Graph each line. Explain your work. x = 4 2y = 6 c) y 2 = 6 d) 2x + 3 = For each equation below: Make a table for the given values of x. Graph the equation. 3x + y = 3; for x = 2, 0, 2 x 2y = 8; for x = 2, 0, Graph these equations on the same grid. x + y = 6 y = 1 x y = 6 Which shape is formed by these lines? 15. Match each equation with a graph on this grid. y = 2x 1 y = x + 4 c) y = 3x 3

9 16. Match each equation with a graph on this grid. y = 1 0 = x + 1 c) 2 = 2x Match each equation with a graph on this grid. Justify your answers. x + y = 5 x y = 5 c) x + y = Which equation describes this graph? Justify your answers. y = x + 2 y = x + 2 c) y = x Which equation describes this graph? Justify your answers. x y = 4 x 4y = 4 c) 4x y = This graph represents a linear relation. Determine the value of x for each value of y. i) y = 1 ii) y = 3 iii) y = 0 Determine the value of y for each value of x. i) x = 2 ii) x = 8 iii) x = This graph represents a linear relation. Determine the value of x for each value of y. i) y = 3 ii) y = 2 iii) y = 7 Determine the value of y for each value of x. i) x = 0 ii) x = 2 iii) x = This graph represents a linear relation. Determine the value of x for each value of y. i) y = 2 ii) y = 0 iii) y = 5 Determine the value of y for each value of x. i) x = 0 ii) x = 3 iii) x = The graph shows how the cost of a long distance call changes with the time for the call. Estimate the cost of a 7-min call. Is this interpolation or extrapolation? Explain. The cost of a call was $1.00. Estimate the time for the call. c) The cost of a call was $1.50. Estimate the time for the call.

10 Unit 5 Review: Polynomials 1. Identify the polynomials in the following expressions. 2m x 2 1 c) 4x d) x 2 e) 0.25y + x 2 2. Name the coefficients, variable, degree, and constant term of each polynomial. 8y 12 c) 2b 2 b + 10 d) 4 b 3. Identify each polynomial as a monomial, binomial, or trinomial. 19t g 4g c) 1 + xy + y 2 d) 4 11w 4. Identify the equivalent polynomials. h h 3 + 4h h 2 c) 5m 3 d) 2 + y 2 + 5xy e) y 2 + 5xy 2 f) 3 + 5m 5. Use algebra tiles to model each polynomial. Sketch the tiles. 5 + y 2 2x 1 c) 3a 2 2a + 1 d) 3z e) v 2 4v 6. Write a polynomial to match the following conditions. 2 terms, degree 1, with a constant term of 4 3 terms, degree 2, with the coefficient on the 2nd degree term 2 7. From the list, identify terms that are like 2w 2. Explain how you know they are like terms. 5w, 6w 2, 2, 4w, 3w 2, w 2, 11w, 2 8. Use algebra tiles to model each polynomial, then combine like terms. Sketch the tiles for the simplified polynomial. 4 + x x + 1 3y 2 + 3y 2 c) 2x x 2 + 5x 2 d) 3y + 7y y 2y 3y 2 9. Simplify each polynomial. 7d 2d k 5k c) 4 + 2a + 7 4a d) 3p 6 4p Simplify each polynomial. 3a 2 2a 4 + 2a 3a z z z 2 7 c) d 2 + 3d d d) 6x x x 7x Identify the equivalent polynomials. Justify your responses. 5y 2 3y 4 10x 1 c) 1 + x x 2 d) 2y y 2 3y + 16 e) 7 + 5x 7x x f) 5x x 6x 2 6 x 2x 12. Write a polynomial to represent the perimeter of each rectangle. 13. Use algebra tiles to model each sum. Sketch your tile model. Record your answer symbolically. ( 4h + 1) + (6h + 3) (2a ( 5a c) (3y 2 2y + 5) + ( y 2 + 6y + 3) d) (3 2y + y 2 ) + ( 1 + y 3y 2 ) 14. Add these polynomials. Use algebra tiles if it helps. (x 5) + (2x + 2) (b (b 2 3 c) (y 2 + 6y) + ( 7y 2 + 2y) d) (5n 2 + 5) + ( 1 3n 2 )

