year 8 maths

630
8 a b c
9 a b c
10
Faces (F) Vertices (V) Edges (E)
6
5
5
7
4
11
8
4
6
7
4
11
12
8
9
12
6
20
d
10 a 4 and 4 b 3 and 3 c 0 and 2
11 a b
12 a i no ii no
b isosceles trapezium
13 a 9 b 3 c 4
d 1 e infinite f infinite
Exercise 6G
e
1 a vertices b seven c congruent
d seven
e octagonal
2 a 24 b 7 c 8
3 a 6, 8, 12 b 5, 6, 9 c 7, 7, 12
4 A, cube; B, pyramid; F, rectangular prism;
G, tetrahedron; H, hexahedron
5 a hexahedron b tetrahedron
c pentahedron
e nonahedron
g undecahedron
d heptahedron
f decahedron
h dodecahedron
6 a 8 b 6 c 4 d 5
e 7 f 9 g 10 h 11
7 a triangular prism b pentagonal prism
c square prism
8 a rectangular pyramid b heptagonal pyramid
9 a
c triangular pyramid
Solid
Faces
(F)
Vertices
(V)
Edges
(E)
F + V
cube 6 8 12 14
square
pyramid 5 5 8 10
tetrahedron 4 4 6 8
octahedron 8 6 12 14
b F + V is 2 more than E.
11 a 26 b 11 c 28
12 a true b false c true d true
e false (sphere) f true g false
13 a yes b yes c no d yes e yes
14 F = 12, V = 12 and E = 24 so Euler’s rule does not apply.
15 a hexahedron, rectangular prism
b undecahedron, decagonal pyramid
16 a V = E − F + 2 b F = E − V + 2
17 a V = 8, E = 14, F = 8 and V + F − 2 = E
b V = 16, E = 24, F = 10 and V + F − 2 = E
c V = 6, E = 12, F = 8 and V + F − 2 = E
18 a true b true
19 a i convex ii non-convex iii non-convex
b Answers will vary.
Puzzles and challenges
1 a b
2 a b
3 a 30 b 150
4 125°
5 a yes
Net
b no
6 180. Find each angle in the interior pentagon in terms of
a, b, c, d and/or e. Then solve the sum equal to 540° for a
pentagon.
Multiple-choice questions
1 D 2 A 3 E 4 C 5 C
6 B 7 B 8 C 9 D 10 C
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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