A1.1 Homework 1 Answers - Cambridge Essentialsessentials.cambridge.org/media/CEMKS3_E7_A1_1_WS_HANS3.pdf · Cambridge Essentials Mathematics Extension 7 A2.2 Homework Original material

Cambridge Essentials Mathematics Extension 7 A1.1 Homework 1

Original material © Cambridge University Press 2008 1

A1.1 Homework 1 Answers

1 a ☺ = 25 b ☼ = 8 c ♦ = 96 d ∇ = 15

2 a 11 b 4 c 6 d 24

3 ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ = 10 × ▲ = 10 × 7 = 70

So 90 – (▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲) = 90 – 70 = 20

4 a 21 b 7 c 60 d 25

5 ● = 6 and □ = 2 (or ● = –2 and □ = –6)

6 a ◊ + 6 b ◊ ÷ 2 c ◊ × 3 d ◊ × 43 or ◊ –

4◊

7 a p = 3 b t = 10 c f = 7 d k = 18 e m = 12

8 a 26 b 12 c 16 d 10 e 80 f 15

9 Four different value for a and b such that a × b = 72.

10 a seven less than x b two more than x c three times x

d a quarter of x e x more than eight (or 8 more than x or the sum of 8 and x)

f x less than six g double x h one more than double x

11 a n – 2 b 5 × n c n + 10 d n ÷ 2 e 2 × n

f n – 7 g 12 × n h n + 6 i 10 – n

12 a ii c = 13 iii c = b – 3 (or equivalent) iv a = b + c + 3 (or equivalent)

b ii Brad’s age and Carla’s age add up to 29.

iii Ahmed is twice as old as Brad.

iv Ahmed is 19 years older than Carla.




1 a 13, 19, 25, 31, 37, 43 Add 6 b 65, 53, 41, 29, 17 Subtract 12

c 14, 23, 32, 41, 50, 59 Add 9 d 3.5, 7, 10.5, 14, 17.5, 21, 24.5 Add 3.5

2 99, 86, 73, 60, 47

3 112, 56, 28, 14, 7

4 a Pattern 2 has 5 circles; Pattern 3 has 7 circles.