11 15. Add these polynomials. Use algebra tiles if it helps. ( 7x + 5) (4x 2 3) + (2x 8) + ( 8x 2 1) c) (x 2 4x + 3) d) (3x 2 4x + 1) + ( x 2 2x 3) + ( 2x 2 + 4x + 1) 16. Add. (y 2 + 6y 5) + ( 7y 2 + 2y 2) ( 2n + 2n 2 + 2) + ( 1 7n 2 + n) c) (3m 2 + m) + ( 10m 2 m 2) d) ( 3d 2 + 2) + ( 2 7d 2 + d) 17. For each shape below, write the perimeter as a sum of polynomials and in simplest form. i) ii) iii) iv) 18. The sum of two polynomials is 4r + 5 3r 2. One polynomial is 8 2r 2 + 2r; what is the other polynomial? Explain how you found your answer. 19. Use algebra tiles. Sketch your tile model. Record your answer symbolically. (4x + 2) (2x + 1) (4x + 2) ( 2x +1) c) (4x + 2) (2x 1) d) (4x + 2) ( 2x 1) 20. Use algebra tiles to model find each difference. Sketch your tile model. Record your answer symbolically. (2s 2 + 3s + 6) (s 2 + s + 2) (2s 2 + 3s 6) (s 2 + s 2) c) ( 2s 2 + 3s + 6) ( s 2 + s + 2) d) (2s 2 3s + 6) (s 2 s + 2) 21. Use a personal strategy to subtract. Check your answers by adding. (2x + 3) (5x + 4) (4 8w) (7w + 1) c) (x 2 + 2x 4) (4x 2 + 2x 2) d) ( 9z 2 z 2) (3z 2 z 3) 22. The difference between two polynomials is (5x + 3). One of the two polynomials is (4x + 1 3x 2 ). What is the other polynomial? Explain how you found your answer. 23. A student subtracted (3y 2 + 5y + 2) (4y 2 + 3y + 2) like this: = 3y 2 5y 2 4y 2 3y 2 = 3y 2 4y 2 5y 3y 2 2 = y 2 8y 4 Explain why the student s solution is incorrect. What is the correct answer? Show your work. 24. Subtract. (mn 5m 7) ( 6n + 2m + 1) (2a + 3b 3a 2 + b 2 ) ( a 2 + 8b 2 + 3a c) (xy x 5y + 4y 2 ) (6y 2 + 9y xy) 25. Multiply. Sketch the tiles for one product. 2(3 2(6h) c) 4(2b 2 ) d) 2(2x 2 ) e) 2( y 2 ) f) 3( 2f) 26. Divide. Sketch the tiles for one division statement. 12d 4 20d 5 c) 8d 4 d) 12y 2 4 e) 14x 2 2 f) 10q Determine each product. 4(3a + 2) (d 2 + 2d)( 3) c) 2(4c 2 2c + 3) d) ( 2n 2 + n 1)(6) e) 3( 5m 2 + 6m + 7)

12 28. Here is a student s solution for a multiplication question. ( 5k 2 k 3)( 2) = 2(5k 2 ) 2(k) 2(3) = 10k 2 2k 6 Explain why the student s solution is incorrect. What is the correct answer? Show your work. 29. Determine each quotient. (16v + 16) (8) (25k 2 15k) (5) c) (20 8n) ( 4) d) (18x 2 6x + 6) (6) e) (7 7y + 14y 2 ) ( 7) 30. Here is a student s solution for a division question. ( 12r 2 8r 16) ( 4) 2 12r 8r 16 = = 3r 2 2r + 4 Explain why the student s solution is incorrect. What is the correct answer? Show your work. 31. Write the multiplication sentence modelled by each set of algebra tiles. c) 32. For each set of algebra tiles in question 31, write a division sentence. 33. Write the multiplication sentence modelled by each rectangle. 34. For each rectangle in question 33, write a division sentence. 35. Multiply. v(3v + 1) 3c(5c + 2) c) (8 + 4y)(6y) d) 5p( 5 2p) e) (7k 3)( m) f) ( 1 10r)( r) 36. Divide. (6x + 3) 3 (14w 7) 7 c) ( 15 10q) 5 d) (8z 2 + 4z) 2z e) (12c 2 6c) 3c f) (9xy 6x) 3x 37. Here is a student s solution for a division question. ( 12x 2 9x 12xy) ( 3x) 2 12x 9x 12xy = 3x 3x 3x = 4x xy Explain why the student s solution is incorrect. What is the correct answer?

