IGCSE Maths Practice Book Answers

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers 1

Number and language

●● Exercises 1.1–1.5 1 83, 89, 97 2 (a) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 (b) 1, 2, 4, 5, 10, 20, 40, 50, 100, 200 3 (a) 52 (b) 24 × 3 4 (a) 17 (b) 36 5 (a) 48 (b) 48

●● Exercise 1.6 1 (a) Rational (b) Rational (c) Irrational (d) Rational (e) Rational (f) Irrational (g) Rational

2

2 (a) Student’s shapes e.g. cuboid, triangular prism, pyramid 3 (a) Student’s shapes likely to include a circle/ semicircle 4 (a) Student’s shapes e.g. sphere, cone, cylinder

●● Exercises 1.7–1.9 1 (a) 0.9

(b) 

7 3

2 (a) -6

(b) 

5 2

●● Exercise 1.10 1 (a) 570 m 2 1700 m

(b)  1080 m

Accuracy

●● Exercises 2.1–2.3 1 (a) 50 2 (a) 5.0 3 (a) 20

(b) 1300 (b) 18.0 (b) 0.043

(c)  525 000 (c) 0.00 (c) 3.05

2 (a) 16.4, 16.6 (c) 484.7575, 495.2475 (e) 0.04, 0.16 3 27.72, 29.13 (2 d.p.)

(b)  28.4375, 29.6475 (d)  9.3, 9.5

●● Exercise 2.7

●● Exercise 2.4

1 18.7975, 19.6875 km² 2 (a) 0.17%, 1.7% (b) A percentage error of 0.5 out of 30 is more significant than a percentage error of 0.5 out of 303 3 11.5 km, 12.070 125 km

Answers may vary 1 (a) ≈ 10 (b)  ≈ 3 2 ≈ 119 cm²

●● Exercise 2.5 1 23.8 m 2 70.5 × 11.5 3 715 000 ÷ 1550

●● Exercise 2.6 1 (a) 355.25, 395.25 (c) 4497.75, 5502.75 (e) 1.98, 2.03 (2 d.p.)

(b)  2741.25, 2891.25 (d)  0.5 , 1

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1

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers

Calculations and order

3

●● Exercises 3.1–3.2

●● Exercises 3.3–3.5

1 –2

–1

0

1

2

3

4

5

2 12.1  t  15.8 3 0.055, 0.5, 0.505, 0.550, 5.005, 5.500

Integers, fractions, decimals and percentages

4

●● Exercises 4.1–4.4

●● Exercise 4.5

1 (a) 12 (b) 64 (c) 45.5

1 (a) 380.75

33 5 2 3 (a) 4 9

(b) 

53 17

(b) 

2 15 5

4 (a) 3.45

(b) 7.76

2 (a)

(c) 0.3125

0.065

(d) 3

308%

25 i

1 (a) 2

66.6% i

19 18

(f)

(b)  -2

1 30

(b) 5.375

38 99

-

17 30



23 90

=

(b)  1

139 450

127 990

105.5%

Further percentages

●● Exercises 5.1–5.3 1 (a) 25% (c) 37.5% 2 (a) 50 (c) 50 (e) $120 3 (a) 95%

(b) 60% (d) 87.5% (b)  150 (d) $390 (f) 35 (b) 5% (ii) 80%





(ii) 60%

(c) (i) 2

i

5 3 (b) (i) 5 3

●● Exercise 5.4 1 (a) 225 2 (a) 135 3 (a) $38 4 £428 640 5 670 625

4 (a) (i) 4

(ii)  66.6%

5 Ahmet = 30%, Jo = 45%, Anna = 25% 6 77.7% (1 d.p.) 7 (a) $4.32 (b) 56.8% 2

23 72

●● Exercise 4.11

i

(e) 0.6

(b) 

3 (a) 3. 4

(b) 0.45 45% 13 200 2

17 30 22 2 (a) 45 i

1 (a) 1

3 4

(c)

(b) 961.54

●● Exercises 4.6–4.10

5 (a) 75%

5

1 (a) 234 (b) 9 (c) -3 2 (a) no brackets needed (b) 15 ÷ (3 + 2 ÷ 2) = 3.75 (c) 15 ÷ (3 + 2) ÷ 2 = 1.5 3 1