b

9 circles

11 circles

c 3, 5, 7, 9, 11

d Add 2

5 The 5th term is 6 × 5 = 30 The 10th term is 6 × 10 = 60

The 100th term is 6 × 100 = 600 The nth term is 6 × n

6 a 9, 10, 11, 12, 13 b 21, 22, 23, 24, 25

c 11, 15, 19, 23, 27 d 94, 88, 82, 76, 70

7 21

8 a The number of hexagons in Pattern 4 is 1 + 4 × 3 = 13

b The number of hexagons in Pattern 10 is 1 + 10 × 3 = 31

c The number of hexagons in Pattern n is 1 + n × 3

9 a 7n b 4n + 1

c 8n + 2 d 75 – 5n

10 a 5n + 1 arrows

b 101 arrows

Cambridge Essentials Mathematics Extension 7 A1.2 Homework


A1.2 Homework Answers

1 a 2 13

8 → 11 + → 19

17 28

b n n – 7

25 → 7 − → 18

n + 4 n – 3

c 3 45

5 → 15 × → 75

n 15n

d 30 6

50 → 5 ÷ → 10

15n 3n

2

3 a 3 20

0.5 → 2 + → 4 × → 10 n 4(n + 2) or 4 × n + 8

b 14 1

2n → 2 ÷ → 6 − → n – 6 10n 5n – 6

4 a 8 → 4 − → 3 × → 6 + → 18

b 8 → 3 × → 6 + → 4 − → 26 or 8 → 3 × → 4 − → 6 + → 26

c 8 → 6 + → 3 × → 4 − → 38

5 a 1 1

2→ 3 × → 3 ÷ → 2

3 3

b 1 4

2→ 3 × → 1+ → 7

3 10

c 1 1.5

2→ 3 × → 2 ÷ → 3

3 4.5

5.275.155.65.2

5.2

251340

→+→



6 2 8 2 8

5 → 4 × → 20 14 → 6 + → 20

9 36 9 15

7 x → 12 ÷ → 4 × → 3x

8 x → 2 × → 1 − → 1 + → 2x or x → 1 + → 1 − → 2 × → 2x

9 x → 6 + → 6 − → 2 ÷ → 4 × → 2 ÷ → x

or x → 2 ÷ → 6 − → 6 + → 4 × → 2 ÷ → x

10 a x 1 2 3 4 5 6

y 5 8 11 14 17 20

b

11 n → 4n – 2




1 a 13 b 1 c 30 d 23

e 11 f 3.5 g 8 h –2

i 25 j 12 k 25 l 25

2 a 9 b 12 c 12 d –3

e 27 f 9 g –1 h 36

i 10 j 6 k 2 l 5

3 a 9 b 3 c 18 d 0

e 12 f 9 g 21 h 27

i 5 j 9 k 5 l 8

m 54 n 108 o –13 p 45

4 a x + 13 b x + 4 c x + 20 d 4x

e 2x f –3x g 5x h x + 3y

i 2x + 3y j 7xyz k 5k l –4x + 2m + 7

m 3x2 + x + 6 n 4k2 – 10 o 3p2 + 10p – 7

5 a Divide n by 3 and then add 6.

b Add 6 to n and then multiply by 2.

c Add 6 to n and then divide by 3.

d Double n, then add 6 and then divide by 3.




1 a P = 3x + 1 b P = 2x + 16 c P = 4p + 10

d P = 4m + 7 e P = 12y f P = 6t + 4

g P = 2x + 8y + 10 h P = 10x + 8 i P = 6x + 6y

2 a

b c

3 a g = 5 b g = 25 or 2.5 c g =

51 or 0.2 d y = 7.8

4 a i Pupils’ predictions.

