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Cambridge Essentials Mathematics Extension 7 GM1.1 Homework 1
Original Material © Cambridge University Press 2008 1
GM1.1 Homework 1 Answers
1 a 6.3 cm b 2.2 cm c 6.7 cm
2 a Accurate drawings
b i 5.7 cm ii 5.7 cm iii 5.8 cm iv 5.8 cm
c If drawn accurately: i Triangle CDE is an isosceles triangle as ED = EC.
ii Triangle JKL is an equilateral triangle as JK = JL = KL.
3 a 14 cm b 9 mm c 4 m d 21 m e 143 cm
4 Yes. Draw a line 14.8 cm long. The 8.7 cm and 9.4 cm sides will meet above the line.
5 a 15.6 cm b 102 mm c 4.8 cm d 5
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Cambridge Essentials Mathematics Extension 7 GM1.1 Homework 2
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GM1.1 Homework 2 Answers
1 a 18 cm b 42 cm
2 48 cm
3 a 76 cm b 13.4 m
4 18 cm
5 If the side lengths are a, a and b, then a + a + b = 2a + b = 18 cm, so a < 9 cm.
The sum of any two sides must be greater than the third side, so 2a > b.
b = 18 cm − 2a, so 2a > (18 cm − 2a) and 4a > 18.
Therefore a > 4.5 cm. There are four possibilities:
(a, a, b) = (5 cm, 5 cm, 8 cm); (6 cm, 6 cm, 6 cm); (7 cm, 7 cm, 4 cm); (8 cm, 8 cm, 2cm)
6 50 cm
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Cambridge Essentials Mathematics Extension 7 GM1.2 Homework 1
Original Material © Cambridge University Press 2008 1
GM1.2 Homework 1 Answers
1 a 13.5 cm2 b 3.6 cm2 or 360 mm2
c 2.16 m2 or 21 600 cm2
2 a 144 cm2 b 48 cm
3 a 72 mm2 b 0.72 cm2
4 100 cm2
5 25 cm2
6 a 33 cm2 b 77 m2
c 224 mm2 d 129 cm2
7 a D
b The diagonal of a square is longer than the side of a square. The shape with the greatest perimeter is made by drawing as many diagonals of squares as possible. Here is one example.
Many other shapes will have the same perimeter.
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Cambridge Essentials Mathematics Extension 7 GM1.2 Homework 2
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GM1.2 Homework 2 Answers
1 a 99 m2 b 139 m2 c 196 m2
2 a 12 cm2 b 84 mm2 c 71.5 m2
3 a 26 cm2 b 121.5 cm2
4 a 40 cm2 b 93 cm2
5 Approximately 75 km2
6 31.5 cm2
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Cambridge Essentials Mathematics Extension 7 GM2.1 Homework 1
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GM2.1 Homework 1 Answers
1 a i 120° ii 70° iii 90° iv 310° v 38° vi 154°
b i obtuse ii acute iii right angle iv reflex v acute vi obtuse
2 a 127°
More pupils measured the angle as 127° than any other size and two pupils measured it only 1° above or below 127°. It is difficult to measure accurately to the exact number of degrees using a protractor.
b Toby must have used the wrong scale on the protractor, because 180° – 52° gives 128°, which is very nearly the correct size of 127°.
3 a 7 b 150°
4 a i 132° ii 48° iii 73°
iv 59° v 59°
b 180°
c 180°. They add up to 180° or 2 right angles.
d They are the same.
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Cambridge Essentials Mathematics Extension 7 GM2.1 Homework 2
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GM2.1 Homework 2 Answers
1 a =133° b = 144° c = 58° d = 122°
e = 122° f = 41° g = 139° h = 62°
i = 62° j = 56° k = 304° l = 65°
m = 115° n = 30°
2 a = 34° b = 112° c = 56° d = 56°
e = 27° f = 27° g = 29° h = 61°
i = 29° j = 61° k = 54° m = 56°
n = 34° p = 85°
3 a = 15°
4 x = 12° y = 72° z = 48°
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Cambridge Essentials Mathematics Extension 7 GM2.2 Homework
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GM2.2 Homework Answers
1 a CF, DE, AH
b DC, DE, AB, AH, EF, CF, BG, HG
2 a Equilateral b 3 c Pupil’s construction
d A rhombus
3 a It is a trapezium.
b It is a kite.
4
5 a Pattern with exactly one line of symmetry.
b Pattern with exactly four lines of symmetry.
