Check 1

Check 2

Check 3

Check 4

Check 5

Check 6

1 (a) {11, 13, 17, 19, 23, 29} (d) {(0, 8), (1, 7), ... , (8, 0)}

2 (a) {4, 5} (d) {2, 3, 4, 5, 6, 8} (g) {1, 4, 5, 6, 7}

4 13,8 s 19 6 (a) {3, 4, 5, 6, 7, 8}

1 25,36 6 9, -11

2 63, 127 7 17' 19

3 4, 16 8 1 .l.. f6, 32

Answers

(b) {1t} (c) ¢ (e) {30, 150} (b){3, 5, 7, 8} (c) {1, 4, 6} (e) {1, 2, 4, 6, 7} (f) { 3, 5, 8}

(b) {4, 5, 6} (c) { -oo, ... , 0, 1, 2}

4 125,216 s 2.5, 1.25 9 42,89 tO 29,41

1 8.69, 26.13, 0.09, 0.10, 2.02, 2.19, 10.00 2 86.4, 187, 0.0900, 2.00, 170, 3.00, 8690, 10 000

(a) 94 (b) 140 (c) 1128 (d) 11 (e) 61 (f) 35 (g) 420 (h) 587 (i) 2133 U) 2343

1 110000, 1010110, 10001, 10111011000, 10111, 11001111, 111110, 1011100 2 13,27,333,125

1 10100 7 417

13 1202

2 100001 8 31

14 2225

3 1111 9 33

15 1215

4 1443 s 10100 10 -111 11 11110

6 35552 12 14

267

Check 7

Check 8

Check 9

Check 10

Check 11

Check 12

Check 13

Check 14

268

1 1i 7-!-

13 t 19 8~

1 0.6 7 0.27

2 fs 8 1t

14 24 20 t'

2 0.12 8 0.368

3 1-tz 9 I-t

15 ffo 4-fo

10 t 16 3

5ro 11 6t 17 29-t

3 o.625 4 o.714 5 o.i8 9 0.4375 10 0.354

1 40, 279, 16-t, 3.75, 0.5, 55, 150,9.8 2 ~ .1!! .!. ..L ~ ....ll..

3 ' 25' 8 ' 500' 25 ' 200

6~ 12 1-i\ 18 Hi

6 0.52

1 4.86 X 102 , 6.93 X 103 , 8.57 X 105 , lQ-2 , 9.6 X lQ-2 , 8.31 X lQ-3 , 9.09 X lQ-2

2 45 000, 3840, 8 010 000, 0.085, 0.000 695, 0.000 008 801

0.9, 0.007, 40, 0.1, 1, 100,400000,0.006

1 6.../2, 7 .j6, ..j2, 5vff0, o, y'7; -y'IT, 6.Jf, 10y'2- 2y3, 5...j5

2 .j2 vs Vi Vi 00 vs vi?+ y'2 2 ' 25 ' 2 ' 2 ' 2 ' 5 ' 5

1 -6 2 -16 3 12 4 -It 5 -t 6 -7 7 -fo 8 -tz 9 -1-fio 10 112 11 -10 12 7ft 13/o 14 0

15 35~

1 100 2 9 3 0.3 4fs- 5t 6 4 7 1 8 7 9 4 10 +s 11 2x3 12 5p-8 /4 13 12x-6

14 -27m3 15 3x2 16 5y8 17 4q413 18 u 19 9v4 20 f,

Check 15

Check 16

Check 17

Check 18

1 y(a+4y) 2 t(3t2 +2t+5) 3 p2 q2 (q-p) 44(p-2) 5 (p+q)(y-z) 6 (r-p)(q+s) 7 (t-3)(t-p) 8 (x-y)(a+b+c) 9 (x-3)(x-8) 10 (x+3)(x-1)

