Math 9: Review for final - Mr. White's course site -...

Math 9: Review for final

1

Lesson 1.1: Square Roots of Perfect Squares

1. Use each diagram to determine the value of the square root.

a)

1

9 b)

0.16

2. Which numbers below are perfect squares? How do you know?

a)

25

121 b) 2.89 c)

2

50 d) 0.004

3. Calculate the number whose square root is:

a)

5

7 b) 1.6 c) 0.92 d)

10

9

4. Determine the value of each square root.

a)

225

49 b)

9

25 c)

6.76 d)

327.61

5. The area of a square garden is 12.25 m2.

a) Determine the perimeter of the garden.

b) The owner decides to put a gravel pathway around the garden. This reduces the area

of the garden by 4.96 m2. What is the new side length of the garden?


2

Lesson 1.2: Square Roots of Non-Perfect Squares

6. Use benchmarks to approximate each square root to the nearest tenth.

a)

11.6 b)

0.39 c)

21

2 d)

11

52

7. In each triangle, determine the unknown length to the nearest tenth of a unit where necessary.

a) b)

Lesson 1.3: Surface Areas of Objects Made from Right Rectangular Prisms

8. Each cube has edge length 1 unit. Determine the surface area of each object.

a) b) c)

9. Determine the surface area of this composite object.


3

Lesson 2.1: What Is a Power?

10. Complete this table.

Power Base Exponent Repeated Multiplication Standard Form

44

(–10)3

–6 2

1 × 1 × 1 × 1 × 1

11. Evaluate each power. For each power:

• Are the brackets needed?

• If your answer is yes, what purpose do the brackets serve?

a) (–6)5

b) –(6)5

c) –(–6)5

d) (–65)

12. Predict whether each answer is positive or negative, then evaluate.

a) (–3)2 b) (–3)

3 c) –3

2 d) –(–3)

3

13. Is the value of –24 different from the value of (–2)

4? Explain.


4

14 . Stamps are sold in a 10 by 10 sheet. The total value of a sheet of stamps is $60.00.

a) Express the number of stamps as a power and in standard form.

b) What is the value of one stamp?

Lesson 2.2: Powers of Ten and the Zero Exponent

15. Evaluate each power.

a) 40 b) 23

0 c) (–6)

0

d) 10 e) –1

0 f) (–1)

0

16. Write each number as a power of 10.

a) 10 000 b) 1 000 000 c) ten

Lesson 2.3: Order of Operations with Powers

17. . Evaluate.

a) 52 + 3 b) 5

2 – 3 c) 4

3 × 2 d) 4

3 ÷ 2

e) (4 × 2)3

f) (18 ÷ 32 + 1)

4 – 4

2 b) g) 3

3 ÷ 9(3

0 – 2

2)


5

h) [(–3)4 – (–2)

3]0 ÷ [(–4)

3 – (–3)

2]

0

Lesson 2.4: Exponent Laws 1

18. Write each product as a single power.

a) 43 × 4

2 b) 5

0 × 5

0 c) (–2)

2 × (–2)

4

a) 87 ÷ 8

5 b) 10

4 ÷ 10

0 c) (–1)

6 ÷ (–1)

3

d) 4

4

3

3 e)

5

10

9

9

f)

9

6

11

11

a) 23 × 2

6 ÷ 2

9 b) (–5)

8 ÷ (–5)

4 × (–5)

3 c)

42

53

66

66

19. Simplify, then evaluate each expression.

a) (42 × 4

3)0 – (3

2)2 b) (2

3 ÷ 2

2)3 + (7

4 × 7

3)0


6

Lesson 3.1: What Is a Rational Number?

20. Write the rational number represented by each letter as a decimal.

21. In each pair, which rational number is greater? Explain how you know.

a) 7.3, 7.2 b) 4 5

, 5 4

c) 1.2, 1.3 d) 10 10

, 13 11

Lesson 3.2: Adding Rational Numbers

22. Write the addition statement that each number line represents.

a)

b)

23. Determine each sum.

a) 3 1

4 2 b)

3 1

4 2


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24. Sarah borrowed $40.25 from her parents for a new sweater. She earns $17.50 for a night of

baby-sitting and gives this to her parents.

a) Write an addition statement to represent this situation. _________________________

b) How much does Sarah now owe? __________________________________________

Lesson 3.3: Subtracting Rational Numbers

25. Determine each difference. Describe the strategies you used.

a) 3 1

4 2 b)

3 13 5

5 2

26. 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.