13 Unit 6 Review: Linear equations and Inequalities 1. Solve each equation and verify the solution c x c) b d) w Solve each equation and verify the solution. d p c) a 1. 5 d) 4r e) 3 8 c A taxicab charges $2.50, plus $1.78 per kilometre. How long is a trip that costs $21.19? 4. Solve each equation and verify the solution. 22 x 6 3.2v c) m 9 12 d) g Solve each equation and verify the solution. 3y 6 9y 2a 4 3a c) c c 4. 9 d) 12.6 f 6.1 f e) w 6. The sum of three times a number, plus five is equal to seven less than seven times the number. Write an equation to model this situation. Solve the equation to determine the number. Verify the solution. 7. State 3 values of the variable that satisfy each inequality. c < 7 a 3 c) 5 < n d) 1 y 8. Solve each equation and verify the solution. 2 h 1 3 h y 1.025y 0.5 c) d) 3 4 (2x 3) = 6 (3x + 1) 5 2 b b 3 4 6

14 9. Write the inequality that is graphed on each number line. c) d) 10. Write an inequality to describe each situation, then graph it. The gas tank in a car contains no more than 55 L of gas. The minimum age you must be to watch the movie is Match each inequality with the graph of its solution. g m 2 c) 2 y 4 d) 1 f 3 i) ii) iii) iv) 12. Solve, then graph each inequality. 7t 4 3t s s

15 c) p Do not solve each inequality. Determine which of the given numbers are solutions of the inequality. 3t 5 5 3d 2 d 3, 0, 1 5, 0, Solve each inequality and graph the solution. 3.5a 1.3a f c) x 1.1x d) 3 n n 15. Nadia gets paid $1000 per month plus 5% commission on her sales. She wants to earn at least $2200 this month. Write an inequality to represent this situation, then solve it to determine how much Nadia must sell to reach her goal. Unit 7 Review: Similarity and Transformations 1. Scale diagrams of different circles are to be drawn. The diameter of each circle, and the scale factor are given. Determine the diameter of each circle on its scale diagram. Write the answers. Diameter of original circle Scale factor 8 cm 6 40 mm 15 4 c) 3.5 cm 5.8 d) 0.6 mm 20.5 Diameter of scale diagram 2. The actual length of a needle is 6 cm. The length of the needle on a scale diagram is 9 cm. What is the scale factor of the diagram? 3. Draw an enlargement of an equilateral triangle with side length 3 cm. Use a scale factor of 5 3.

16 4. Draw a scale diagram of this model of an mp3 player. Use a scale factor of The dimensions of a photo of a mountain bike are 15 cm by 12 cm. An enlargement is to be made for a poster with dimensions 4.0 m by 3.2 m. What is the scale factor of the poster to the nearest tenth? 6. Here is scale diagram of a picnic table. The actual length of the picnic table is 180 cm with legs 60 cm. What is the scale factor for this diagram? 7. A rectangular playground has dimensions 24 m by 16 m. Draw a scale diagram of this playground with a scale factor of A reduction of each object is to be drawn with the given scale factor. Determine the corresponding length in centimetres on the scale diagram. 1 Fishing rod length 280 cm, scale factor 50 Boogie board length 1.5 m, scale factor 0.05 c) Jogging route 10 km, scale factor The scale diagram below has a scale factor of What are the dimensions of the actual rectangle? 10. Which rectangles are similar? Give reasons for your answer. 11. For the given polygon draw a similar larger polygon and a similar smaller polygon. Write the scale factor for each diagram.

17 12. These polygons are similar. PT Determine each length. BC 13. Which statements are true? Justify your answers. All regular octagons are similar. All quadrilaterals are similar. c) All circles are similar. d) All pentagons are similar. 14. Identify the similar triangles in the following diagrams. Equal angles are marked on the diagrams. c) 15. A person who is 1.9 m tall has a shadow that is 1.5 m long. At the same time, a flagpole has a shadow that is 8 m long. Determine the height of the flagpole to the nearest tenth of a metre. Draw a diagram. 16. A surveyor wants to determine the width of a river. She measures distances and angles on land, and sketches this diagram. What is the width of the river, PQ? 17. Determine the length of XY in each pair of similar triangles.

