Unit Square Roots and the Pythagorean Theorem

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```					                     Math Makes Sense 8 Homework and Practise Book - Answers

Unit 1 – Square Roots and the Pythagorean Theorem

Pg.1
What Do You Notice The final result is 6174
The final result is 6174, no matter what the original number.
Letter Symmetry HIOX
Pg.3
Check 1. a) 6cm x 3 cm = 18 cm² b) 8.5 Square units c) 25 cm² d) ½ (5cm x 6cm) = 15 cm²
e) 17.5 cm² f) 22.95 m²
Pg.5~6
Practice 1.a) – iii)16 b) – i) 36 c) – ii) 8 2. a) 64 = 8 x 8 = 8² b) 49 = 7 x 7 = 7²
3. a) 4² 4x4 16 b) 3² 3x3 9 c) 7² 7x7 49 d) 11²                       11x11 121
4. a) 25cm² ---- iii) 5cm b) 64cm² ---- iv) 8cm c) 4 cm² ---- i) 2cm d) 100cm²---- ii) 10cm
5. Diagrams may vary. No, 32 is not a square number. 6. Diagrams may vary.
Yes, 64 is a square number.
7. a) 81 , 81 is a perfect square because 81 = 9 x 9 = 9²
b) 18 , 18 is not a perfect square because I cannot draw a square with area 18 square units on a grid paper.
c) 20 , 20 is not a perfect square because I cannot draw a square with area 20 square units on grid
paper. d) 25 , 25 is a perfect square because 25 = 5 x 5 = 5²
8. a) 49 cm² , 7 x 7 = 49, so the length of the side is 7 cm. b) 900 mm² , 30 mm c) 121 cm² , 11 cm
d) 169 m² , 13 m
9. a) side length 6 cm      Perimeter = 6cm + 6cm + 6cm + 6cm = 24cm
b) area 25 m²        Side length is 5 m, because 5 x 5 = 25 so, perimeter = 5 m+ 5m + 5m + 5m = 20m
c) area 144 m²           48 m
10. Sample Answer : Yes. 5² x 2² = 25 x 4 = 100 = 10²
Pg. 8
1. a) 196: 1, 2, 4, 7, 14, 28, 49, 98, 196       Square number with square root 14
b) 200: 1, 2, 4, 5, 10, 20, 40, 50, 100, 200 not a square number
c) 441: 1, 3, 7, 9, 21, 49, 63, 147, 441      Square number with square root 21
2. a) square number: 16 square root: 4 b) square number: 49 square root: 7
3. a) 25  5 because 52  25 b) 49  7 because 72  49 c) 100  10 because 102  100
d) 144  12 because 122  144
4. a) 16  4 because 42  16 b) 64  8 because 82  64 c) 81  9 because 92  81
d) 121  11 because 112  121 5. a) 9 – iv) 3 b) 81 – ii) 9² c) 3² – i) 9 d) 9 – iii) 81
6. a) 8 b) 20 c) 15 d) 18 7. a) 5 b) 8 c) 16 d) 54 8. a) 172  289 b) 484 c) 900
Pg.10
1. a) 162  256 b) 100  10 c) 252  625 2a) A = 81 cm², l = 9cm; whole number b) A = 30 cm², l =
30 cm c) A = 144mm², l = 12mm; whole number d) A = 58m², l = 58 m
3a) l = 7cm, A = 49cm² b) l = 15m, A = 255m² c) l = 36 cm, A = 36cm²
d) l = 50 mm, A = 50mm² e) l = 24 cm, A = 24cm² f) l = 121 mm, A = 121mm²
4. a) 16 , 2 , Area of shaded square = area of large square – 4 x area of each triangle
= 16 square units – 4x2 square units
= 8 square units
side length = 8 units
b) 17 square units; 17 units c) 20 square units; 20 units 5. a) 26 square units, 26 units
b) 8 square units; 8 units c) 25 square units; 5 units
Pg 11
1. a) between 2 and 3 b) between 4 and 5 c) between 7 and 8 d) between 1 and 2
pg. 12 2. a) between 11 and 12 b) between 14 and 15 c) between 10 and 11 d) between 12 and 13
e) between 13 and 14 3. a) False b) True c) True d) True 4. a) Not a good estimate b) Good
estimate 5. a) 4.5 b) 7.5 c) 10.7 d) 13.2 6. a) A = 50cm²; s = 7.1cm b) A = 125cm²; s = 11.2cm c) A =
18cm²; s = 4.2cm 7. 9.95 ; methods may vary
8 250m2 = 15.81m, 15.81m + 15.81m + 15.81m + 15.81m = 63.24m, 63.24m of fencing is required.
Pg. 14
1. a) j and p are legs; g is hypotenuse b) n and r are legs; d is hypotenuse 2. a) 89 b) 5 c) 17

82  l 2  6 2
h 2  32  7 2
64  l 2  36
h  9  49
2

64  36  l 2  36  36
3a) h 2  58            b)                             c) h  15.62units d) l  5units
28  l 2
h  58
28  l
h  7.62units
5.29units  l
4a) 45  6.7units b)         244  15.6units c) 141  11.9units
p. 16
1a) is, 100  64  36 b) is not, 8  15  17 2a) right triangle because 20  48  68 b) not a right triangle
because 42  40  72 c) not a right triangle because 6  8  10
p. 17
202  302  1300
3a)                    b) 302  402  502 c) 202  212  292 d) 602  112  622
40  1600
2

not a right triangle      a right triangle    a right triangle     not a right triangle
20  30  40
2      2      2

4. 72  242  252 5a) is not a Pythagorean Triple 102  502  602 b) is 122  352  372
6a) 25, square root, squares,     72  242  49  576 b) 34 c) 24
 625
 25
7. Right. 10 m 24 m  26 m . The triangle formed by the width, length, and diagonal is a right
2  2    2   2     2   2

triangle, so the lawn is a rectangle.
p.19
1. 4, 6, 8, 64, 52 2. a) 11.7mm b) 10.3 cm c) 20.2 mm d) 5.7 cm
3. h2  a 2  b2
82  32  b2
64  9  b2
64-9 = 9+ b 2 -9
55 = b 2
b = 7.4
7.4 m
p.20
4. Diagrams may vary. 15.6 km 5. 793 m 6. 50m, 50m, 30m + 40m = 70m, 70m – 50m = 20m
7. 100, 10, hypotenuse, 10cm, 10cm, 14.1cm
p.21
Square Root: a number that, when multiplied by itself, results in a given number. For example, 5 is the
square root of 25
Legs Of A Right Triangle: the sides of a right triangle that form the right angle
Hypotenuse: the side of a right triangle that is opposite to the right angle; the longest side of a right
triangle
Pythagorean Theorem: the rule that states that, for any right triangle, the area of the square on the
hypotenuse is equal to the sum of the areas of the squares on the legs
Pythagorean Triple: three whole-number side lengths of a right triangle. For example, 3-4-5 is a
Pythagorean triple.