Lesson 3.4: Multiplying Rational Numbers

27. Predict the sign of each product. Determine each product.

a) ( 1.2) 0.3 b) 0.34 ( 0.5)

c) 2 1

5 2

d) 3 1

2 7

Lesson 3.5: Dividing Rational Numbers

28. Determine each quotient.

a) 16 2 b) ( 0.6) ( 3)


8

c) 3 5

4 2

d) 5 2

9 3

Lesson 3.6: Order of Operations with Rational Numbers

29. Evaluate this expression. Round the answer to the nearest hundredth.

9.6 12.6 5.1 ( 7.4) 0.6

( 2.9) 1.3 ( 6.5)

Lesson 4.1: Writing Equations to Describe Patterns

31. 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

1 7

2 10

3 13

4 16

a) P = 3n + 7 b) P = 7n + 3 c) P = 3n + 4 d) n = 3P + 7

32. In each equation, determine the value of A when n is 3.

a) A = 2n + 1 b) A = 3n – 2


9

33. Rachel takes care of homes during the summer while their owners are away on vacation.

She charges $8, plus $2.50 a day.

a) Create a table that shows the charges when the owners are away for up to 5 days.

b) 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?

Lesson 4.2: Linear Relations

34. 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.


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a) x y b) x y

1 5 1 1

2 12 3 3

3 19 5 7

4 26 7 13

5 33 9 21

35. Create a table of values for each linear relation and then graph the relation.

Use values of x from –2 to 2.

a) y = x + 4 b) y = 2x + 1

36. A computer repair company charges $80 for a service call, plus $50 an hour for labour.

a) Create a table to show the relation between the time in hours for the service call

and the total cost.

b) 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? Lesson 4.3: Another Form of the Equation for a Linear Relation

37. Which equation below describes each graph?

a) b)


11

i) x = 2 ii) x = –2

iii) y = 2 iv) y = –2

38. Graph each line. Explain your work.

a) x = 4 b) y – 2 = –6

Lesson 4.4: Matching Equations and Graphs

39 . Match each equation with a graph on this grid.

a) y = 2x – 1

b) y = –x + 4

c) y = 3x – 3

Lesson 4.5: Using Graphs to Estimate Values

40. Determine the value of y for each value of x.


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i) x = 2 ii) x = 8

iii) x = –6

41. The graph shows how the cost of a long distance

call changes with the time for the call.

a) Estimate the cost of a 7-min call.

Is this interpolation or extrapolation? Explain.

b) 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.

Lesson 5.1: Modelling Polynomials

42. . Identify the polynomials in the following expressions.

a) 2m2 + 1 b)

123x c) –4x d)

1

x2+ x

e) 0.25y2

43 . Name the coefficients, variable, degree, and constant term of each polynomial.


13

44. Use algebra tiles to model each polynomial. Sketch the tiles.

a) –5 + y2 b) 2x – 1

45. Write a polynomial to match the following conditions.

a) 2 terms, degree 1, with a constant term of 4

b) 3 terms, degree 2, with the coefficient on the 2nd degree term –2

Lesson 5.2: Like Terms and Unlike Terms

46. Simplify each polynomial.

a) 3a2 – 2a – 4 + 2a – 3a

2 + 5 b) 7z – z

2 + 3 + z

2 – 7

c) d2 + 3d + 1 + 4d

2 + 2 d) –6x

2 + 10x – 4 + 4 – 12x – 7x

2

coefficients variable degree constant

–8y

12

–2b2 – b + 10

–4 – b


14

Lesson 5.3: Adding Polynomials

47. Add.

a) (y2

+ 6y – 5) + (–7y2

+ 2y – 2) b) (–2n + 2n2

+ 2) + (–1 – 7n2

+ n)

c) (3m2

+ m) + (–10m2

– m – 2) d) (–3d2

+ 2) + (–2 – 7d2

+ d)

48. a) For each shape below, write the perimeter as a sum of polynomials and in simplest form.

i) ii)

Lesson 5.4: Subtracting Polynomials

49. Subtract.

a) (mn – 5m – 7) – (–6n + 2m + 1)

b) (2a + 3b – 3a2 + b

2) – (–a

2 + 8b

2 + 3a – b)

c) (xy – x – 5y + 4y2) – (6y

2 + 9y – xy)

Lesson 5.5: Multiplying and Dividing a Polynomial by a Constant

50 . Divide.

a) 12d ÷ 4 b) –20d ÷ 5 c) 8d ÷ –4


15

51. Determine each product.

a) 4(3a + 2) b) (d2 + 2d)(–3)