18 18. Draw in the lines of symmetry in each design. 19. Draw the image of ΔPAM after each reflection below. Write the coordinates of the larger shape formed by ΔPAM and its reflection images. Draw the lines of symmetry of the larger shape. Reflect ΔPAM in the horizontal line passing through 2 on the y-axis. Reflect ΔPAM in the vertical line passing through 5 on the x-axis. c) Reflect ΔPAM in the oblique line passing through the points (2, 2) and (5, 5). 20. Identify the shapes that are related to the shape X by a line of reflection. Describe the line of symmetry in each case.

19 21. Which polygons have rotational symmetry? State the order of rotation and the angle of rotation symmetry for each. 22. Draw the rotation image for each rotation of quadrilateral ABCD. Rotate quadrilateral ABCD clockwise about vertex D by: c) 180 d) 240 e) 300 Consider the larger shape formed by quadrilateral ABCD and these rotation images. Describe the symmetry of this shape. 23. What is the order of rotation and the angle of rotation symmetry, if any, for: an equilateral triangle a regular polygon with 9 sides c) a kite that is not a rhombus d) the plus sign Plot the kite FISH on a coordinate grid. The vertices of FISH are F(3, 4), I(5, 2), S(3, 1), H(1, 2). Rotate the kite FISH: 90 clockwise about vertex F 180 about vertex F c) 270 clockwise about vertex F Draw each rotation image. Look at the shape formed by the kite and its rotation images. Write the coordinates of this shape. Describe any rotational symmetry in this shape. 25. Draw the rotation image for each transformation of quadrilateral ABCD. 180 about vertex B 90 clockwise about vertex A c) 90 counterclockwise about point E 26. For each pair of shapes, determine whether they are related by line symmetry, by rotational symmetry, by both line and rotational symmetry, or by neither. Describe the symmetry, if any. c) d)

20 27. Which of the rectangles A, B, C, D is related to rectangle X: by rotational symmetry about the origin? by rotational symmetry about one of the vertices of rectangle X? c) by line symmetry? 28. Identify and describe the types of symmetry in the petal shapes. c) d) e) 29. Draw the image of quadrilateral WXYZ after each transformation. Write the coordinates of each shape formed by quadrilateral WXYZ and its image. Describe the symmetry in each of these shapes. reflection in the x-axis rotation 90 clockwise about the origin c) rotation 90 clockwise about the point (1, 0) d) translation 1 square right and 1 square down Unit 8 Review: Circle Geometry 1. Draw and label a diagram to illustrate the property of a tangent to a circle. 2. Point O is the centre of the circle. Points P and Q are points of tangency. Determine the values of xand y. Justify your solutions. 3. Point O is the centre of the circle. Point P is a point of tangency. Determine the value of x to the nearest tenth. Justify your solution.

21 4. A wheel has radius 30 cm. It rolls along the ground toward a tack that is 58 cm from the point where the wheel currently touches the ground. What is the distance, d, between the tack and the closest point on the circumference of the wheel? Give the answer to the nearest tenth of a centimetre. 5. A circular plate has radius 13 cm. It is packed in a square cardboard frame whose 4 edges just touch the plate. What is the distance, d, from the centre of the plate to a corner of the frame? Give the answer to the nearest tenth of a centimetre. 6. Draw and label a diagram to illustrate the relationship between a chord, its perpendicular bisector, and the centre of a circle. 7. Point O is the centre of the circle. Determine the values of x and y. 8. A circle has diameter 70 cm. A chord in the circle is 50 cm long. How far is the chord from the centre of the circle? Give the answer to the nearest tenth of a centimetre. 9. Point O is the centre of the circle; OF = 18 cm; and GJ = 14 cm. Determine the values of x and y to the nearest tenth of a centimetre where necessary.

22 10. A circle has diameter 22 cm. Two chords are drawn on opposite sides of the centre of the circle. One chord is 16 cm long and the other chord is 12 cm long. Which chord is closer to the centre of the circle? How much closer to the centre is this chord? Give the answer to the nearest tenth of a centimetre. 11. Draw and label a diagram to illustrate each property. an inscribed angle and a central angle subtended by the same arc inscribed angles subtended by the same arc c) an angle inscribed in a semicircle 12. Point O is the centre of each circle. Determine the values of xand y. Justify your solutions. c) 13. A student looked at the diagram below and concluded that x= y. The student justified that conclusion by saying that both angles are subtended by arc AB. What is the student s error? What are the values of xand y? 14. Point O is the centre of the circle; DB is a diameter. Determine the values of w, x, y, and z. Justify your solutions. Unit 9 Review: Probability and Statistics 1. Indicate whether each decision is based on theoretical probability, experimental probability, or subjective judgment. Explain how you know. The last 10 times Jerome tried to access a certain Internet website, he got an error message saying that the site was unavailable. So, he decides the site no longer works and does not try to access it again. When Karen s mother learns she is pregnant, she celebrates by buying a pink baby blanket because she has a feeling the baby will be a girl. c) Aaron chooses a long password because it is more difficult to determine a long password than a short one.