6 a False b True c False d True e False
7 a
b (2, –2)
c (–4, 4)
0
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Cambridge Essentials Mathematics Extension 7 GM3.1 Homework 1
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GM3.1 Homework 1 Answers
1 a 500 litres b 5 ml c 8 litres d 250 ml
2 a 145 g b 40 g c 77 kg d 1.5 kg e 4 kg
3 Pupils’ own lists of items.
4 Pupils’ own lists of items.
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Cambridge Essentials Mathematics Extension 7 GM3.1 Homework 2
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GM3.1 Homework 2 Answers
1 a 5 b 20 c 35 d 34 e 38 f 1.636
g 2.6 h 3.1 i 3.9 j 1.624 k 1.632 l 1.636
2 44 mph
3 a 14 cm = 140 mm b 35 mm = 3.5 cm c 165 cm = 1.65 m
d 5.7 m = 570 cm e 3.28 m = 328 cm f 0.6 m = 60 cm
4 a 350 ml = 0.35 litres b 58 cl = 580 ml c 593 ml = 59.3 cl
d 5.7 litres = 5700 ml e 0.8 litres = 80 cl f 285 cl = 2.85 litres
5 a 685 g = 0.685 kg b 5.4 kg = 5400 g c 70 g = 0.07 kg
6 Yes, the bus can go under the bridge. 12 feet 10 in = 3.95 m to 3 s.f.
7 £10 806
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Cambridge Essentials Mathematics Extension 7 GM3.2 Homework 1
Original Material © Cambridge University Press 2008 1
GM3.2 Homework 1 Answers
1 a A, D
b B
c B, C
d D
e A
2 AC = 4.5 cm, angle BAC = 86°
3 a i 7.5 cm
ii 3.1 cm
b Area = 5 × 3.1 = 16 cm2 to the nearest cm2.
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Cambridge Essentials Mathematics Extension 7 GM3.2 Homework 2
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GM3.2 Homework 2 Answers
1 b i AB = 11.7 cm
ii AC = 17.2 cm
iii XY = 10.0 cm
2 ML = 4.9 cm, MN = 3.3 cm
3 Angle PQR = 77°
4
The two circles don’t intersect. There is no point that is 4.8 cm from U and 5.4 cm from V. This means that the triangle can’t be drawn.
U V
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Cambridge Essentials Mathematics Extension 7 GM3.3 Homework 1
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GM3.3 Homework 1 Answers
1 a
b D
c F
d 4 cm × 3 cm × 2 cm
e 52 cm2
2 a Triangular prism
b i 6.5 cm ii 6 cm iii 6 cm
c 165 cm2
d i 10 cm × 6 cm × 2.5 cm ii 200 cm2
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Cambridge Essentials Mathematics Extension 7 GM3.3 Homework 2
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GM3.3 Homework 2 Answers
1 a Trapezium
b V = 8, F = 6, E = 12
V + F – E = 8 + 6 – 12
= 14 – 12
= 2
2 a 72 cm
b 180 cm2
3 a There are only two possible nets for a tetrahedron.
b If this were a net for a square-based pyramid, the edges labelled p and q in the
diagram below would meet.
However they are different lengths, so this is not a net for a square-based pyramid.
p
q
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Cambridge Essentials Mathematics Extension 7 GM3.4 Homework
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GM3.4 Homework Answers
1 a Triangular prism
b Cube
c Cuboid
d Tetrahedron
e Square-based pyramid
2
3
4 No. There are three places where two faces meet, so there are six covered faces.
The surface area is given by 4 × 6 cm2 − 3 × 2 × 1 cm2 = 24 cm2 – 6 cm2 = 18 cm2.
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Cambridge Essentials Mathematics Extension 7 GM4.1 Homework
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GM4.1 Homework Answers
1 a
b
c
d
2 b, c
c y = x
d C(2, 6), C′(6, 2). The coordinates use the same numbers but they are reversed (x→ y and y → x).