ii

b l = c × s

c i l = 20 ii l = 60 iii s = 4

5 a 100 °C = 212 °F b 10 °C = 50 °F c 0 °C = 32 °F

x + 2x + 2

2x + 3

2x + 3

xx

2x + 5

2x + 5

2x 2x

x + 5

x + 5




1 a x + 6 b 7x c 10x d x – 1 e 4x – 3

f 25x+ g 2(x + 5) h 5x + 2 i

74−x

2 a x → 3 × → 2 + → b x → 2 + → 3 × → c x → 3 × → 2 + →

d m → 9 − → 2 ÷ → e y → 3 ÷ → 1 + → f y → 1 + → 3 ÷ →

g d → 4 + → 5 × → h m → 4 × → 5 + → i k → 2 × → 7 − →

3 a x = 4 b x = 3

4 a Subtract 6 b Divide by 7 c Multiply by 3 d Add 2

e + 1 f ÷ 4 g × 6 h + 11

i ÷ 100 j + 5.6 k – 2.1 l × 4.8

5 a x ← 5 × ← 1 + ← 7 b x = 40

6 a i x → 3 × → 8 − → 4 b i t → 7 × → 8 + → 15

ii x ← 3 ÷ ← 8 + ← 4 ii t ← 7 ÷ ← 8 − ← 15

iii x = 4 iii t = 1

c i d → 2 + → 3 × → 9 d i m → 5 + → 6 × → 72

ii d ← 2 − ← 3 ÷ ← 9 ii m ← 5 − ← 6 ÷ ← 72

iii d = 1 iii m = 7

e i p → 2 × → 4 − → 11 f i c → 4 − → 2 × → 3

ii p ← 2 ÷ ← 4 + ← 11 ii c ← 4 + ← 2 ÷ ← 3

iii p = 7.5 iii c = 5.5



6 g i t → 5 ÷ → 1 − → 6 h i k → 51 − → 9 ÷ → 11

ii t ← 5 × ← 1 + ← 6 ii k ← 15 + ← 9 × ← 11

iii t = 35 iii k = 114

i i y→ 2 × → 1 + → 3 ÷ → 5

ii y ← 2 ÷ ← 1 − ← 3 × ← 5

iii y = 7

7 a She is not correct. b 5x + 1 = 7 means x → 5 ÷ → 1 + → 7

x ← 5 × ← 1 − ← 7

x = 30

5

1+x = 7 means x → 1 + → 5 ÷ → 7

x ← 1 − ← 5 × ← 7

x = 34

8

1

22

972

=

=

=+

d

d

db

7

426

25176

=

=

=−

z

z

zc

25

55

415

=

=

=−

q

q

qd

5.8

172

1342

=

=

=−

g

g

ge

2

84

19114

=

=

=+

m

m

mf

15

53

943

=

=

=+

t

t

tg

7

61

24)1(4

=

=−

=−

x

x

xh

4

73

49)3(7

=

=+

=+

p

p

pi

3

93

813

42

13

=

=

=−

=−

y

y

y

yj




1 a 3(n – 5)

b Start with x, add 9 and divide the answer by 4.

c 6

2 a 3n is n multiplied by 3. n + 3 is n added to 3.

b i 3n → 3 ÷ → n ii n + 3 → 3 − → n

3 b 3x + 4 → 4 − ⎯→⎯3

x

3 × → x b 2(x – 3) → 2 ÷ ⎯⎯→⎯ −3x 3 + → x

d 7

6x → 7 × ⎯→⎯ x6 6 ÷ → x or 7

6x → 6÷ ⎯→⎯7x

7 × → x

4 a x = 48 b x = 8 c x = 242

d x = 12 e x = 20 f x = 7

5 a (x – 1 cm) + (x + 6 cm) + 2x = 41 cm ⇒ 4x + 5 cm = 41 cm

b x = 9 cm

c 8 cm, 15 cm, 18 cm

6 a n + (n + 5) + 21 (n + 5) = 40 ⇒ 2.5n + 7.5 = 40 or 5n + 15 = 80

b n = 13

c Zac has 9 points.

7 a n + (n + 2) + (n + 4) + (n + 6) = 88 ⇒ 4n + 12 = 88

b n = 19

8 a 2x + 3x + (3x − 40°) + (x + 70°) + (x + 90°) = 540°

10x + 120° = 540°

b x = 42°

c The largest angle is x + 90° = 132°.




1 You can add numbers in any order and you will get the same answers.

For example, 2 + 5 = 7 and 5 + 2 = 7.

This is not true with subtraction: 8 – 6 = 2, but 6 – 8 = –2.

2 m = x – n and n = x – m are true.

3 a 3xy b 3mx + 2my c 3 + 6kt

4 a 7x + 14y + 21 b 13m – 12

c 3a + 11b d 11x + 23

5 a 6(2a + 3b) b 12a + 18b

6 a c = 7 b x = 4

c y = 1 d x = 2

7 a x = 2 b x = 18

8 a n = 6 b




1

2 a

b

c

d

3 a

b

4 y = 2

4+x or y = 22+

x

5 a

y = 3(x –2)

b

x → 5x – 1

c

y = 42x+

x → 2x – 3 x → 3x – 7x → x + 1 x → 2x – 3




1 a y = 3 b x = –2 c x = 4 d y = –2

2 a (2, 5) b (–1, 10) c (4, 4)

d (10, 10) e (6, 7) f (19, 17)

3 a x = –10

b y = –9

c i y = x + 2 ii y = x – 1 iii y = x + 3 iv y = x – 4




1 a x 0 1 2 3 4

y 1 3 5 7 9

c i (4, 9) ii (4, 5) iii (2, 5)

b

2 a x 0 1 2 3 4

y –3 –1 1 3 5

c i (1.5, 0) ii (0, –3)

b

3 a x 0 1 2 3

y –2 1 4 7

d (2, 4)

b, c




1 a i £88 ii £68 iii £34 iv £96

b i 3.7 m ii 1.5 m iii 7.4 m iv 5.3 m

2 a x 0 1 2 3 4

y –5 –2 1 4 7

b i x = 2 ii x = 4 iii x = 3

iv x = 2.5 v x = 1 vi x = 0.5

c 3x – 4.5 = –3

3x – 5 = –3.5 (subtracting 0.5 from both sides)

x = 0.5 (from the graph of y = 3x – 5).