23 2. Name a problem with each data collection. To discover common fears, Chris asks his classmates if they are frightened by spiders, snakes, rats, or slugs. To find out the proportion of people who recycle tin cans, a person counts the number of households with tin cans in their recycling bins. c) To estimate how much meat to buy for a barbecue party, Sarah asks her guests: Do you prefer beef or chicken kebabs? 3. Kevin thinks his drama club should spend more money on props. During the intermission of the spring play, he surveys the audience and the cast to see if they agree. Describe how the timing of his question may influence the responses. In what setting might the responses be different than those Kevin received? 4. Rena wanted to find out how often people in her neighbourhood used the local bike paths or walking trails. She asked her neighbours the question: How much time do you spend outdoors each month? How do you think her neighbours will interpret this question? How could the question be rewritten so it would more accurately reflect what Rena wants to know? c) Who might be interested in her findings? Why? 5. Describe how each question reveals a bias of the questioner. i) Do you think it would be a good idea to ban French fries because they contain trans fats? ii) Old gasoline-powered lawn mowers pollute more than cars. Do you agree that the government should offer rebates to people who replace them with more efficient mowers? iii) Which sport is your favourite: soccer, tennis, or judo? Rewrite each question to eliminate the bias. Explain how your question is an improvement. 6. In each case, describe the population. A social networking site wants to know the typical age of a person who uses the site. A book retailer wants to know which demographic groups buy travel books. c) A music store wants to know how many school-aged students take piano lessons. 7. Should a census or sample be used to collect data about each topic? Explain your choice. The number of people in your neighbourhood who use public transit at least once a week The number of grade 9 students in your school who participate in extra-curricular sports programs c) The number of hours members of your family spend on the computer in a week d) The effectiveness of a new vaccine 8. Suppose you are on the town council. You want to know whether residents would prefer a new tennis court or soccer field. What population are you interested in surveying? Would you survey a sample or population? Explain. c) If you had to use a sample, what would you do to make sure your conclusions are valid? 9. In each case, do you think the conclusion is valid? Justify your answers. Ingrid surveyed 20 residents to find out if they thought pesticides were harmful to the environment. All of the residents said yes. Ingrid concluded that all residents in the town were in favour of a ban on pesticide use. A reporter asks 5 people on the street this question: In light of the many recent home invasions, do you think police are doing all they can to keep us safe? Four of those interviewed say the police are not keeping us safe. The reporter concludes 4 out of 5 citizens are worried about personal safety. 10. Identify a potential problem with each sampling method. A politician wants to know what people think of the healthcare system. He interviews people as they leave a walk-in medical clinic about their opinions. A movie theatre wants to predict the success of several new movies. On its website, it posts a poll asking people to vote for the movie they most want to see.

24 11. Explain whether each sample is appropriate. Justify your answer. Suppose you want to know what sports equipment people in your community are most likely to purchase. You survey every 10th customer who makes a purchase at your store. A researcher phones every 10th person on a union s membership list to determine union members opinions about the services the union provided. c) A town s recreation director wants to know what residents think about building a swimming pool in the community centre. He posts a survey in the local newspaper and tells people they can mail it to him or drop it off at the community centre. 12. In each case, will the selected sample represent the population? Explain. i) To find out consumers reaction to a new soft drink, a soft-drink company invites people to rate how much they like the new drink on its website. ii) To discover the most popular shoe brands purchased at a mall, Laurel asks every customer entering a shoe store which brand they are most likely to buy. iii) To determine the effectiveness of a new advertisement campaign, a company tracks sales of the product at every tenth store on the list of stores to which they distribute the product. If the sample does not represent the population, suggest another sample that would. Describe how you would select that sample. 13. Describe an appropriate sampling method for each situation. Justify your answers. The city council wants to know what citizens who live near a two-lane road think about widening the road to four lanes. A college wants to know high school students opinion of a career in the entertainment industry.