Square number, perfect square, irrational number
p.22
1. Diagrams may vary. 36, 121 2 a) 64 b) 7 c) 144 d) 11 3 a) 1, 2, 5, 10, 25, 50
b) 1, 2, 4, 7, 14, 28, 49, 98, 196 c) 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 d) 1, 3, 5, 7, 15, 25, 45, 75, 225
4. a) 18 cm b) 13cm (circle) c) 200 cm 5. 10 square units. 10 units
p.23
6. 20 units 7. a) 8 b) 54 c) 153 8. a) 6 and 7 b) 4 and 5 c) 7 and 8 d) 11 and 12
9. a) 6.7 b) 4.2 c) 7.4 d) 11.6 10. a) 8.66             b) 9.49 11. a) 32 m2    b) 100 cm 2 12. a) 25 units
b) 8.9 units      c) 10 units 13. a) not a right triangle because 52cm2  31cm2  82cm2
b) right triangle because 15mm2  20mm2  35mm2
p.24
14. a) 10, 24, 26       d) 11, 60, 61 15. 16.64 km 16. 10.82 m
p.27
1. a) +4 b) –5 c) –1 d) +2 2. a) 0 b) +6 c) +16 d) -11 e) -5 f) -8
p.28
3. a) +9 b) +1 c) 0 d) +14 e) -11 f) +2
4. From 8 degrees C to 3 degrees C ---- (+3) – (+8) ---- -5
From 8 degrees C to -3 degrees C ---- (-3) – ( +8) ---- -11
From -8 degrees C to 3 degrees C ---- (+3) – (-8) ---- +11
From -8 degrees C to -3 degrees C ---- (-3) – (-8) ---- +5
p.29
1. a) (-2) b) 3 x (+11) c) 3 x (-5)
p.30
2. a) – 4 b) (+4) + (+4) + (+4) + (+4) + (+4), +20 c) (-3) + (-3), -6 3. a) -6 b) 5, +10
c) (-2), (-3), +6 d) (-9) x (-2) = +18 e) 4 x (-3) = -12 4. a) -14 b) +15 c) -6 d) -20
p.31
5. a) +12 b) -10 c) +14 d) -18 6. -2 represents a fall of 2 degrees C, 4 represents 4 hours,
4 x (-2) = -8 The temperature dropped 8 degrees C in 4h.
p.32
1. a) 0, (-1), -3, -6, -9 b) 0, (-3)(-1) = +3, (-3)(-2) = +6, (-3)(-3) = +9
p.33
2. positive, negative, negative, positive, positive, negative 3. a) -14 b) +12 c) -72 d) -50 e) -35
f) +36 i) +7 j) 0 k) -400 4. a) -5 b) -11 c) +32 d) -4 e) -7 f) -5 g) +12 h) -10 k) -8
5. -3, +9, -27, +81 ---- Start at -3. Multiply by -3 each time.
+2, -10, +50, -250 ---- Start at 2. Multiply by -5 each time.
+3, -3, +3, -3 ---- Start at 3. Multiply by -1 each time.
+1, -10, 100, -1000 ---- Start at 1. Multiply by -10 each time.
-1, -2, -4, -8, -16 ---- Start at -1. Multiply by 2 each time.
p.35
1. a) (+6) x (+10) = +60, (+10) x (+6) = +60 b) (-4) x (-9) = +36, (-9) x (-4) = +36
c) (+5) x (-9) = -45, (-9) x (+50 = -45 d) (-8) x (+2) = -16, (+2) x (-8) = -16
2. (21)  (3)  7 , seven steps 3a) -3 b) +4 c) +5 d) +2
p.36
4a) -3 b) +2 c) -2 5) -4 represents the drop each hour, -28 represents the total drop, (28)  (4)  7
It took 7 hours for the water level to drop 28cm. 6a) +5 b) +5 c) -5 d) -5 They are all either +5 or -5
7) -12 represents a drop of 120 C, +4 represent 4 hours, (12)  (4)  3 , The temperature dropped 30 C
every hour.
p.37
+3, positive +2, positive -3, negative -2, negative -3, negative +2, positive +3, positive -2, negative
p.38
0                    0
(2)  (2)  1     (4)  (4)  1
2) positive, negative 3a)                       b)                     positive, negative
(4)  (2)  2     (8)  (4)  2
(6)  (2)  3     (12)  (4)  3
4) a) -5 b) -8 c) -9 d) +6 e) -12 f) +8 g) +7 h) +12 i) -8 5) a)  4   2  2
b) (12)  (3)  4 c) (12)  (1)  12 d)  12  (2)  6 6) a) -19 b) +23 c) +11 d) -45

p.39
526       3(8  12)  4  2  3  21  ( 7)  5
10   5  3  9 8  15  (3)  7
             f)
1) a)  3  6 b)  3  4 c)  4  6 d)  3  5       e)
 1                    6
 3         12      2           15
(3)(8)  24  (2)
g)
 12

p.40
35  9
2
3( 4)    (4)(2)
30  (5  10)  2 30  (5  10  2)  30  5  10   2 30  5  10  2       
2)                                                                         3) a)      2   b)    8
 12              2               8                 14
12        1

2
 6

3(10  2)  4 (6)(6)  (4) 4  (3)  24  2     5  12  4  (2)
(6)(4)  8     2( 7  3) 8  12  4
 3(5)  4     (6) 2  ( 4)  12  24  2         5  3  (2)
c) (2)  4 4)  2( 4)  8  3
 15  4       36  (4)      12  12             5  (6)
2               8        5
 19           9            0                     11
10  2( 3)
19  3  4  (6) 6(8)  1
2 4
 19  12  (6) 12           10  6
48      
 19  (2)             1     9 1     MEET ME AT THE CORNER
12
 19  2                       16
 4 1     
 21                            8
3
2
p.41
( 8)
Quotient: the answer to a division question. For example, in the division equation              4 , -4 is the
( 2)
quotient.
Zero pair: two opposite integers, such as +4 and-4, whose sum is 0.
Commutative property: order does not matter when multiplying integers. For example,
(2)  (3)  (3)  (2) .
Zero property: The answer when multiplying an integer by 0 is 0. For example, 4  0  0  4  0 .
Order of operations: The order to perform operations in a mathematical expression. For example,
in 3  (2)  5  (4) , perform the addition in brackets first, then do the multiplication, and finally do the
3  (2)  5  (4)
 1  5  (4)
 1  (20)
 19
Number line, opposite integers, multiplying by 1 property, distributive property, numerator, denominator

p.42
(5)  (2)                               (3)  (5)             (3)  (3)
1) a)  (2)  ( 2)  ( 2)  ( 2)  ( 2) b)  (5)  (5)  (5) c)  (3)  (3)  (3)
 10                                       15                    9
(4)  ( 2)  ( 2)  ( 4)
d)  (4)  (4)                2) a) (5)  (1)  5 b) (3)  (4)  12 c) (2)  (6)  12
 8
d) (4)  (5)  20

p.43
3) a) +2 represents a rise of 2°C, +6 represents 6h, (6)  (2)  12 , the temperature rose 12°C in 6 h b)
(4)  (12)  8 , the temperature after 6 h was 8°C 4) Models may vary
5) a) Negative b) zero c) Positive 6) a) +6 b) -24 c)+220 d) -720 e)+180 f) +126 g)-162 h)0
7) a) (6)  (4)  24 b) (9)  (3)  27 c) (7)  (3)  (21) d) (4)  (6)  24
e) (20)  (15)  300 f) (32)  (5)  160

p.44
8) a) (4)  (25)  100 or (25)  (4)  100 b) (4)  (7)  28 or (7)  (4)  28
c) (3)  (5)  (15) or (5)  (3)  15 d) (4)  (12)  48 or (12)  (4)  48
9) Models may vary 10) a) Positive, +5 b) negative, -4 c) negative, -6 d) zero, 0
11) a) -5 b) +3 c) -6 The quotients from least to greatest are: -6, -5, +3
1, (16)  (1)  16
2, (16)  (2)  8
2, (16)  (2)  8
4, (16)  (4)  4
12) 4, (16)  (4)  4
8, (16)  (8)  2
8, (16)  (8)  2
16, (16)  (16)  1
16, (16)  (16)  1

p.45
1
13) a) +256, -1023, +4096 Pattern rule: Start at +1. Multiply by -4 each time. b) -4, +1,             Pattern rule:
4
1
Start at -128. Divide by –4 each time. c) +25, -5,      Pattern rule: Start at -3125. Divide by -5 each time.
5
14) a) multiply (2)  (3) b) divide (20)  (4) c) subtract (4  5) d) multiply (4)  (2)
(20)  (4)  (2)                   5  3  (4)  (2)
(8)  (2)  ( 3)                           (2)(4  5)
 (5)  (2)                           538
15) a)  (8)  (6)       b)                     c)  (2)( 1) d)
 (5)  (2)                           28
 14                                          2
 7                                    10

p.46
21  2(3)
(3)  ( 3)
48  4  2(3  4)                    (6)(8  2)                                        21  6
(4)                                      
 48  4  2(1)                                     (3)  (3)  (4)  (4)       (3)  ( 3)
17  4  4                           2  4  9        (6)(6)
 12  2(1)                                          (9)  (4)  (4)
c)  2  36 d)  4
27
16) a)  17  16 b)                                                     e)                            f) 
 12  (2)                                           (9)  (16)                  (3)  (3)
1                                    38             36
 12  2                                             25                           27
4                                        
 10                                 9
9
3
p.47
Sample answer: cart, raft, craft, ratio, ration,…
p.48
5                                  24 3
3                                          
8                                   8 8
1 2 3         3 6 42          5 25 50             15 4          49      67      49        27              5
1) a) , ,         b) , ,        c)     , ,          2a)          b)       c)      d)      3a)            b) 2
4 8 12        2 4 48         12 60 120             5 5          9       20      24         8             18
19                                        3
3
5                                        8
11        5
c) 2     d) 2
15       12
p.49
21 5