x
8
7
6
5
4
3
2
1
y
1 2 3 4 5 6 7 8
B
C
D
0
B′
A
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Cambridge Essentials Mathematics Extension 7 GM4.1 Homework
Original Material © Cambridge University Press 2008 2
3
4 a (5, –4)
b (–8, 5)
c (–2, –6)
5 a x = 2 b y = –1 c (–5, –3)
6 Pupil’s own answer.
–8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8
8
7
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6
–7
–8
x
y
y = –x
0
A B
CD
A'B'
D'C'
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Cambridge Essentials Mathematics Extension 7 GM4.2 Homework
Original Material © Cambridge University Press 2008 1
GM4.2 Homework Answers
1 a
b
c
2
rotation of 90° clockwise rotation of 180° rotation of 90° anticlockwise
3
5
4
3
2
1
–1
–2
–3
–4
–5
A
y
–5 –4 –3 –2 –1 1 2 3 4 50
B
C
x
B A ×
A
B×
A
B
×
×P
×P
× P
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Cambridge Essentials Mathematics Extension 7 GM4.2 Homework
Original Material © Cambridge University Press 2008 2
4 a
parallelogram
b
parallelogram
c
rectangle
5 a
b P′(–2, 3)
c Rotation through 90° clockwise with centre (–1, 1)
Q
P R
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Cambridge Essentials Mathematics Extension 7 GM4.3 Homework
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GM4.3 Homework Answers
1 a, b
c A′(1, –3), B′(3, –1), C′(5, –3), D′(3, –5) d 6 squares to the left and 7 squares up.
2 a 3 squares to the right and 5 squares up.
b B′(2, 6), C′(5, 7)
3 a 5 squares to the left and 7 squares down.
b (–4, –9)
c (8, 6)
4 a, b, c c ⎟⎟
⎠
⎞⎜⎜⎝
⎛−−
65
5 Pupil’s own pattern.
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Cambridge Essentials Mathematics Extension 7 GM5.1 Homework
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GM5.1 Homework Answers
1 a 3 b 4 c 1 d 6
2 a
b There are many possibilities; this is an example.
3 There are several possibilities; these are some examples.
a i
ii
b i
ii
4 Number of lines of symmetry
0 1 2 3 4 1 C
2 F 3 D A
Order of rotational symmetry
4 B E 5 a 6 right
b Rotation of 180° about any of the points marked with a cross in this diagram.
6 a i Rotation of 90° clockwise about (0, 0) ii Translation 6 squares right.
b There are many possible answers including:
i rotation of 180° about (0, 0) followed by translation 6 squares right.
ii rotation of 90° clockwise about (–2, –2) followed by translation 4 squares up.
iii rotation of 90° clockwise about (2, –2) followed by translation 4 squares left.
× × × ××
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Cambridge Essentials Mathematics Extension 7 GM5.2 Homework 1
Original Material © Cambridge University Press 2008 1
GM5.2 Homework 1 Answers
1
Size of large cube
No. of small cubes with no yellow faces
No. of small cubes with 1 yellow face
No. of small cubes with 2 yellow faces
No. of small cubes with 3 yellow faces
Total no. of small cubes
3 × 3 × 3 1 6 12 8 27
4 × 4 × 4 8 24 24 8 64
5 × 5 × 5 27 54 36 8 125
6 × 6 × 6 64 96 48 8 216
7 × 7 × 7 125 150 60 8 343
⋮ ⋮ ⋮ ⋮ ⋮ ⋮
2
n × n × n (n – 2)3 6(n – 2)2 12(n – 2) 8 n3 3
Any kite with diagonals a and b can be divided along the line of symmetry into two equal triangles. Dividing along AC, the area of each triangle is
21 × base × height
= 21 × b ×
2a = 1
4ab
Since the kite is made of two such triangles the area of the kite is
21 ab or half the product
of the diagonals.
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Cambridge Essentials Mathematics Extension 7 GM5.2 Homework 2
Original Material © Cambridge University Press 2008 1
GM5.2 Homework 2 Answers
1 w = 33° w + 27° = 360° ÷ 6 because the shape has rotational symmetry of order 6.
so w + 27° = 60°
2 No, Jason cannot draw the triangle. When the 12 cm side is drawn at 30° to the base line,
the other end is more than 5 cm above the base line.
If you reflect the triangle in its base line it forms
a triangle in which angles x and y must be equal.
But the third angle in the triangle is 60°,
so x = y = 60°. This means that the triangle is an
equilateral triangle and the vertical side is
therefore 12 cm. Two lines of 5 cm each are
together less than 12 cm, so the triangle is
impossible to draw.
3 A square be divided into 4, 6, 7, 8, 9 … n squares.
Once you have any number of squares, say n, you can make n + 3 squares by dividing one
of the squares into 4.
Since you can make 6, 7, or 8 squares, you can therefore make any numbers of squares
above that.
You cannot make 2 or 3 squares, because one small square would have to have at least 2
of its corners at the corners of the big square. Then it would be the same size as the big
square.
For 5 squares you would have to have a different square in each corner of the big square,
but this cannot leave one single space for 1 more square. So you cannot make 5 squares.