(b) 150 (b) 105 (b) 262

(c) 875 (c) 5

●● Exercise 5.5 1 (a) $450 (c) 340% 2 260 3 225 4 4 cm

(b) $620 (d) 160%

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Chapter 6 Ratio and proportion

Ratio and proportion

6

●● Exercise 6.1

12 25

1 50 2 240

1 2

●● Exercises 6.2–6.4 5 9

1 (a)

(ii)  18 hrs

(b) (i) 6 people 14 4 hrs 15 54 hours quicker

(ii)  2 people

(b)  1 kg

2 (a) 3 : 2 (b)  3 2.5 kg 4 384 g 5 30° 6 64 cm and 36 cm 7 (a) 21

13 (a) (i) 22 hrs

1 4

2 5



●● Exercise 6.5

(c) 18

1 (a) 400 2 (a) 187.5 3 (a) 80

litres of petrol, 3

3 4

litres of oil

●● Exercise 6.6

2 3

(b) 1416 ml 8 $750, $850, $900 9 48°, 192° 10 $480 11 Speed (km/h) 60 Time (h)

1.5

(b) 625 (b) 187.5 (b) 30

30

22.5

120

90

240

3

4

0.75

1

0.375

1 27 × 18 cm 2 5 : 2 3 (a) (i) 288 cm² (ii)  648 cm² (b) 9 : 4 4 (a) (i) 156.25 cm³ (ii)  10 000 cm³ (b) 64 : 1

Indices and standard form

7

●● Exercises 7.1–7.4 3

2

3

1 (a) 2 × 3 × 4 (c) 32 × 43 × 53 2 (a) 196 (c) 25 088 3 (a) 117 × 612 (c) 124 4 (a) 94 (c) 28 5 (a) 92 (c) 16-1 1 4

4

●● Exercise 7.7 5

2

(b) 2 × 4 × 5 (d) 2 × 74 × 112 (b)  3 359 232 (d)  8 870 472 (b)  511 × 611 (d) 133 (b) 1710 (d) 86 (b) 7 (d) 3-2

6 (a)

(b) 0.7

(c) 0.03 7 (a) 4 (c) 4 8 (a) 3 (c) 6 9 (a) 6 (c) 1.5

(d) 1 (b) 2 (d) 0.1 (b) 4 (d) 0 (b)  2 (d) 7

●● Exercises 7.5–7.6 1 (a) 3.7 × 107 2 8.64 × 103 3 (a) 6.75 × 103 km 4 (a) 4.5 × 10-5 5 (a) −5

(b) 4.63 × 108 (b) 4.2 × 104 km (b) 3.67 × 10-10 (b) 5

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1 2 3 4 5 6 7 8

7 15 5 100 7 5 3 12

●● Exercise 7.8 1

1 4

2 1 3

1 2

4

1 8

5

1 2

6 1 7 11 8 1 9

1 32

10

1 = 37

1 2187

3

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers

8

Money and finance

●● Exercise 8.1 1 (a) €57.69

(b) €6.17

●● Exercise 8.5 (c)  NZ $93.75

●● Exercises 8.2–8.4 1 (a) €103.50 (b) €84.87 2 (a) Option 1: $1275 extra Option 2: $4180 extra (b) e.g. The customer may not be able to afford the initial deposit 3 142% 4 5%

9

●● Exercise 8.6 1 $162 067.50 2 $66 550 3 $518.40 4 14.9% 5 20.6% 6 (a) 1.25 ≠ 2

1 14 52

2 05 51 3 (a) 126 hrs 40 mins

(b) Monday (c) 2310

Set notation and Venn diagrams

●● Exercise 10.1 1 (a) Capital cities (b) Student’s two capital cities 2 (a) Currencies (b) Student’s two currencies 3 Student’s coordinates which satisfy y = x2 + x e.g (1, 2) 4 (a) Numbers from −1 up to but not including 7 (b) Student’s numbers

●● Exercise 10.4 1 (a)