30 30                                 1 1                          15 6                                 6
3 4                                                                 2
26                13                  3 2              5            20 20          11                   9            5
4) a)                b)          c)                     d) 4         5a)              b)         c) 6, 10,            d) 3
30                14              5                   24              9            24                     4         12
7                                                                     1
13                                6                                   20                                  9
15
p.50
20             3            2          1
1) a) 4,             b) 4         c) 2       d) 3
7                8            3          2
6
2
7
p.51
5 20            1              2 14             4            2 10          1          3                            4
2) a) 4 x  , or 3               b) 7 x  , or 2                c) 5 x  , or 3           3a) 1       b) 15 c) 12 d) 4
6 5              3             5 5              5            3 3           3          4                            9
3         5                                                         3
e) 3      f) 5       4a) iii b) v c) iv d) i e) ii 5) 9
5         8                                                         4
p.52
1 1             1          1 1 1               1 5 5
1) a)            b)          c) x              d) x 
2 3            10          3 3 9               2 6 12
p.53
3         1                   3                      1 6 3 1 3
2) Models may vary. a)                b)       3) Tom ate of the pie. 4) , , , , . The numerator of the
16         3                   8                     20 20 20 10 10
answer fraction is the product of the numerators of the fractions being multiplied. The denominator of the
answer fraction is the product of the denominators of the fractions being multiplied.
3         5          8           7
5) a)        b)        c)          d)
10        12         21          15
p.54
1x1           1          7         4        1
1) a) 3, 4,             b)         c)        d)        e)
2 x5           2         12        15        6
1

10
p.55
1           1          5          2           1       4         1       2         4         1        6          1
2) a) 1      b) 2          c)       d) 2        3a) 1      b)       c)       d)      4a)       b) 1      c)        d) 1
2          12          6          3           8       7         4       9        15         3       13          8
2
1        3                   5        5    7
5) a) iii b) i c) iv d) ii 6)                    7)                 8) , 1  
10        1 2 1              12       12 12
x 
4 3 6
p.56
13        19        19          19           3          1          2         3
1) a)        b)        c)          d)        2a) 5       b) 3       c) 5      d) 6
5         4          6         12           8          6          3         4
p.57
 1 1  1 1                                    21 12
(1x 2)  1x    x 2    x                                 x
 2 6  6 2                                    8 7
1 1 1                                                   9              3          3                 3           4
3) a)  2                                        b) 3 4a)                  b) 5       c) 3      d) 6 e) 9          f) 10
2 3 12                                                  2              5          4                 7           5
11                                                           1
2                                                          4
12                                                           2
5) George practises for 3h on Saturdays.
p.58
1        1       3          7
1) a) 6 b) 6 c) 3 d) 2 2a)                     b)      c)       d)
8        8       8         16
p.59
2          1           1         1         3         3         5        1
3) a) 14 b) 9 c) 6 d) 10 4a) 2                      b) 4       c) 5       d) 3       e)        f)        g)        h)
3          2           3         3        10        20        12        8
1                                                3                   3                                         12
6) a)       b) 18 7a) Sample answers: 4   16 or 12   16 b) Sample answers: 3   1 or
9                                               12                   4                                          4
12
4  1
3
p.60
7        8        15          8           1          2          1
1) a)       b)       c)         d)       2a) 2       b) 2        c) 1
4        3        11          7           4          3          2
p.61
3          1         1                             1                    1                 7          4
3) a) 2, 2 b) 1          c) 1      d) 2       4a) 2, There are 3 two-eights, 3                   b) 8 c) 1        d) 2
5          3         3                             2                    2                 8          7
3
2
27          11           2        1                               1                      1                     1
5) a)         b) 2          c) 6       d)       6a) 3 servings b) 4 servings c) 2 servings d) 1 servings
8           12           3        6                               2                      4                     2
3
3
8
1      1 1
7) a) 3 , 5, ,
4      4 24
p.62
37        26          29         31            2 1 14 25                 36 21           42 25           27 20
1) a)        b)         c)         d)        2a) 6, , ,            ,        b) ,            c) ,           d) ,
8         7         12          9             6 6 6 6                   10 10           10 10           12 12
p.63
19      9           2          1          1                 4 14          5           1
3) a) 19, 19, 10, 19 10 ,           ,1         b) 2       c) 1       d) 3      4a) 7, 9, , , or 1              b) 2
10 10               5          2          5                 9 9           9          10
4            4           9           5          10                                2        3        3          2
c) 3 d) 1        5a) 2         b) 1        c) 2        d) 2         6) 4 7) 5 8) A: 3 , B: 3 , C: 3 , A, 3
5            9          16          14          21                                3        5        8          3
p.64
1) a) addition b) division c) multiplication
p.65
1 1          1 1 4 3                 7       7                          11           1 2          3
2 a)  ,                                   ,       b) 8 c) 124 3) 5             4) 1 ,          5)      6) 10
3 4          3 4 12 12 12 12                                            20           4 3          7
p.66
7      7              3    2       7    1    5
7a) 1     b) 1     8) 6 9a)     b)   10a)    b)   c)
8      8              5    5      12    4    6
p.67
1) a) Add the functions in the brackets b) Multiply c) Subtract the fractions in the brackets
d) Divide the fractions in the brackets. 2) Her answer is not correct. She multiplied first instead of
dividing first.
p.68
1 5           12 1
              
3 4 1           3 7          3 24          35 5
  x              
6 6 7           4 4            1 24          12 7
 x            
7 1               3 4          3 5           35 35        2     21         1     17           4
3) a)  x            b)  x       c)            d)            4a)    b)       c) 4    d)        5a) 1
6 7               4 7          8              5           5     40         2     24           5
             
1                 3            5             35
                 
6                 7             3            1
1            
5            7
3        1     3        8      1       13             1     15
b)     c) 1    d)      6a)     b)      c)      d) 1 e) 7    f)
5        3     4        9      2       15             8     28
p.69
Simplest form of a fraction: a fraction in which the numerator and the denominator have been divided by
their greatest common factor.

Reciprocal of a fraction: a fraction, either proper or improper that is inverted. For example, the reciprocal
5     7
of is .
7     5

3
Mixed number: a number consisting of a whole number and a fraction. For example, 5            is a mixed
8
number.

Quotient: the result when one number is divided by another.

Order of operations: the rules that are followed when simplifying or evaluating an expression; brackets,
multiplication and division, addition and subtraction.

Product, factor, equivalent fraction, divisor, dividend.
p.70
2        1       4    3 1      18        39       27
1) a) 6, or 3 b) 4, or 5 3a)         b)      c)     4) ,   5a)        b)       c)
3       12       9    4 2       5         8       16
p.71
1               23                                  2       4         11       2         18           1
6) a) 11      b)16 c) 3        7) Models may vary. a) 6 b) 6      c)       8a)       b)      c)        9a) 1
4               32                                  3       5         24       3         25           5
5         4
b)      c) 1     10a) 6
8         5
p.72
19 5                     9       24          3
11) ,           12) 9 13a)        b)       14) 1
24 24                   10       35          5
p.73
Handshakes: 6, 10, 15, 21. Starting from 1, as the number of people increases by 1, the number of
handshakes increases in this pattern 1, 2, 3, 4, …