1 a 6ab b 4a + 6b

2 a 5x + 7

b Any expressions with a mean of 3x

c 5x + 1

3 a n + 3 b 2n + 5

4 a a + 2b

b i ah ii 21 bh iii ah + bh

5 a 3b – 4 b 3a + 2

6 a n + 2

b n + (n + 2) + (n + 4) + (n + 6) = 4n + 12

c n + 3

7 a Q (n + 5, 3n)

b R (n + 7, 3n – 2)

c T (–n – 2, 3n)

8 (4m – 2, 7n + 4)




1 P = 6(a – 2b)

2 C = 100x – 35n

3 a Number of tables 1 2 3 4 5

Number of children 4 6 8 10 12

b 22

c c = 2t + 2

4 a 14 b 18 c 38 d 4n + 6

5 a b Pattern number 1 2 3 4 5

Number of white tiles 8 10 12 14 16

c 26 d Pattern 17 e 2n + 6

6 a 31, 38 b 66 c 7n – 4

7 a y = 5(x + 3) b y = 2x – 4

c y = 3x – 5 d y = 5

1−x

8 a x → 2 − → 3 ÷ → y

b i x → 2 + → 3 −× → 7 + → y

ii y = 1 – 3x y = → 3 −× → 1 + → y




1 a p = 318 b y =

43 c m =

214

d q = 109 e t =

413 f a =

522

2 a x = 1.5 b m = 1.3 c n = 2.25

d q = 1.4 e a = 0.8 f c = 4.75

3 a x = 20° b x = 25°

4 a 6a + 5° = 38°

a = 5.5°

b 8a – 7° + 115° = 180°

a = 9°

5 x + x + 5 + x + 10 + x + 15 = 130

x = 25

6 Let April have n chocolate eggs.

Then Melanie has 2n, Peter (2n – 5), and Jack (2n – 6).

So n + 2n + 2n – 5 + 2n – 6 = 38

n = 7

April has 7, Melanie 14, Peter 9 and Jack 8.




1 n + (n + 1) + (n + 7) + (n + 8) = 124

4n + 16 = 124

n = 27 so the numbers in the square are 27,, 28, 34 and 35.

2 a x = 5 b x = 14 c x = 8

3 a x = 3 b p = 7 c c = 431

4 a m = 40 b t = 15 c a = 20

5 a 4

73 +n = 16 ⇒ n = 19

b When 4

73 +n = 100, n = 131. Therefore there are 130 terms less than 100.

c If 4

73 +n = 20 then n = 3124 .

For a term to be in the sequence, it must have a value of n that is a whole number.




1 a 1.5 km b 5 minutes c 7.5 minutes d 30 minutes

e 2.5 km f 6.5 km g 10 minutes h 50 minutes

2 C, because the ball is thrown up at a high speed, gradually slows down, stops at the

highest point, then speeds up as it falls. So the speed starts high, slows down to zero, then

increases again.

3 a i G The depth of water increases less and less quickly as the beaker gets wider towards the top.

ii E The depth of water increases at a steady rate because the beaker has a constant width. iii C The depth of water increases less quickly as the beaker widens and then

increases more quickly as the beaker narrows again towards the top.

b

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A1.1 Homework 1 Answers - Cambridge Essentialsessentials.cambridge.org/media/CEMKS3_E7_A1_1_WS_HANS3.pdf · Cambridge Essentials Mathematics Extension 7 A2.2 Homework Original material