P

1 (a) B = {2,3,5,7} (b) C = {1,4,9} 2 (a) {a, b, c}, {a, b}, {a, c}, {b, c}, {a}, {b}, {c}, {ø} (b) {a, b}, {a, c}, {b, c}, {a}, {b}, {c}

g

e a

Q o

i r

m d

n h

u

R

(b) (i) {b,r,i,g,h,t,o,n,d,u,a,m} (ii) {r} (iii) {h,t,o,n} 2 (a)

●● Exercise 10.3 1 Girl’s names not beginning with the letter A 2 (a) (i) even numbers up to 30 (ii) multiples of 3 up to 30 (iii) multiples of 5 up to 30 (b) (i) 6, 12, 18, 24, 30 (ii) 3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30 (iii) 30 (iv) 5, 15, 25 3 (a) (i) 2, 3, 4, 5, 6, 7, 8, 9, 10, 12 (ii) 3, 4, 9, 12 (b) Z

t

b

c

●● Exercise 10.2

A

S

6

10

11

3

(b) (i) 6

(ii) 3

●● Exercise 10.5 1 (a) (i) z = 1 (b) 14

4

(b)  4 years

Time

●● Exercise 9.1

10

1 1% 2 7 years

(ii)  x = 6

(iii)  y = 0

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Topic 1 Exam focus

Topic 1 Exam focus 1 Rational as 81 = 9 2 (a) 225.5 cm² (b)  15.02 cm 3 (a) 16

(b) 224

(c) 250 4 27 : 8

(d) 35

25

5 (a)

1 25



(b) 1

(c)  59.93 cm

7 2.6652 × 10-26 kg 8 (a) $14 000 (b)  $10 500 (c) $9500 (d)  $21 632 9 (a) (i) 2, 3, 7, 8 (ii) 2, 3, 7 (iii) 6, 9 (b) No, as 3 is an element in R but not P

6 (a) (i) 0.707 (3 d.p.) (ii) 1.837 (3 d.p.) (iii) 9.882 (3 d.p.) (b) 4.6

11

Algebraic representation and manipulation

●● Exercises 11.1–11.3 1 -5x - 20 2 -3y + 6 3 8ab + 16a 4 12c - 48 5 -6a3 + 9a2b 6 48 7 15a + 5 8 10x + 14 9 7x + 6y 10 6x - 23y 11 p - 21 12 6q + 6r + 29qr 13 -4xy + 6xz - 4yz + 4y2 14 3a + 8ab 15 p - pq 16 a2 + 12a + 32 17 b2 - 9 18 c2 - 18c + 81 19 1 - 2m + m2 20 jk - jm + k2 - km

●● Exercise 11.4 1 2 3 4 5

3(a + 2b) -14(c + 2d) 21x(2x - y2) m(m2 - mn - n2) Cannot be factorised

●● Exercise 11.5 1 2 3 4 5

0 20 -12 24 -124

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●● Exercise 11.6 1 c = d - ab 2 b = d + c a 3 m = 8(2r - 3) 4 q = r(p - s) p 5 q = r+s

●● Exercise 11.7 1 2 3 4 5

4d2 - 9 9e2 - 42e + 49 4f2 - 9g2 16 - 25h2 6x2 + x - 1

●● Exercise 11.8 1 2 3 4 5

(a + b)(c + 1) (3d + 4e)(c + 1) (f - 6)(g - 4) (p - 2r)(p - 2q) (4m + 11)(4m + 11n)

●● Exercise 11.9 1 2 3 4

(4m - 11n)(4m + 11n) (x3 - y3)(x3 + y3) (3a2 - 12b2)(3a2 + 12b2) (9m - 4n)(9m + 4n)

●● Exercise 11.10 1 (17 - 16)(17 + 16) = 33 2 (32 - 1)(32 + 1) = 8 × 10 = 80 3 (98 - 2)(98 + 2) = 96 × 100 = 9600 5

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers

●● Exercise 11.11 1 2 3 4 5 6 7 8 9

V pr 2 (b) 10.0 cm (1 d.p.) 5 (a) h =

(a + 3)(a + 2) (b - 5)(b + 2) (c - 8)(c - 2) (d - 9)(d - 9) or (d - 9)2 (2e + 1)(e + 1) (3f - 2)(f + 1) (2g + 1)(g - 1) (3h + 2)(3h - 2) (j + 2k)(j + 2k) or (j + 2k)2