Word Search: 2) MATH IS GREAT
p.74
1) a) 42, 42 b) 9.52 cm 2 2a) b = 6.4 cm, h = 3.5 cm, A = 11.2 cm 2 b) b = 8.6 cm, h = 4.2 cm,
A = 18.06 cm 2
p.75
3) a) 24, 12, 452.389, 452 cm 2 , centimetre b) 254.469, 254 m2 , metre c) 95 mm2 , millimetre
d) 201 km 2 , kilometre 4a) 12, 37.7 cm b) 8, 50.3 m c) 17.6 mm d) 23.9 m
p.77
3) B 4a)A  E, B  F, C  D b) A and E represent s regular pentagonal pyramid with one pentagonal
base and five isosceles triangles. B and F represent a regular square pyramid with one square base and four
isosceles triangles. C and D represent a hexagonal prism with two hexagonal bases and six squares.
5a) hexagonal pyramid b) triangular pyramid c) square prism d) right triangular prism
p.78
1) B
p.79
2) a) Is. It is the net of a hexagonal pyramid b) Is. It is the net of a triangular prism c) Is not. Move
either square on the bottom edge to anywhere along the top edge to make the net of a cube. 3) triangular
prism with two congruent right triangle faces and three rectangular faces.
p.80
4) a) right cylinder b) square prism c) pentagonal pyramid 5a) Add a 13cm by 5 cm rectangle to form
the net of a right triangular prism b) Add a 12 cm by 5 cm rectangle to form the net of a triangular prism.
c) Add a regular pentagon of edge length 5 m to form the net of a pentagonal prism.
p.81
1) 12cm2  32cm2  24cm2  32cm2  12cm2  24cm2  136cm2 2) Rectangle A has area 8m 1m  8m2 ;
Rectangle B has area 5m 1m  5m2 ; Rectangle C has area 8m  5m  40m2 ; Surface Area =
2(12  20)  2(12  8)  2(20  8)
2  8m2  2  5m2  2  40m2
3) Glenda’s package: SA=  480  192  320                      The surface area is
 106m2                                                       992
2(24 10)  2(24  6)  2(10  6)
992cm²; Louis’s package: SA=  480  288  120                         The surface area is 888cm². 992  888
 888
Glenda’s package has the greater surface area. 4) a) Area of each face  294cm2  6  49cm2 b) Edge
1
length = 7cm 5)  200m  50m Total Area to be covered = 2  60m  50m  2  40m  50m  10000m2
4
p.83
1) Rectangle A has area 2m  3m  6m2 ; Rectangle B has area 2m  4m  8m2 ; Rectangle C has
1                                          1
area 2m  5m  10m2 ; Triangle D has area  4m  3m  5m 2 ; Triangle E has area  4m  3m  6m 2 ;
2                                          2
Area = 6m  8m  10m  6m  6m  36m . The area of the net is 36m².
2      2       2      2      2       2