Lesson 5.6 Multiplying and Dividing a Polynomial by a Monomial

52. Write the multiplication sentence modelled by each set of algebra tiles.

a) b)

c)

53. .Multiply.

a) v(3v + 1) b) 3c(5c + 2) c) (8 + 4y)(6y)

54. Divide.

a) (6x + 3) ÷ 3 b) (14w – 7) ÷ –7 c) (–15 – 10q) ÷ 5

Lesson 6.1: Solving Equations by Using Inverse Operations

55. Solve each equation and verify the solution.


16

a) 1137

d

b) 26

16 p

c) 5.12.01.3 a

56 . A taxicab charges $2.50, plus $1.78 per kilometre.

How long is a trip that costs $21.19?


a) 622 x b) 8.1232.3 v

Lesson 6.2: Solving Equations by Using Balance Strategies


a) yy 963 b) aa 342 c) 9.423.14 cc

59. 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.

60. Solve the following equation and verify the solution.

3312 hh


17

Lesson 6.3: Introduction to Linear Inequalities

61. State 3 values of the variable that satisfy each inequality.

a) c < 7 b) 3a c) 5 < n d) y1

62. Write the inequality that is graphed on each number line.

a)

b)

c)

63. Write an inequality to describe each situation, then graph it.

a) The gas tank in a car contains no more than 55 L of gas. _________________

b) The minimum age you must be to watch the movie is 13. _________________


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64. Match each inequality with the graph of its solution.

a) 93 g b) 25 m c) 42 y d) 31 f

i)

ii)

iii)

iv)

Lesson 6.5: Solving Linear Inequalities by Using Multiplication and Division

65. Solve each inequality and graph the solution.

a) 6.63.15.3 aa

b) 52.01.15.23.1 xx


19

66. 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.

Lesson 7.1 Scale Diagrams and Enlargements

67. 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?

68. 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 Diameter of

scale diagram

a) 8 cm 6

b) 40 mm

4

15

c) 3.5 cm 5.8

d) 0.6 mm 20.5

Lesson 7.2 Scale Diagrams and Reductions

69. Here is scale diagram of a picnic table.


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The actual length of the picnic table is 180 cm with legs 60 cm.

What is the scale factor for this diagram?

70. A rectangular playground has dimensions 24 m by 16 m.

Draw a scale diagram of this playground with a scale factor of 200

1 .

Lesson 7.3 Similar Polygons

71. Which rectangles are similar? Give reasons for your answer.

Lesson 7.4 Similar Triangles

72. 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.


21

73. 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?

74. Determine the length of XY in each pair of similar triangles.

a)

b)


22

Lesson 7.5 Reflections and Line Symmetry

75. Draw in the lines of symmetry in each design


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Lesson 7.6 Reflections and Line Symmetry

77. Which polygons have rotational symmetry? State the order of rotation and the angle of

rotation symmetry for each.

a) b) c)

Lesson 7.7 Identifying Types of Symmetry on the Cartesian Plane

78. 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.

a) b)

Lesson 8.1 Properties of Tangents to a Circle

79. Draw and label a diagram to illustrate the property of a tangent to a circle.

Point O is the centre of the circle.

Points P and Q are points of tangency.

Determine the values of x and y.

Justify your solutions.


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80. Point O is the centre of the circle. Point P is a point of tangency.

Determine the value of x to the nearest tenth.

Lesson 8.2 Properties of Chords in a Circle

81. Point O is the centre of the circle.

Determine the values of x and y.

82. 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.

Lesson 8.3 Properties of Angles in a Circle

83. Point O is the centre of each circle. Determine the values of x and y. Justify your

solutions.

a) b) c)


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Lesson 9.1: Probability in Society

84. Indicate whether each decision is based on theoretical probability, experimental probability, or

subjective judgment. Explain how you know.

a) 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.

b) 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 email password because it is more difficult to determine a long password

than a short one.

Lesson 9.2: Potential Problems with Collecting Data

85. Name a problem with each data collection.

a) To discover common fears, Chris asks his classmates if they are frightened by spiders, snakes,

rats, or slugs.

c) 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?”

Lesson 9.3: Using Samples and Populations to Collect Data

86. In each case, describe the population.

a) A social networking site wants to know the typical age of a person who uses the site.

b) A book retailer wants to know which demographic groups buy travel books.

d) A music store wants to know how many school-aged students take piano lessons.


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Lesson 9.4: Selecting a Sample

87. 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.

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