●● Exercise 11.15 1 2 3 4 5

●● Exercises 11.12–11.13 1 a =

pr 2 xq

2 a =

6 m

2

2

3

2p b 4 a = t

4

( )

2 5 a = 3b 2c

●● Exercises 11.16–11.17 1

( )

bt 3 a = 2r

2

5

●● Exercise 11.14

4a 15de 6 15 4xy

3a + 4b 12 c 12 5a 6 -5e 21 10f 9

●● Exercise 11.18

C 2p (b) r = 3.0 cm (1 d.p.) A 2 (a) r = p (b) r = 5.0 cm (1 d.p.) A 3 (a) p = l (b) p = 6 cm A -r 4 (a) h = 2pr (b) 7.0 cm (1 d.p.) 1 (a) r =

1 2 3 4 5

3p + 5 ( p + 3)( p - 1) a b a a +1 a a+3 a

Algebraic indices

12

●● Exercises 12.1–12.2 8

9

2

1 (a) a × b × c (c) m 2 (a) a2c8 (c) b

7

7

(b)  p × q × r (d)  a5 × b5 × e (b)  m2 (d) 24b9

●● Exercise 12.3 5

1 (a) a 4 -3 2 (a) ( 5 b ) 3 (a) a

-

1 12

-

17 6

(c) a

13

6

a = 12 b = -3 c = -11 d = 14

(b)  a

-

10 3

Equations and inequalities

●● Exercise 13.1 1 2 3 4



7

(b)  a 2 7 (b)  ( 9 b )

5 e = 18 6 f = 10 7 g = 5 8 h = 4 9 j = 1 10 k = 5

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Chapter 13 Equations and inequalities

●● Exercise 13.2 1 50°, 50°, 80° 2 40°, 80°, 60° 3 x = 25 cm 4 130°, 50° 5 12 cm, 36 cm 6 105°, 150°, 45°, 60° 7 48°, 112° 8 85°, 85° 9 j = 60° 10 92°, 92°, 122° 11 15°, 75° 12 220°, 90°, 100°, 20°, 110° 13 35°

●● Exercises 13.3–13.5 1 a = 7 b=5 2 c = 3 d = 10 3 e = 4 f=7 4 g = -5 h = -7 5 p = 3 q=3 6 r = -3 s = -2 7 w = 5 x = -5 8 x = 1.5 y = 0.5 9 a = 3 b=2 10 c = 5 d=1 11 e = -1 f = -1 12 g = 1 y = 0.5 13 h = 2.5 j=4 14 k = 0.2 l=4 15 m = 4 n = -7 16 p = 2 q=1 17 r = 10 s=2 18 t = 1 w = 0.25 19 24, 13 20 5, -7 21 10 and 8 22 a = 7 b=4 23 (a) x = 8 y = -3 (a) 256 units2 (b) 64 units 24 16 yrs and 64 yrs

●● Exercise 13.6 1 -7 2 -6 3 -68 4 ±15 5 (a) x - 2, x + 3 (b) Zach = 7 yrs, Leda = 5 yrs, Spot = 10 yrs 6 18°, 54° 7 160°, 140°, 60° 8 ±10

●● Exercise 13.7 1 2 3 4 5 6 7 8

3, -4 3, 6 -3, -7 -2, -1 -5, 7 7, 6 ±13 ±7

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●● Exercise 13.8 1 -1, -3 2 -1, 3 1, 4 5 6 7

1 3

1 5

±6 ±3 No solution No solution

8 ± 1 2

9 ±

1 4

10 ±

2 3

11 ±

8 5

12 No solution

●● Exercise 13.9 1 2 3 4 5

$7 base = 12 cm, height = 10 cm 5 and 12 23 and 24 6 balls

●● Exercise 13.10 2 3

1 - , -3 2 -0.27, -3.73 3 0.19, -2.69 4 0.85, -1.18 5

3 , 2

-5

1 4

6 - , - 1 7 −0.58, 2.58 3 2

8 -4, 7 2

9 - , 10 -2

1 5

●● Exercises 13.11–13.12 1 2 3 4 5 6 7

16 + 2x < 10 Number line showing x < -3 19  9x + 1 Number line showing x  2 1 - 3x  13 Number line showing x  -4 1 x 2