p.84
2) a)200cm² b)360m² c)161cm² d)173.1m² 3) The surface area is 1104cm² 4) The area of the net is
210cm² 5) The surface area is 454mm²
p.85
V  Ah
1) a)  60  8 The volume is 480cm³. b) The volume is 216 cm³. c) The volume is 108m³.
 480
p.86
 Ah
 8.5  7
2) a) A           V  59.5  6 The volume is 357m³. b) The volume is 151.2cm³. c) The volume is 49mm³.
 59.5
 480
3) a) The volume is 960cm³. b) The new length is 8cm and the new height is 10cm. The new volume is
960cm³. 4) a) The volume is 97.2m³. b) The volume is 97.336m³; the volume of prism B is greater
5) a) The volume is 24 m. b) The height for this calculation is 1.5m. The length is 400cm, the width is
300cm, and the height is 150cm. The volume is 18000000cm³. This is the same as 18000L.
p.87
V  Al
1) a)  5  12 The volume is 60cm³. b) The volume is 280cm³.
 60
p.88
1
A  bh
2    V  Al
1
2) a)   4  7  14  12 The volume is 168cm³. b) The volume is 30m³. c) The volume is 5.7mm³.
2
 168
 14
3) The area of each triangular face is 5.56cm². 4) A = 1cm² l = 6cm; A = 2cm² l = 3cm; A = 3cm² l =2cm;
A= 6cm² l =1cm
p.89
V  1200ml  1200cm3
1
A  10 15  75
2
5) The volume is 270cm³. 6) a) The volume is 1500cm³. b) V  Al                    The depth of water is
1200  75  l
l  16
16cm.
p.90
 2   r 2  2 r  h
1) a) Area of net  2    42  2    4 12 ; 402cm².
 402.1
p.91
1) b) 107cm² to the nearest square centimetre. c) The diameter = 2cm, so the radius = 1cm. The area is
 2   r 2  2 r  h
1407cm². 2) a) Surface area of cylinder  2    82  2    8 12 ; Surface area is 1005cm², to the nearest
 1005.3
square centimetre. b) The diameter of each circle is 9m, so the radius of each circle is 4.5m. The surface
area is 319m², to the nearest square metre. c) The surface area is 292cm², to the nearest square centimetre.
  r 2  2 r  h
3) a) The diameter is 15m, so the radius is 7.5m. Surface Area of cylinder    7.52  2    7.5 12 ; the
 506.6
surface area of the cylinder is 506.6m², to one decimal place.
p.92
3) b) The diameter is 4.8cm, so the radius is 2.4cm. The surface area of the cylinder is 364.9cm², to one
decimal place.
 2 r  h
4) The diameter is 1.8m, so the radius is 0.9m. Curved surface area of roller  2    1.8  2.6 . The area of
 29.4
the curved surface of the roller is 29.4m².
Circumference  2  r
Area  circumference  height                                     37.7  2  r
5) a) 377  circumference 10         ; the circumference = 37.7cm. b)      37.7                ; radius = 6cm.
r
37.7  circumference                                                   2
r  6.00
p.93
 area  height
1) a) volume of a cylinder  27.6  4         ; The volume is 110cm³, to the nearest cubic centimetre.
 110.4
b) The volume is 3807cm³, to the nearest cubic centimetre. c) The volume is 4775m³, to the nearest cubic
metre.
p.94
  r 2h
2) a) Volume    32  9 ; the volume is 254cm³, to the nearest cubic centimetre. b) The diameter is 18mm,
 254.47
so the radius is 9mm. The volume is 8906mm³, to the nearest cubic millimetre. c) The diameter is 48m, so
the radius is 24m. The volume is 16286m³, to the nearest cubic metre. 3) a) 5428.7cm³
b) Diameter = 16.8m, the radius = 8.4m; the volume is 1197.0m³. 4) Volume of cylinder A = 411.8cm³;
volume of cylinder B = 418.2cm³ so cylinder B has the greater volume by 6.4cm³. 5) a) 785.4cm³
b) Double the radius is 10cm; the new volume is 3141.6cm³, which is 4 times the original volume.
c) Double the height is 20cm; the new volume is 15708cm³, which is 2 times the original volume.
p.95
Net: A pattern that can be folded to make a solid
Polyhedron: An object whose faces are polygons
Regular prism: An object with 2 congruent faces that are regular polygons, and with remaining faces that
are rectangles
Regular pyramid: An object whose base is a regular polygon and whose other faces are triangles
Surface area: The total area of the surface of an object
Volume: The amount of space occupied by an object
p.96
1) A square with 6cmx6cmsides and 4 triangles with a base of 6cm and a height of 10cm
2) Figure B is not the net of a cube. 3) Net A = object 2; Net B = object 1; Net C = object 3
p.97
4) The area of the net is 208cm². 5) a) The area of one face of the cube is 384cm2  6  64cm2 ; the length
of one edge is 8cm. b) The volume of the cube is 512cm³
6) a) l = 8, w = 1 h = 1; l = 4, w = 2, h = 1; l = 2, w = 2, h = 2 b) 34cm², 28cm², 24cm²
p.98
7) The surface area is 200m². 8) The volume of the triangular prism is 1800m³; the volume of the
rectangular prism is 5400m³. The total volume is 7200m³. 9) a) The diameter is 16m, so the radius is 8m.
The volume of the tank is 603m³. b) The area to be painted is 352m².
p.99
One at a time – Sample answer: 1st step: you get RADIO or PATIO. Working backward from RATES,
words, such as RATED, require more than 2 steps to get to RADIO or PATIO.
cad, lam, lid; 4-letter words: lame, lace, male, dame, dime, mice, mace, dale, dial, dice, made; 5-letter
words: laced, lamed; 6-letter words: malice; 7-letter words: claimed, declaim, medical
p.100
3                7               3
 3  50          7  25        35
50               25               5
9                    1                  11
1) a)  0.06        b)  0.28        c)  0.6      2) a)36% = 0.35 =       b) 5% =0.05 =        c) 44% = 0.44 =
25                   20                  25
 6%              28%             60%
43
d) 86% = 0.86 =          3) a) 6: 6, 12, 18, 24, 30 b) 9: 9, 18, 27, 36, 45 c) 15: 15, 30, 45, 60,75
50
p.101
4) a) Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150,… Multiples of 25: 25, 50, 75, 100, 125,
150… Two common multiples of 15 and 25 are 75 and 150. b) 30, 60 c) 60, 120
3650                      5260             17  1000 g
        m                       L                                   75 1000m
5) a) 3650cm 100             b) 5260mL 1000 c)17kg                          d) 75km
 17000 g                 75000m
 36.5m                    5.26 L
p.103
6                    87                      48
1) a) 30% b) 7% c) 86% 2)a) 6% =                =0.06 b) 87% =         = 0.87 c) 48% =         =0.48
100                   100                     100
39.25 3925                                  80.5 805
3) a)                    0.3925  39.25% b)                   0.805  80.5%
100 10000                                   100 1000
48.5 485                               10.75 107.5 1075
4) a) 48.5%                    0.485 b) 10.75%                              0.1075
100 1000                                100    1000 10000
p.104
0.75      75                         0.4      4
5) a)0.5% b) 0.95% 6) a) 0.75%                          0.0075 b) 0.4%                  0.004
100 10000                            100 1000
10                     15                        17
7) a)        0.02  2% b)          0.075  7.5% c)          0.0425  4.25% 8) a) Explanations may vary
500                    200                        400
6      3                                            19
b)       or     c)0.06 or 6% 9) In the parking lot,         or 47.5% of the cars are hybrids.
100 50                                                40
1                                                     825
10) 8 % is the same as 8.25%. The interest rate is                  or 0.0825.
4                                                    10000
p.105
1) a) 125% b) 150% c) 200% 2) a) 175% = 1.75 b) 0.5% = 0.005 3) a) 2.3 b) 1.85 c) 3.24 d) 0.0074
e) 0.007 f) 0.0009
p.106
4) a) 50% b) 150% c) 250% d) 1% e) 0.5% f) 1.5% 5) a) 1cm x 1cm b)The new square has sides of length
2 cm. 6) a) i) 80 ii) 8 iii) 0.8 b) Each answer is one-tenth the size of the previous answer. c) i) 800 ii) 0.08
7) 0.0085 45412  386 runners completed the run in under 40 min. 0.0013 45412  59 runners
completed in under 34min.
120%of 0.3%of \$1000  1.2  0.003  \$1000  \$3.60
8)                                                         120.3% of \$1000 is the greater amount of money.
120.3%of \$1000  1.203  \$1000  \$1203
p.107
1) a) 40 b)120 c) 75 d) 200
p.108
28%  56          150%  35
1%  1.5                                                                                      4cm 1
2) a)               b) 1%  2        c) 1%  0.24 3) a) Increase = 4cm; Increase as a fraction =           ;
100%  150                                                                                    8cm 2
100%  200        100%  24
1                                            1
Percent Increase = 100%  50% b) Percent increase = 33 %. 4) a) Decrease = 8L; Decrease as
2                                            3
8L 1                            1
fraction =        ; Percent decrease = 100%  20% b) Percent decrease = 10%. 5) There were 600
40 L 5                           5
eggs in the batch.
p.109
6) a) \$12 b) \$6 7) a) The population of Quebec is about 7500000. b) About 40% of the population of
Yukon Territory lives in rural areas. 8) The new volume of water is 27L. 9) The result is 217.
10) a) The new production rate is 1008 items/week. b) The new unit cost is \$63.
p.110
0.14  \$288      0.14  \$36.50 0.14  \$149.99            1.15  \$2.40 1.15  \$3428 1.15  \$128.79
1) a)              b)                 c)                 2) a)               b)             c)
 \$40.32          \$5.11            \$21.00               \$2.76           \$3942.20      \$148.11
3) a) Discount: 0.3 \$92  \$27.60 ; Sale Price: \$92  \$27.60  \$64.40 b) Discount: 0.15  \$476  \$71.40
Sale Price: \$476  \$71.40  \$404.60
p.111
4) Discount: \$2.90; Sale Price: \$26.05; 13% tax: \$3.26; Total cost: \$29.31 b) Discount: \$59.75; Sale price:
\$179.25; 13% tax: \$22.41; Total cost: \$201.66 5) Increase in price: \$9.00; Total cost: \$45.00.
6) Assume \$100 sales. Find the selling price: Store A: 0.9  0.8  \$100  \$72 Store B: 0.75  \$100  \$75 ;
75%of \$256  0.75  \$256  \$192
Store A offers greater discount. 7) The original price is \$180. 8) a)
115%of \$192  1.15  \$192  \$220.80
115%of \$256  1.15  \$256  \$294.40
b)                                                ; Discounts are the same for both. 9) 113% is \$32.77.
75%of \$294.40  0.75  \$294.40  \$220.80
\$32.77
1% is:           \$0.29 ; 100% is: \$0.29 100  \$29.00 ; The fishing pole cost \$29.00 before sales tax.
113
p.112
1) a) 3:5 b) 7:6 c) 5:9
p.113
5                      7
2) a) 5:12,    , 41.67% b) 7:12,       , 58.33% 3) a) 3 b) 8:3 c) 3:11 4) a) 13:6 b) 13:19 c) 6:19
12                     12
p.114
5) a) 3:5 b) 5:3 c) 3:8 d) 5:8 e) 4:4 f) 2:1:2 6) a) Carrots b) carrots c) tomatoes to carrots to cauliflowers
d) cauliflowers to carrots e) tomatoes to total vegetables f) cauliflowers to total vegetables
7) a) red: green = 3: 5; yellow: red = 7:3; black: total pencil crayons = 1:16; yellow: total pencil crayons =
7:16; yellow: red: green = 7:3:5 b)10:16; 62.5% c) 5:4 d) red: green = 3:3; yellow: red = 5:3;
black: total pencil crayons = 1:12; yellow: total pencil crayons = 5:12; yellow: red: green = 5:3:3
p.116
1) a) 8:10, 12:15, and 16:20 b) 16:12, 8:6, 4:3 c) Three ratios equivalent to 16:28 are 4:7, 8:14, and 32:56.
2) a) Sample answer – 16:10:4, 24:14:6 b) Sample answer – 12:8:6, 6:4:3
p.117
 (10  2) : (4  2)           (6  3) : (15  3)
3) a) 10:4                        b) 6:15                      c) 1:2 d) 5:2 4) a) i) 5:6 = 15:18; 18:3 = 6:1;
 5: 2                         2:5
9:18 = 1:2; 4:20 = 8:40 ii) 1:8 = 2:16; 3:27 = 1:9; 12:36 = 1:3; 18:2 = 9:1 b) 12:36 and 1:3 are equivalent
because 12 12  1 and 36 12  3 5) sample answer – 12 cats and 15 dogs = 20 cats and 25 dogs; 8 cats
and 10 dogs = 16 cats and 20 dogs = 32 cats and 40 dogs 6) the poster is 60 cm wide; 3:2 = 90:60
p.119
1) a) 2 mixture A and 1 scoop; 2 and a half of mixture B and 1 scoop b) Mixture A is stronger because it
has less water for every scoop of powder.
p.120
2) a) 20 mice in each cage; 40 mice in total b) 8 white mice in A; 15 white mice in B; cage B contains
more white mice. 3) Red paint to white paint – A 4:3 B 7:5; A 20:15 B 21:15; 20  21 ; Mixture B will give
p.121
3:5                                                                2:3
4) Jan’s school  (3  3) : (5  3) ; 9 computers to 15 students; Karl’s school  (2  5) : (3  5) 10 computers
 9 :15                                                             10 :15
5:6
to 15 students; Karl’s school has more computers 5) Hamid  (5  11) : (6 11) 55 laps in 66 minutes;
 55 : 66
8 :11
9                 7
Amelia  (8  6) : (11  6) 48 laps in 66 minutes; Hamid jogs faster. 6)  0.6  60% ;               0.58  58%
15                12
 48 : 66
The Rebels have won 60% of their games, and the Sabres have won about 58% of their games. The Rebels
have the better record.
p.122
p : 4  9 :12
p 9

4 12
1) a) 6 b) 15 c) 3 2) a)                 b) c:12 = 5:6 c=10 c) 3:14 = t:70 t=15
p 9
4   4
4 12
p3
p.123
3) a) 8 b) 32 c) 2 d) 8 e) 6 f) 20 4) p:70 = 7:5; There are 98 purple cubes. 5) PQRS is 45cm.
l    1

