Workbook Answers Example: 8 - Wikispaces Worksheets...  Answers • MHR 153 Workbook Answers

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  • Answers MHR 153

    Workbook Answers1 Get Ready

    1. Triangle ABC is translated 4 units up.

    2. P'(3, 3)

    3. a)

    x

    r

    y b)

    x

    ry

    4. a)

    x

    y

    A

    D

    E (3, 7) (6, 7)

    (6, 6)(3, 6)F

    D

    GG

    FE

    b) a 270 counter-clockwise rotation5. 286 cm26. a) 5 b) 3

    1.1 Line Symmetry1. True2. False. Example: An isosceles triangle has one

    line of symmetry.3. True4. False. Examples: A shape that has a line of

    symmetry is symmetrical. A shape that does not have a line of symmetry is asymmetrical.

    5. False. Example: A curved shape may have lines of symmetry.

    6.

    7. Example:

    8888

    8. Three lines of symmetry

    9. a) Four lines of symmetry

    b) Two lines are oblique.

    10. a) There are none.

    b) One line

    11. a) K(2, 8), L(8, 8), M(5, 2)

    b)

    x

    y

    -2 2 4 6 8-4

    2

    4

    6

    8K L

    M

    c) K'(-4, 8), L'(2, 8), M'(-1, 2)

    d) Yes. They show symmetry along a vertical line.

    e) x = 2

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  • 1.2 Rotation Symmetry and Transformations

    1. a) rotation b) order c) symmetry d) centre e) circle

    2. Both. Example: Parts of the design have rotational symmetry. The octagon has an order of 8 and the square has an order of 4. There is line symmetry because there is a refl ection along any side of any fi gure.

    3. Shape

    Lines of Symmetry

    Order of Rotation

    Angle of Rotation

    Small square 4 4 90

    Octagon 8 8 45

    4. a) Example:

    b) Example: The letter E; horizontal

    c) Example: The design with F has an order of rotation of 2 and an angle of rotation of 180.

    5. a) Example:

    b) Example: 180

    6. a) Four

    b) Example: Yes. Susan could repeat the pattern using rotational symmetry, or line symmetry, or both.

    7. a) 2 b) 2 c) 2

    d) 2. Note that if the letter is perfectly square, there may be four lines of symmetry.

    e) Examples: I, O

    f ) Examples: A, B, C, D, E, I, K, M, O, T, U, V, W, Y

    1.3 Surface Area

    1. a) 675 cm2 b) 706.9 cm2 c) 1488 cm2

    d) 477.5 cm2 e) 1.5 m2

    2. Example: The total area of all of the surfaces of a shape.

    3. Example: The can has the greater surface area of approximately 596.9 cm2. The surface area of the tetra box is 444 cm2. The difference between the objects is approximately 152.9 cm2.

    4. a) 280 cm2 b) 460 cm2

    5. a) 30 240 cm2 b) 22 680 cm2 c) 52 920 cm2

    6. a) 53 176.4 m2.

    b) Each side is 21 513.6 m2. The total surface area of the four triangular sides is 86 054.3 m2.

    c) The total area of the pyramid is 139 230.7 m2.

    7. 1738.2 cm2

    8. a) 72 cm2 b) 108 cm2

    1 Chapter LinkAnswers will vary.

    1 Vocabulary Link

    1. line of symmetry

    2. line symmetry

    3. rotation symmetry

    4. symmetry

    5. centre of rotation

    6. translation

    7. angle of rotation

    8. surface area

    9. symmetrical

    154 MHR Answers 978-007-097344-2

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  • Answers MHR 155

    Chapter 1 Review

    1. a) rotational symmetry

    b) horizontal, vertical, and rotational symmetry

    2.

    3. a) Example: A type of symmetry where an image can be divided into two identical refl ected halves by a vertical line of symmetry.

    b) Example: A type of symmetry where an

    image can be divided into two identical refl ected halves by a horizontal line of symmetry.

    c) Example: A type of symmetry where an

    image can be divided into two identical refl ected halves by a diagonal line of symmetry.

    d) Example: A type of symmetry where an image can be turned about its centre of rotation so that it fi ts onto its outline more than once in a complete turn.

    4. a) rotation symmetry

    centre ofrotation

    b) This design is not symmetrical. Example: To give the design symmetry, refl ect a row of cats. The two rows of cats would then have symmetry along the line of refl ection.

    5. a)b)

    x

    y

    -4 -2

    -2

    -4

    -6

    20 4 6-6

    2

    4

    6E

    E E

    E(1, 6)

    (2, 3)

    (6, 3)(2, 3)

    (1, 6)(5, 6)

    (6, 3)

    (5, 6)

    (2, 3)(6, 3)

    (5, 6)(1, 6)

    F

    F F

    F

    G

    G G

    GH

    H H

    H

    6. a) 167.5 m2 b) 277.7 m2

    7. a) 128.425 m2 b) 1285

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  • 156 MHR Answers 978-007-097344-2

    2 Get Ready

    1. a) 152.85714 b) 272.430 c) 390.166 00

    2. It is less than 349 since we are multiplying by a number less than 1.

    3. a) 3 __ 4 , 0.75 b) 4 __ 10 , 0.4

    4. a) 7 __ 10 , 3 __ 4 b)

    2 __ 7 ,

    1 __ 3 ,

    3 __ 8

    5. a) 1 __ 5 + 3 __ 10 b)

    2 __ 3 -

    3 __ 5 6. a)

    7 __ 8 b)

    1 __ 12

    7. a) 5 __ 8 b) 33

    __ 8 or 4 1 __ 8 8. a) 10 b)

    10 __ 3 or 3

    1 __ 3

    2.1 Comparing and OrderingRational Numbers

    1. a) 2.1, - 3 __ 2 , 3, -55

    b) 3.0, __

    9 , -21 ____ -7 ,

    3 __ 1

    2. a) - 14 __ 5 , -2.1, - 3 __ 4 , 0 __ 3 ,

    3 __ 4 ,

    5 __ 4 ,

    6 __ 4 , 1.8

    b) - 3 __ 4 , 3 __ 4 c)

    3 __ 4

    3. a) C b) B c) A d) E e) D f) Example: I estimated where the rational

    number would go on the number line, then identifi ed the related letter.

