IGCSE Maths Practice Book Answers
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Answers for IGCSE practice book Pimentel Wall...
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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
© Hodder & Stoughton Ltd 2013
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
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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
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