6.4 4
l   1
6) 6.4        6.4 ; The actual length is 1.6 cm. 7) There are 24 boys and 4 teachers
6.4 4
l  1.6
p.125
1) a) 4km/h b) 3 books/ week c) 25 drops/min 2) a) 150km  2  75km ; Average driving speed = 75km/h
b) 180  3  60km ; The helicopter’s rate of travelling is 60km/h. c) Gerald’s rate of walking is 4km/h
3) a) rate: \$10.89 per kg b) Ratio: 3:7 c) rate: 620km per 6 h d) ratio: 5:4:6 e) rate: 23 points per 7 games
4) a) Maria charges \$5/h. b) Maria charges \$25. c) 10 h
p.126
\$3.95  5  \$0.79
5) a) 75km b) 75km/h 6)                      ; I can buy 15 bars. 7) a) \$525.00 Can b) \$168.30Can/day
\$0.79 15  \$11.85
c) \$38.05 US
p.127
\$3.96
1) a)         \$0.66 / bottle b) 70words / min c) \$141/week d) \$1.30/100mL
6
\$3.80                  \$6.30
2) a)         \$0.80 /100 g ;        \$0.84 /100 g ; ; First one is the better buy.
475 g                  750 g
\$5.39                     \$5.72
b)           \$1.40 /100mL;             \$1.43/100mL ; First one is the better buy.
385mL                     400mL
p.128
3) a) 60.5 km/h b) 62km/h c) 61.8km/h; Greatest average speed = 62km/h 4) Tasha 5) a) 14.5points/game
b) 377points 6) Twenty-four 500-mL bottles for \$9.18 is the better buy. 7) a) British Columbia
b) Saskatchewan c) Ontario d) British Columbia
p.129
Discount: The amount that a price is reduced due to a sale.
Sales tax: The tax based on a percent of the selling price that is set by the government. It is calculated at
the place of sale, collected by the retailer, and passed onto the government.
Ratio: A comparison between two quantities measured in the same unit.
Equivalent ratios: Ratios that are equal. For example, 8:6 and 4:3 are equivalent ratios because you can
multiply each term in the ratio 4:3 by 2 to get 8:6
Rate: A comparison of two quantities with different units. For example, 10km travelled in 2 h is a rate.
You compare distance (10km) with time (2h).
x 12
Proportion: A statement that two ratios are equal. For example,  . The value of an unknown x can
5 15
be found by solving the proportion.
Other mathematical words: percent increase, percent decrease, two-term ratio, three-term ratio, part-to-
whole ratio, part-to-part ratio, unit rate
p.130
15                   40                       875 87.5                            3     0.3
1) a) 0.15       15% b) 0.4          40% c) 0.875                   87.5% d) 0.003                0.3%
100                  100                      1000 100                           1000 100
20
2)      62.5%;62.5%  61% , so Analise’s class has a greater ratio of girls to students.
32
85                     0.7      7                        139                     412
3) a) 85%        0.85 b) 0.7%                 0.007 c) 139%            1.39 d) 412%         4.12
100                    100 1000                           100                     100
4                  8                     3                         15
4) a)  0.8  80% b)  1.6  160% c)               0.003  0.3% d)             0.0025  0.25%
5                  5                  1000                        6000
5) a) 1.15  2120  2438 ; the population was 2438 in 1905 b) 2438  2120  318 ; the increase in population
was 318.
p.131
6) a) 700kg b) 68cm c) 17500L 7) Four students completed this distance. 8) a) percent increase = 4%
b) Percent decrease = 17.5% 9) The volume of the water in the tank after 1 h is 1419L.
10) a) Before: \$112.50; After: \$126.00 b) Before: \$1365; After: \$1528.80 c) Before: \$5.78; After: \$6.47
11) The regular price is \$878 12) \$56 1.3 0.85  \$61.88 ; the selling price is \$61.88.
p.132
13) a) 6:5 b) 12:6 c) 5:18 14) a) 2 : 5  (2  2) : (5  2)  4 :10 ; 2 : 5  (2  3) : (5  3)  6 :15 ;
2 : 5  (2  4) : (5  4)  8 : 20 b) 36 :18  (36 18) : (18 18)  2 :1 ; 36 :18 : (36  2) : (18  2)  72 : 36 ;
36 :18  (36  6) : (18  6)  6 : 3
p.133
15) a) 25 :15  (25  5) : (15  5)  5 : 3 b) 28 : 35  (28  7) : (35  7)  4 : 5
c) 45: 72  (45  9) : (72  9)  5:8 16) 3: 7  (3  5) : (7  5)  15 : 35 ; 2 : 5  (2  7) : (5  7)  14 : 35 ; Class
8B has more globes. 17) s:45=3:5; 27 students sailed. 18) 75 cubes are red.
p.134
19) a) 1 cm on the map represents 6000000cm of actual distance; The actual distance is
1248km  124800000cm
8.7  6000000cm  52200000cm  522km . b)                                                   ; The distance between the
124800000cm  6000000  20.8
two towns on the map is 20.8cm. 20) a) The van travels at an average speed of 70km/h. b) Mikki jogs at an
average speed of 6 km/h. 21) 3.8L of detergent for \$5.78 is the better buy. 22) It will take 43.75h to travel
1050km. 23) The United Kingdom, with a population density of about 245 people/km 2
p.135
Date Palindrome: 20022002,
Sample Answers: 17022071 (Feb 17, 2071), 14022041 (Feb 14, 2041)
Sample Answer: 21022012 (Feb 21, 2012)
Word Scramble:
MULTIPLY, SUBTRACT, VARIABLE, PERCENT, FRACTION, SOLVE, INTEGER
Four Fours:
4  (4  4)  4  2,(4  4  4)  4  3
p.136
1) T(0,2), I (2,3), G(4,5), E(7,4), R(6,0) 2) A(0,5), B(2,4), E(4,3), R(5,0) 3) a) 6 bracelets b) 5h
p.137
4) a) Add 2 to both sides. Divide both sides by 3. b) Subtract 3 from both sides. Multiply both sides by 2.
p.139
1) a) x+2=3; x=1 b) 5=2x+3; x=1 c)-3x+5= -4; x=3 2) Models may vary a) x+3=9; x=6 b) 3=2x-5; x=4
c) 4x+3 = 11; x=2 d) 14=5x+4; x=2
p.140
3) Models may vary a) a+4 =5; a = 1 b) 6 = c – 4; c=10 c) y – 2 = 4; y = 6 d) 5= x+3; x = 2
4) Models may vary a) 2v=6; v=3 b) 4n = - 8; n= - 2 c) 5=5y; y = 1 d) – 6=3r; r = -2
p.141
5) Models may vary a) 3x+2 = 11; x = 3 b) -5=5+2y; y = -5 6) a) 2n+5=7 b) Models may vary; n =1
c) Answers may vary. The number is 1. 7) Models may vary; 3n – 1 =11; n =4
p. 142
1) a) 3x+1 = -5; x = -2 b) 5 = -2x – 1; x= -3
p.143
6 m  5  7
6m  5  5  7  5 3c  2  2
2) Models may vary a) 2y – 1 = 7; y = 4 b) -4 = 2+3a; a = - 2 3) a) 6m  12           b)    4
c
6m 12                   3

6     6
m  2
1
c) 2+5y=2; y = 0 d) 4 – 3x = -5; x=3 4) a) y = 4 b) x  1 5) a) 3n – 4 = 14; n = 6 b) 2n+12 =44; n= 16
2
p.145
c
 3
6
n          16  5 y
c                     14
1) a ) division b) multiplication c) addition d) multiplication 2) a)  6  3  6 b) 2         c)       16
6                              y
n  28            5
c  18
b

3
a
9             b                              21
d)       4 3) a)  7 b) b = 21 c) Left side  ; Right side = 7; There were 21 basketballs altogether.
3                               3
a  36
7
p. 146
w
6 2
3
w
66  26
3
y
j                                                              w                     1   3
4) a)  22 b) j = 88 c0 There were 88 jellybeans in the bag. 5) a)  4                   b)       4
4                                                               3
y  16
w
 3  4  3
3
w  12
x                    c
 2  10 4   8
c) 5             d) 10
x  40         c  40
p.147
j
6) w = 12 7) a) Let j represent the number of cookies that were in the jar to start.  4  9 b) j = 25
4
c) There were 25 cookies in the jar to start.
p.148
1) a) 4(c+5) = 4c+20 b) 4(a - 3) = 4a – 9
p.149
2) a) 2(y+5) = 2y +10 b) 3(w – 1) = 3w – 3 3) a) 3(u – 6) = 3u – 18 b) 2(5 – q) = 10+ 2q c) 5(r+1) =5r+5
d) 7(3 – p) = 21 – 7p 4) a) – 6(a – 7) = -6a+42 b) 4(-5 – w) = -20 – 4w c) – 2(x – 20) = -2x+40
d) – 1(b+8) = - b – 8 5) Yes, she made an error; 3(y – 2) = 3y – 6 6) a) 5(6+4); 5  6  5  4 b) 50; 50
c) 5(6  4)  5  6  5  4
p.150
4(r  3)  8
4r  12  8
4r  12  12  8  12
1) a) 4r  20               b) 15= 3(p – 7) ; p = 12
4r 20