< 2

Number line showing x < 4 1 x 3

1

Number line showing x  3 8 < 4x < 16 Number line showing 2 < x < 4 9 < 9x < 45 Number line showing 1 < x < 5 7

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers 8 9

4 < 2x - 16 < 10 Number line showing 5 < x < 8 3  2x + 1 < 9 Number line showing 1  x < 4

10 10  2x - 5  20 Number line showing 7.5  x  12.5

Linear programming

14

●● Exercise 14.1 1 x  1

2

1 2

2 x  2 3 -9  y < -7

−3 −2 −1 0 −1 −2 −3

●● Exercise 14.2 1

1 (a) x > 5 y>7 x + y  15 (b) y

1 −4

−3

−2

−1

0

1

2

3

4

5

x

16

−1

14

−2

2

y

12

4 3 2 1

10 8

−8 −7 −6 −5 −4 −3 −2 −1 0 −1 −2

3

6

1 2 3 4 5 6 7 8 9 10 11 12 13 x

4

y 3 2 1 −8−7−6−5−4−3−2−1 0 −1 −2 −3 −4

2 x −1 0

1 2 3 4 5 6 7 8 9 101112 x

1 2 3 4 5 6 7 8 9 10

−2

(c) 6 male + 8 female 7 male + 8 female 6 male + 9 female

●● Exercise 14.3 1

1 2 3 4 5 6 7 8 x

●● Exercise 14.4

y

−5

y 4 3 2 1

y 4 3 2 1 −10−9−8−7−6−5−4−3−2−1 0 1 2 3 4 5 6 x −1 −2 −3 −4

Sequences

15

●● Exercises 15.1–15.2 1 29, 32 2 26, 37 3 37, 45 4 (a)

(b) 8

Number of white squares

2

3 4

5

6

Number of shaded squares

4

6 8 10 12

(c) 2n (d) 100 5 (a) (i) 49, 64 (ii) square numbers (b) (i) 60, 72 (ii) term to term +12 (c) (i) 21, 34 (ii) add the two previous terms together (Fibonacci sequence) 6 (a) 4n + 3 (b) 2n + 5 (c) n2 + 2

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Chapter 16 Variation

●● Exercise 15.3

3 1,

1 (a) 215, 342 (b) n3 - 1 2 (a) 218, 345 (b) n3 + 2

1 10

4 (a) u1 = 2, u2 = 6, u3 = 18 (b) n=7 5 (a) 1 4

(b) 64

●● Exercise 15.4

(c) un = 64 ×

1 4, 2 2 0.5, 0.05

() 1

n-1

4

1 4096

(d)

Variation

16

●● Exercise 16.1

4 p =

1 (a) d = kp (b) k=2 (c) 40 (d) 1 k 2 (a) a = b

3

r2

●● Exercise 16.2 1 500

●● Exercise 16.3

(b) a =

1 2

3 (a) p =

0.5 1 or p = 2 q2 2q

(b) 0.02 (c) ± 10

k

1 (a) 1800 b.h.p. (b) 50 kg 2 330 m/s 3 2 N

Graphs in practical situations

17

2 (a)

●● Exercise 17.1

110

12

100

10

90

8

80

6

70 Percentage

Cost ($)

1 (a)

120

4 2

60 50 40

0

5

10

15

20

25

30

35

40

45

50

55

60

Units

(b), (c)

30 20

 he following method should be clearly T seen in student’s work. 12

10 0

20

40

60

80

100 120 140 160 180 200

Mark

10

Cost ($)

8 6 4 2 0

5

10

15

20

25

30

35

40

45

50

55

60

Units

(b) ≈ $4.60 (c) ≈ 37.5 units

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9

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers (b), (c)

 he following method should be clearly T seen in student’s work.