    4. a) b)

    -2 -1 0 1 2

    116

    2.21.1-1.1

    -

    116

    -

    -

    108

    787

    8

    108- 2.2

    5. a) - 3 __ 2 b) 6.

    _ 8 c) 2 1 __ 5

    6. a) 1.125, -1. _ 6 , 0.

    __ 54

    b) -1.7, -1 2 __ 3 , 0.511, 6 __ 11 ,

    9 __ 8

    7. a) 0.8 _ 3 , -2.4, -1.75

    b) 5 __ 6 , 0.7, -1 3 __ 4 , -2.1. -

    12 __ 5

    8. Examples: a) -6 ___ 8 b) - 2 __ 3 c) 3 __ 2 d) -

    10 __ 6

    9. Examples: a) - 5 __ 8 b) 7 __ 9 c) -

    1 __ 4 d) - 8 __ 7

    10. a) 1 __ 3 b) 3 __ 5 c) -1

    1 __ 6 d) -

    3 __ 4

    11. a) 2 __ 3 b) - 11 __ 12

    c) - 7 __ 4 d) -2 5 __ 6

    12. a) 0.25, 0.125; Example: 0.13

    b) -0. _ 6 , -0.8; Example: -0.7

    13. a) 6.5 C, 0.1 C, -15.7 C, -17.0 C, -22.1 C, -23.2 C, -23.6 C, -32.2 C

    b) -22.2 C 14. a) > b) > c) < d) =

    2.2 Problem Solving With Rational Numbers in Decimal Form

    1. adding 2. negative 3. positive

    4. a) fi rst b) multiply c) subtract

    5. a) 3, 2.5 b) -18, -17.87 c) -14, -13.84

    d) 7, 6.79

    6. a) 24, 26.66 b) -5, -5.2 c) -36, -34.71

    7. a) -24.96 b) 5.154 c) -16.7658. a) 11.2 b) -14.4 c) -14.3 d) 10.8

    e) -85.548 f) 64.49

    9. 0

    10. a) -6.9 b) -9.8 c) -2.2 d) -7.5

    11. a) -0.73 b) 0.25

    12. a) Example: -12.7 - 6.9 b) 19.6 C

    13. a) Example:

    [-0.5(3 60)] + 0.7[(1 60) + 15]

    b) -37.5 m

    2.3 Problem Solving With Rational Numbers in Fraction Form

    1. e) number line

    2. a) adding the opposite

    3. b) improper fractions

    4. d) positive fractions

    5. c) multiplication and division

    6. a) -1 1 __ 2 , -1 b) 1, 1 1 __ 6

    c) 1, 1 3 __ 4 d) 7 1 __ 2 , 7

    2 __ 3

    7. a) -1, - 2 __ 5 b) 1 __ 4 ,

    1 __ 6

    c) 1 __ 2 , 5 __ 14 d) -2, -1

    7 __ 8

    8. a) 1, 1 1 __ 6

    b) -1, -1 1 __ 11

    c) 4, 3 1 __ 7 d) 1 __ 2 ,

    4 __ 9

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  • Answers MHR 157

    9. Examples:

    1 - 2 __ 5 - 1 __ 3 =

    4 __ 15 h,

    60 - ( 2 __ 5 60 ) - ( 1 __ 3 60 ) = 16 min10. $495 11. 9.6 m

    2.4 Determining Square Roots ofRational Numbers

    1. d) 2. e) 3. b) 4. c) 5. a)

    6. a) Any rational number between 25 and 36 is correct. Example: 26

    b) Any rational number between 9 and 16 is correct. Example: 12

    7. a) 4, 4.84 b) 81, 75.69

    c) 121, 127.69 d) 1, 0.8464

    8. a) 196 cm2, 216.09 cm2 b) 4 km2, 5.29 km2

    9. a) Yes, both 4 and 9 are perfect squares.

    b) 0.4 = 4 __ 10 . No, 10 is not a perfect square.

    c) 0.81 = 81 ___ 100 . Yes, both 81 and 100 are perfect squares.

    d) No, 2 is not a perfect square.

    10. a) 0.16 = 16 ___ 100 . Yes, both 16 and 100 are perfect squares.

    b) No, 90 is not a perfect square.

    c) 0.001 = 1 ____ 1000 . No, 1000 is not a perfect square.

    d) 8 __ 18 = 4 __ 9 . Yes, both 4 and 9 are perfect squares.

    11. a) 17 b) 0.19 c) 35 d) 2.3

    12. a) 1.5 cm b) 19 m

    13. a) 5, 6 b) 7, 8 c) 0.4, 0.5 d) 0.8, 0.9

    14. a) 5.5 b) 7.2 c) 0.42 d) 0.88

    15. 2.3 m 16. 7.5 cm

    17. N