4     4
r 5
p. 151
2
1) c) m= - 5 d) x = 6        e) r = -12 f) h = 2 2) a) Sample Answer : C b) c – 4 c) 2(c – 4)
5
d) 2(c - 4)=12; c =10 e) Brittany had 10 cookies to start.
p. 153
1) a) y = -10, -9, -8, -7, -6, -5, -4 b) y = 17, 16, 15, 14, 13, 12, 11 c) y = 9, 6, 3, 0, -3, -6, -9
2) a) x = -3, -2, -1, 0, 1, 2, 3; y = 1, 2, 3, 4, 5, 6, 7 b) x = -3, -2, -1, 0, 1, 2, 3; y = 8, 6, 4, 2, 0, 2, 4
c) x = -3, -2, -1, 0, 1, 2, 3; y = 8, 7, 6, 5, 4, 3, 2
p. 154
33  6r  3
33  3  6r  3  3
3) a) 33 = 6r + 3 b) 30  6r                 4) a) (2, 15) b) (-4, -21) 5) a) (2,14) b) (3,18) c) (12, 54) d) (-4,-10)
30 6r

6    6
5r
6) a) n = 1, 2, 3, 4, 5; c = 4, 8, 12, 16, 20 b) 7 hamburgers would have to be sold
p. 155
1) x = 0, 1, 2, 3, 4; y = 2, 4, 6, 8, 10
p. 156
1) b) When x increases by 1, y increases by 2. The y values start at 2. 2) b) When x increases by 2, y
decreases by 4. The y values start at 5. 3) a) x = -1, 0,1, 2, 3, 4; y = 5, 2, -1, -4, -7, -10
p. 157
4) a) x = 0, 1, 2, 3, 4, 5; y = -4, -1, 2, 5, 8, 11 6) a) n = 1, 2, 3, 4, 5, 6, 7; C= 90, 130, 170, 210, 250, 290,
C  50  40n
410  50  40n
410  50  50  40n  50
330 b) Substitute 410 for c in the equation and solve 360  40n                         ; 9 people could go on the
360 40n

40     40
9n
trip with \$410.
p.158
Distributive property: Multiplying a number by a sum of two numbers is the same as multiplying the first
number by each number in the sum and then finding the sum of the products. For example, 5(a+b) = 5a+5b
Opposite operation: an oper4ation that “undoes” a given operation. For example, multiplication and
division are opposite operations, and addition and subtraction are opposite operations.
Algebra tiles: tiles that can be used to represent numbers and variables. For example, a small white square
tile represents +1, a small black square tile represents -1, and a white rectangular tile represents x.
Ordered pair: Two numbers in order; on a coordinate grid, the first number is the horizontal coordinate of
a point, and the second number is the vertical coordinate of the point. For example, (2, 4) is an ordered
pair.
Table of values: A way of reorganizing a relation in a table; ordered pairs can be read from a table of
values
Linear relation: A relation that has a straight – line graph. For example, y = 2x-3 is a linear relation.
Sample answers: expand, discrete data, isolate, solve
p. 159
4 y  7  13
4 y  7  7  13  7
1) 2x + 1 = -3; x = - 2 2) Models may vary; c = - 3 3) a) 4 y  20                 b) m= - 7
4 y 20

4     4
y 5
p.160
4) Yes, Maria made an error; p = - 1 5) a) let w represent the number of weeks; 147= 74+12w
147  75  12w                                                                             t
4
147  75  75  12 w  75                                                                 2
t
b) 72  12 w                   c) In 6 weeks, Rajinder will have 147 hockey cards. 6) a)  2  4  2
2
72 12w
                                                                                     t 8
12 12
6w
w
 4  2
3
w
 4  4  2  4
3
w
b)  6                 c) x = 15 7) a) 6(v – 3); 6v – 18 b) -9 (3+p); -27 – 9p c) –1(-2+w); 2–w
3
w
 3  6  3
3
w  18
p. 161
8) a) 3(t-4) = iv) 3t – 12 b) -3 (t+4) = ii) -3t – 12 c) 3 (t+4) = i) 3t + 12 d) –3(t – 4) = iii) -3t + 12
5(a  3)  20
5a  15  20
5a  15  15  20  15
1
9) a ) 5a  35                 b) n = 2 c) y =  d) x = 0 10) a) y = 0, 1, 2, 3, 4 b) y = 9, 7, 5, 3, 1
4
5a 35