●● Exercises 17.5–17.6 5

1 (a) acceleration of

120

m / s2 m / s2

110

(b) deceleration of

100

2 (a) Running at a constant speed of 8 m/s

90

Percentage

8 1 4

2

80

(b) acceleration of 4 m/s

70

(c) deceleration of

60

4 3

m / s2

50

●● Exercise 17.7

40 30

1 (a)

20

Time (s)

0

1

2

3

4

Speed (m/s)

0 10

20

30

40

10 0

20 40 60 80 100 120 140 160 180 200

(b)

Mark

(b) ≈ 72% (c) ≈ 63 marks

55 50 45 40

Speed (m/s)

●● Exercise 17.2 1 (a) 5 m/s (b) 105 km/h 2 (a) 800 m (b) 124 200 m or 124.2 km 3 (a) 0.125 h or 7.5 min (b) 100 s

35 30 25 20 15 10 5 0

●● Exercises 17.3–17.4

4

25 20

Speed (m/s)

2 (a) 11 00 (b) 10 km (c) 30 Distance (km)

3

4

(c) 20 m (d) 80 m 2 (a)

1 (e) 8 m/s 3

5

3

15 2 1

5 0 0900 0915 0930

2 Time (s)

1 (a) 2 m/s (b) 12.5 m/s (c) ≈ 175 m (d) stationary

10

1

0945 1000

1015 1030 1045 Time

16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

B A

1100 1115

0

1

(d) 13.75 km/h

2

3 4 Time (s)

5

6

(b) 3 seconds (c) 20 m

10

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Chapter 18 Graphs of functions

Graphs of functions

18

2

●● Exercise 18.1 1

y 9 8 7 6 5 4 3 2 1 −6 −5 −4 −3 −2 −1 0 −1 −2 −3 −4 −5 −6

−5

−4

−3

−2

−1

y

6

0

−2

0

6

2

−1 0 1 2 3 4 5 6 7 8 x −2 −4 −6 −8 −10 −12 −14 −16 −18 −20 −22 −24 −26 −28 −30

1 2 3 4 5 6 x

x



x = 2 and 6

3

y 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 x −9−8−7−6−5−4−3−2−1 −2 1 2 3 4 5 6 7 8 −4 −6 −8 −10



x = -8 and 6

y 8 7 6 5 4 3 2 1 0 −6−5−4 −3−2−1 −1

1 2 3 4 5 6

x

−2 −3 −4 −5 −6 −7

x

−2 −1

0

1

2

3

4

y

−6

4

6

6

4

0 −6

0

●● Exercise 18.2 1

y 8 6 4 2 0 −4 −3 −2 −1 −2

y 10 8 6 4 2

5

●● Exercise 18.3 1 x = 1 and 3 2 x = 3 and 5 3 x = -6 and 4

1 2 3 4 5 6 7 x

−4 −6 −8 −10 −12 −14 −16 −18 −20



x = -1 and 5

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11

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers

●● Exercise 18.4 1

−4

x

−3

●● Exercise 18.7

−2

−1 0

1

2

3

4

1 (a)

y 7 6

−0.375 −0.5 −0.75 −1.5 ∞ 1.5 0.75 0.5 0.375

y

5 4 3

y 4

2

3

1

2

−2

1

3 x

2

−1

−4 −3 −2 −1 0 −1

1

2

−2

4 x

3

−3

−2

−4

−3

−5

−4

(b) Gradient = 3 2 (a) y

−5



0

−1

1

7 6

●● Exercises 18.5–18.6 1 (a)

x

−4

−3

f(x)

4.1

3.1 2.3

(b)

5 4

−2 −1 0 1 2

2

3

3

2

– 0 −1.8 −2.9

1 −1

y 11

0

1

2

3

4

5

6x

–1

10 9

(b) Gradient =

8 7

1 2

6 5

●● Exercise 18.8

4 3 2

1 (a)

1 −4 −3 −2 −1 0 −1

1

2

3 x

−2

11

−3 −4

2 (a)

y 12

10

x

−5

−4

−3

−2

−1

0

1

2

9

f(x)

