Download S2 Book answers

Section 1.2
1.
a) 8
b) 5
c) 9
3.
Answers to 1 d.p.: a) 3.3 b) 4.1 c) 5.7 d) 8.6
4.
a) 23
b) 82 or 43
5.
a) 11
b) 9 or 9
6.
a) 2
8
b) 3
7.
a) 64
b) 8
c) 3
d) 1000 e) 1
10. a) 35
b) 77
c) 66
d) 94
e) 53
f) 75
12. a) c11
b) d6
c) z7
d) t14
e) r6
f) u7
4
d) 121 e) 10
f) 81
g) 1
h) 6
i) 49
j) 5
c) 103 d) 104 e) 106
c) 2 or 2
4
c) 7 × 8
3
d) 7
3
d) 5 × 2
g) 61 (or 6)
h) 40 (or 1)
Section 1.3
1.
a) 1, 2, 4, 7, 8, 14, 28, 56
b) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
c) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
2.
a) 6
b) 9
c) 6
3.
a) 60
b) 75
c) 210 d) 363
4.
a) 2 × 3 × 5
5.
a) 411
6.
7.
d) 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
d) 48
b) 2 × 3 × 7
c) 23 × 32
d) 32 × 11
b) 86
c) 66
d) 46
e) 39
g) 5
a) 6
b) 10
c) 30
d) 2
a) 210
b) 300
c) 1620
f) 75
h) 23
d) 30 800
Section 2.2
1.
p = 100°,
2.
a) i) An exterior angle
ii) An interior angle
b) 75°
63°
3.
96°
82°
iii) An exterior angle
a) x = 91°, interior angles in quadrilateral sum to 360°;
y = 89°, angles on a straight line add up to 180°.
b) s = 55°, t = 55°, angles in a triangle sum to 180° and isosceles triangle has two equal angles
u = 125°, angles on a straight line add up to 180°, or exterior angle of a triangle equals the sum of
the two interior opposite angles.
c) q = 75°, angles on a straight line add up to 180°; p = 47°, angles in a triangle sum to 180°, or
exterior angle of a triangle equals the sum of the two interior opposite angles.
d) d = 88°, interior angles in quadrilateral sum to 360°;
e = 82°, angles on a straight line add up to 180°.
4.
a) Angle x is equal to angle a because they are alternate angles.
b) Angle y is equal to angle c because they are alternate angles.
x + b + y = 180° because they lie on a straight line.
c) Since x = a and y = c, a + b + c = x + b + y. This proves that angles in a triangle sum to 180°
Section 2.4
1. Yes – a square is a rectangle with all sides of equal length.
2. C
3.
Number of
pairs of
parallel sides
Lines of symmetry
0
1
0
kite,
arrowhea
d
1
isosceles
trapezium
2
parallelogram
2
4
Rectangle
rhombus
square
4. b) Parallelogram
5. a) Rhombus
b) A, C
6. a = 60°, b = 30°, c = 60°
7. x = z = 140°, y = 40°
8. a) TUV = 45°
b) TVU = 105°
9. ABE = 180°  90°  72° = 18°.
CBD = 180°  90°  56° = 34°.
(Angles in a triangle sum to 180°.)
c) SVU = 150°
ABC = 90°, therefore EBD = 90°  18°  34° = 38°.
There are other valid approaches.
10 a) FAB = 65° (Opposite angles in a parallelogram are equal.)
b) ABE = 70° (Alternate angles are equal.)
c) CBE = 110° (Angles on a straight line sum to 180°.)|
d) BCD = 115° (Angles in a quadrilateral sum to 360°.)
There are other valid approaches.
Section 2.6
1.
a) Use the formula with n = 4
b) Use the formula with n = 5
2.
a) Divide the sum of the interior angles (found in exercise 1b) by 5.
b) Subtract the interior angle from 180°.
3.
a) i) 360°
ii) 540°
iii) 720°
b) 1440°
4.
The interior and exterior angles lie on a straight line. Angles that form a straight line sum to 180°.
5.
b) Your sum should be close to 360°
c) Your sum should be close to 360°
d) Sum of exterior angles is always 360°.
6.
a) 60°
b) 120°
7.
Regular
polygon
equilateral
triangle
square
regular
pentagon
regular
hexagon
regular
octagon
Number
of sides
Sum of
interior
angles
Size of each
interior angle
Sum of
exterior
angles
Size of each
exterior angle
3
180°
60°
360°
120°
4
360°
90°
360°
90°
5
540°
108°
360°
72°
6
720°
120°
360°
60°
8
1080°
135°
360°
45°
8.
a) (n − 2) × 180°
b) Interior 157.5°, exterior 22.5°
9.
a) i) 20
b)15
ii) 162°
10. No. The sum of the interior angles in a multiple of 180° and 1300 is not divisible by 180.
11. a) 135°
b) 45°
c) 22.5°
Section 3.1
1
a)
i) 0.5 ii) 1
iii) 0
b) Unlikely
2
a) Yes, there are 13 red cards left in the pack.
b) Sabrina
3
a) A
b) Any design with half the squares containing a sun
4
a) Quarter-finals
b) Semi-finals
5
a) No
b) Round 1
6
Bag A
7
a) Tirone
29
19
b) No, because 833 = 0.03481… is greater than 548 0.03467…
Section 3.2
1 a)
D
2 a)
1
4
3 a)
1
2
b) A
c) B
1
2
c) 3
b)
b)
1
8
1
c)
1
2
4 Some possible answers are:
a)
Over 40/under 20
multiple of 8/multiple of 3
even/product of two odd numbers
b)
Over 40
multiple of 3
equal chance
d) C
d)
d)
1
4
1
6
e)
1
16
c)
2
3
2
, 3 , both
1
2
5 a)
b)
i)
1
9
ii)
5
9
6 Greater than 5 (fourteen of the outcomes are greater than 5 and only six are less
than 5).