5     5
a7
11) a) (2, 5) b) (-2, 11) c) (4, 13)
p. 162
12) a) (10, 100) b) When n increases by 1, p increases by 10. The first p value is 0. 13) b) Its graph is a
straight line
p.163
Dartboard design
Region 1:  (1) 2   square units; Region 2:  (2) 2   (1) 2  3 square units; Region 3:  (3)2   (2) 2  5
square units; Region 4:  (4)2   (3)2  7 square units; Sample answer: Start at  square units. Add 2
1              3                  5              7
square units each time. Region 1:      ; Region 2:     ; Region 3 :      ; Region 4:     ;
16             16                 16             16
The area of the 5th region would be 9 square units. Sample answers: The new probabilities in order of the
1 3 5 7               9
regions are:     , , , , and
25 25 25 25          25
p.165
1) a)
Item                         Amount (5)                   Sector Angle                  Percent
Clothing                     100                           100                          100
 360o  180o               100o  50%
200                          200
Books                        30                             30                           30
 360o  54o                100o  15%
200                          200
Sports Equipment             50                             50                           50
 360o  90o                100o  25%
200                          200
Moview                       20                             20                            20
 360o  36o                100o  10%
200                          200
Total                        200                           360o                         100%
p.166
2) a)
Spinner 2                Spinner 2              Spinner 2
2                        3                      4
Spinner 1              1                      1,2                      1,3                    1,4
Spinner 1              5                      5,2                      5,3                    5,4
2 1
b) Two outcomes have 2 odd numbers: 1,3 and 5,3; Probability = 
6 3
2 1
3) b) There are 2 outcomes: T2 , T4, Probability = 
8 4
p.168
1) a) Most popular: Lemon; Least popular: Vanilla b) 6+14+11+8=39 c) It is easier to use the length of the
bars in the bar graph to read data and compare data values. 2) c) It is easier to draw the bar graph. It is
more difficult to draw the many simples and half of a simple for the pictograph.
p.169
3) a) 2006 b) 1996 c) The team would have more than 16 wins in the next year because the line graph
shows and upward trend over the years. d) No. Since the data change over time, people would not be
interested in knowing parts of the whole. 4) a) The data are parts of a whole. The sizes of sectors can be
compared to make conclusions. b) 29%+33%=62% c) Yes, you could use a bar graph, but it is not as
appropriate as a circle graph, which is best a showing parts of a whole.
p.170
5) a) Circle graph = iii) Percent of each math topic on the final exam b) Line graph = i) Change in your
height over time c) Double bar graph = ii) Number of shots by each starting player of the girls’ and boys’
basketball teams d) Pictograph = v) Number of food items donated by 4 grade 8 classes e) Bar graph = iv)
Number of students in a Grade 8 class from 5 different areas of origin. 6) a) I can use a circle graph or a
bar graph since the data do not change over time. With the circle graph, I can compare parts of a whole.
b) A line graph and a double bar graph are not appropriate because the data do not change over time and
there is only one set of data.
p.172
1) Sample Answers: a) The bar for Boys because it is much wider and the type for “Boys” is larger. b)
Make the 2 bars the same width and use the same type size for the 2 labels “Girls” and “Boys”. 2) a) The
sector for “ride” is separated from the rest of the graph and it has the largest type size. b) Keep all sectors
within the circle and keep the type size consistent for all similar labels. c) Burton is most popular. The
sector representing Burton has the largest sector angle, and 35% is the greatest percent.
p.173
3) Sample Answers: a) Hayden’s graph appears to show a greater increase in marks. b) Vanessa: 90% -
75% = 15%; Hayden: 80% - 68%=12% c) The scale on the vertical axis of Hayden’s graph starts at 48%,
which exaggerates the increase in marks. d) To make affair comparison, make the scales on the vertical
axis of the two graphs the same. e) Hayden is more consistent from term to term with a smaller range of
marks between 64% and 80%.
p.174
4) Sample Answers: a) I would use Hayden’s graph because he appears to have improved greatly based on
the steepness of the lines on his graph. b) Vanessa: 90% - 70% = 20%; Hayden: 80% - 64% = 16%
c) The result is different from the impression that the graphs give me. So, my choice was incorrect.
5) a) 0 – 1 city b) Sample Answer: The width of the symbol for 10 or more is about the same width as the
row of symbols form 2 – 3 cities, which represents 8 students. c) Sample Answer: I would agree with
Marie because her number is based on the key of the pictograph – 1 symbol represents 2 students.
d) Sample Answers: Make all symbols the same size and line up all the rows on the left edge for easy
counting of symbols and comparing lengths of rows.
p.176
1      1         1      1 1 1
1) a)    b) c) 1;         d)   e) Sample Answer: The outcome of each coin showing heads is
2      2         4      2 2 4
1                  4 1
independent of the other coin. So, P(2 heads) = P(heads)  P (heads) =         2) a) P(red) =     
4                 12 3
3 1                    1                             1 1 1
b) P(3) =       c) P(R/3) =         ; P(R/3) = P(red)  P(3) =  
12 4                   12                             3 4 12
p.177
1              1                      1 1 1                     2 1
3) a) P(green) = b) P(1) = c) P(green and 1) =                   4) a) P(odd) = 
3              3                      3 6 18                    4 2
1 1 1                                              1 1 1
b) P(I and 4) = P(I)  P(4) =               c) P(vowel and 2) = P(vowel)  P(2) =  
6 4 24                                             2 4 8
1 1 1
5) a) P(red 4 and white 5) = P(red 4)  P(white 5) =             b) P(5 and even)=P(5)  P(even) =
6 6 36
1 1 1                                      1 1 1                                                         2 1
        c) P(3 and 3) = P(3)  P(3)=             d) The square numbers are 1 and 4. P(1 or 4) =  ;
6 2 12                                     6 6 36                                                        6 3
4 2                                1 2 2
P(2,3,5,or 6) =  ; P(square, non-square) =  
6 3                                 3 3 9
p.178
3                4 2                                              3 2 3
6) a) P(dotted) =       ; P(solid) =     ; P(dotted, solid) = P(dotted)  P(solid) =      
10                10 5                                             10 5 25
2                                           2 2 4
b) P(solid) = ; P(solid, solid) = P(solid)  P(solid) =             c) P(not solid) = P(dotted or striped) =
5                                           5 5 25
3 3        6 3                                                             3 3 9                       3
   ; P(not solid, not solid) = P(not solid)  P(not solid) =                   7) a) P(red) =    ;
10 10 10 5                                                                  5 5 25                     10
2 1                                                  3 1 3                        5 1
P(green) =       ; P(red, then green) = P(red)  P(green)=                  b) P(yellow) =       ;
10 5                                                 10 5 50                      10 2
1 1 1                                                      1
P(yellow, yellow) = P(yellow)  P(yellow) =   c) Sample Answer: P(1st ball)  P(2nd ball) =                    ;
2 2 4                                                     10
1                1         1 1 1
Since P(yellow) = , P(green) = , and   , the outcome is either a green ball followed by a
2                5         2 5 10
yellow ball or a yellow ball followed by a green ball.
p.180
1                   1                   1                      1 1 1 1
1) a) i) P(heads) =      ii) P(heads) =     iii) P(blue) =     b) 1 c) P(H/H/B) =                d) 3
2                   2                   4                      2 2 4 16
1 1 3 3
e) P(H/H/R or B or Y) = P(H)  P(H)  P(R or B or Y) =                      2) a) 1; There are 8 possible
2 2 4 16
1                                          1 1 1 1
outcomes. P(H/H/H) = b) P(H/H/H) = P(H)  P(H)  P(H) =   
8                                          2 2 2 8
p.181
1                   1 1 1 1                      1                   1 1 1         1
3) a) P(2,3,5,7,or 13) = ; P(3 primes) =    b) P(4 or 9) = ; P(3 squares) =   
2                   2 2 2 8                      6                   6 6 6 216
c) The probability is 0 since 17 is a prime number that has no factors other than itself and 1, and there are
no cards labelled 1 or 17.
3                   12                       10 2
4) a) P(classical) =       ; P(country) =      ; P(classic rock) =       ; P(classical/country/classic rock) =
25                   25                       25 5
3 12 2         72                                      2 2 12 48
                b) P(2 classic rock/country)=                    5) a) P(red/jack/spades)=P(red) 
25 25 5 3125                                            5 5 25 625
1 1 1         1                                          1 1 1           1
P(jack)  P(spades) =                    b) P(red ace/black/ace of clubs) =         
2 13 4 104                                               26 2 52 2704
3                                   1 1 3         3
c) P(not diamonds) = P(spades or hearts or clubs) = ; P(ace./hearts/not diamonds) =                  
4                                  52 4 4 832
p.182
Appropriate graph: graph with certain features that enables questions to be answered or information to be
drawn easily from the displayed data. For example, a circle graph shows the parts of a whole better than a
line graph does.
Misrepresentation of data: display of data in a way that creates a false impression, leading to incorrect
conclusions or decisions to be made. For example, a wider bar in a bar graph creates the impression that
the data value is greater than it actually is.
Discrete data: data that can be counted and do not change over time. For example, the numbers of
students in several classes are discrete data. The heights of a person are not discrete data since the height of
the person changes over time.
Possible outcomes: possible results of an experiment or action. For example, when a 6 – sided die with a
number on each face is rolled. There are 6 possible outcomes, even if some numbers on the die are the
same.
Probability of an event: the number of outcomes of an event written as a fraction of all possible
outcomes. For example, there are 6 possible outcomes for rolling a regular die. The probability of rolling a
1
5 is .
6
Independent events: two events in which the outcomes of one do not affect the outcomes of the other. For
example, the outcomes of tossing a coin will not affect the outcomes of rolling a die. Tossing a coin and
rolling a die are independent events.
Sample answers: bar graph, line graph, circle graph, pictograph, double bar graph, scale, trend, tree
diagram.
p.183
1) Sample Answers: The line graph is the best since the data change over time. The circle graph is the least
appropriate as the data are not parts of a whole. The bar graph could work but it may not show the trend as
well as a line graph. 2) a) Sample Answer: The circle graph is easier to use. Ms. Papas can simply write the
percent as a fraction. The bar graph requires an extra step of finding the total. b) Sample Answer: The
height of the bar for D in the bar graph provides the answer. The circle graph does not have any actual
number that can answer the question.
p.184
3) a) 8 students b) 20 students c) Sample Answer: The 2 large symbols for the Toronto Blue Jays give the
false impression that the team is more popular than the Boston Red Sox. 4) a) Sample Answer: The total
times for the 3 players seem to be very close. B) Sample Answer: The total time for Wesley seems to be
much less than those for Hartley and Brandon. C) Sample answer: The second graph has its vertical scale
note starting at 0 and uses a larger scale that exaggerates the difference among the penalty times.
p.185
6) Sample Answer: The events in part c) are not independent events. Removing a second card from the
remaining deck of 51 cards depends on what the first card removed from the original deck of 52 cards was.
p.186
3 1 3
7) a) P(red, then blue) = P(red)  P(blue) =            b) P(yellow, then red) = P(yellow)  P(red) =
8 8 64
1 3 3                                1 1 1                                1 1 1
        c) P(blue, then blue) =            8) a) P(odd)  P(tails) =   b) P(5 or 6)  P(heads) =
2 8 16                               8 8 64                               2 2 4
1 1 1                                                  1 1 1 1
  9) a) i) P(H/H/T) = P(H)  P(H)  P(T) =    ii) P(T/T/T) = P(T)  P(T)  P(T) =
3 2 6                                                  2 2 2 8
1 1 1 1
   b) Sample answer: There is only 1 out of 8 possible outcomes that satisfies each event.
2 2 2 8
1 1 1             1                                     5 21 21 2205
10) a) P(A)  P(F)  P(G) =                        b) P(vowel)  P(con)  P(con) =            
26 26 26 17576                                          26 26 26 17576
5 5 5            125
c) P(vowel)  P(vowel)  P(vowel) =                 
26 26 26 17576
p.187
Penny Patterns: 45; n(2n – 1) Mental squares: 85; 8  9  72 ; 7225; No, the product of two 2-digit
numbers is difficult to find using mental math.

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