3.0

2.0

1.0 0.1

−0.7

−1

0

5

8 7

(b)

y 7

6 5

6

4

5

3

4

2

3

1

2

−5 −4 −3 −2 −1 0 −1

1 −5 −4 −3 −2 −1 0 −1 −2 −3

1

2 x

1

2 x

−2 −3 −4

−4 −5

12

© Hodder & Stoughton Ltd 2013

Chapter 19 Functions (b)

3 Rearrange the equation to give 2 - 2 x = - x + 4 x Superimposing the graph of y = -x + 4 gives

2 (a)

10 9

y 12

8 7

11

6

10

5

9

4

8

3

7

2

6

1

5 4

−4 −3 −2 −1 0 −1

3

−2

2

−3

1

−4

−5 −4 −3 −2 −1 0 −1

1

2x

1

(b) Rearrange the equation to give 3x + x = 2 x + 4

−3



1

−5

2 x

−2

2

Superimposing the graph of y = 2x + 4 gives

−4



y 11

y 11

Therefore x ≈ -3.8, -1 and 0.8

10 9 8 7 6 5 4 3 2 1 −4 −3 −2 −1 0 −1

1

2x

−2 −3 −4



−5

Therefore x ≈ -2.6 and 1.7

19

Functions

●● Exercise 19.1 1 (a) 9 1 (c) 4 2

(b) 15

(d) −3 1 2

(e) −15

(f)  1

2 (a) 3 (c) 2 3 (a) 6 (c) 12.5

(b) 9 (d)  -13.5 (b) 1.5 (d) 8.3

© Hodder & Stoughton Ltd 2013

●● Exercise 19.2 1 (a) 6 (c) 3.4 2 (a) 4 (c) -17 3 (a) -2.5 (c) 20

(b) 10 (d) 3.2 (b)  -3 (d)  -3.7 (b)  -25 (d) 5.6

13

Cambridge IGCSE® Mathematics Core and Extended Practice Book Answers

●● Exercise 19.3 1 (a) 128

(b) 8.21

(c) 176

(d)  7

(e) 9

1 (a) f-1(x) = x - 4

1 4

2 (a) 49

(b) 287

(c) 5

(d)  - 7

3 (a) -

●● Exercise 19.5 2 (a) g-1( x ) =

x +5 3

g-1( x ) = (c)

5x + 6 4

9

1 4



(b) −79

(c) −24

(d)  -10

2

(c) 6x + 1

x 5

(b)  g-1( x ) =

2( x + 1) 5

●● Exercise 19.6

1 4

1 (a) 3 2 (a) 1 3 6 4 -1

●● Exercise 19.4 1 (a) 3x + 7

(b)  f -1( x ) =

(b) 6x - 2 3x (d)  +7 2

(b) 1 (b)  -2

●● Exercise 19.7

2 2 (a) 18x - 1 (b) 

1 (a) fg(x) = 2(x + 4) (b) fg(x) = x 2 (a) pq(x) = 2(x + 1) (b) pq(x) = 2x + 1

(c) 4x - 1

3 (a) jk( x ) =

x2 -1 8 (d) 2x2 - 20x + 49

x -1 2

(b) jk(x) = 3x - 7

4 (a) 6

(b)  no solution

Topic 2 Exam focus 1 (a) 9(a + 2b)(a – 2b) mb (c) a = 3c n 2 r = 6.0 cm (1 d.p.) 3 (a) 12a5 (c) a2 4 (a) x2 + 6x = 40 5 (a) 4(x - 3)2 - 7 = 0 6 (a) x + 2y  30

(b) (d + 4)(d – 3) a (d)  a-3 (b) 8a5b3 (d)  a5 (b)  x = 4 (b)  x = 4.3 and 1.7

8 y = 8 9 (a) Stage A (b) 120 km/h² (c) Stage D. As deceleration in stage B is 40 km/ h², whilst deceleration in stage D is 51.4 km/h² (1 d.p.). The graph of stage D is steeper than that of B. (d) 120 km (e) 360 + 135 + 120 + 315 = 930 km 10 x3 + 5x2 - 4 = 0 can be rearranged to form 4 -3= x +2 x2 Superimposing the two graphs gives

1

3 x + y > 15 2

x