11 (x + 13) (x- 2) 12 impossible 13 (2x + 3) (x + 5) 14 (2x + 1) (2x + 3) 15 (3x- 1) (2x- 1) 16 (9x + 2) (x- 1) 17 (4x2 + l)(x- 1) (x + 1) 18 (2x- 5)(2x + 5) 19 (1- x) (1 + x) 20 1r(R- r)(R + r) 21 x(x- 6) 22 (llxy- 2) (llxy + 2) 23 (2x- 3y)2 24 (5x- y)2 25 (5- b)2

(b) 2b + ~ ab

(f) 28x2 - 15y2

2lxy 4x2 + 1 (g)

X

(d) 13x 12

(h) 7a + 12b 8

(e) 25 3y

(i) 2x- 1 6

(j) 7x + 5 (k) -1 (x-l)(x+2) x(x-1)

(1) x 2 - 2x + 1 (m) 4x (x - 3) (x - 2) x2 - 1

2 (a) ~ (b) 4tq (c) 3q y 3 5t

(d) 8x (e)~ 15y 15

(f) 2q 3

c (g) a+ b (h)~

18t (i) 4tp (j) a+ b

a-b

2 kq + ___l!L 3 xy 2000 10

4 150 +X+ y

5 yt+v(50 -y) 6 lOp 11

7 4/ + 6s + 9 8 1. 2%

9 (E-D)/ 10 85W+M 100

1 (a) 2 (b) 4 (g) It (h) - t (m)t (n) 8

(c) -4 (i) !i (o) -¥

(d)-~ mt

(e) 1! (k) ~

(f) t (1) -9

(c) t, -1 (d) 1-, 3 (e) 1 (f) 0, 9 2 (a) 3, -1 (b) 2, 8 (g) 1.85, -4.85 (k) 1.82, 0.18

(h) -1 ± y'2 (i) -4 ± v'f9 (j) -0.11' 2.36

2 (n) ± VJ

3 (a) 5, 2 (b) -2, -5 (g) 1-t, -3

(1) -6 ± v'f9 (m) no solution

(o) 1

(c) 2, 1 (d) 2, 4 (h) 6, -t (i) 5, 1

(e) tt, fo (0 3, 2 (j) -3, -lf

269

Check 19

Check 20

Check 21

Check 22

Check 23

270

1 t 2% 3 121! 4 (a) (x- 1) (x2 + x + 1) (b) (x + 2)(x- 1) (x + 1)

(c) (x- 2)(x2 + 9x + 15) (d) (x 1) (x 2) (x 3) (e) (x- 1) (x + 1) (2x -l)(f) (3x- 1)(x + 1)(x + 2) (g) (x + 2) (x - 3) (x - 5)

5 -1, -t

1 430, 68.4, 40000,5, 0.25, 8.63 X 107 ,4000, 125.5 2 6.25 X IQ-3 , 0.08, 9.4 X IQ-3 , 0.895, 8.69 X IQ-4

3 8000, 40, 0.685, 65 000, 1.8 X IQ-3 , 9 X 105

4 9.6 X 104 , 28.75, 4.8 X 108

5 0.6, 2.8 X 104 ' 2 X 1012

6 72, 6.94, 8

1 10.3, 13.44, 11.72, 15.32, 32.0, 53.92, 92.52, 28.56 22.176x107

3 93.5 em2

4 3.5 5 616, 484, 14, 201-t, 2.2, 10.68, 1232, 2, 38 808, 5544, sot, 2, 91 989, 28,

11.5, 24.64, 91.99, 2.8,205-t, 177.4,331.4,8.06, 314~, 204.3, 282.9, 5, 167.2, 321.2, 7, 7.6, 1797, 905.1' 26.8, 28, 2932, 880, 14.28, 20.

1 3.34 2 7.3 3 8.55 em, 14453 km, 0.448 m, 2513 km 4 14.32 em, 32.17 em, 630.2 km, 203.7 km 5 86, 57, 5, 1

1 -7~y~5,{0,1,4,9},{xER,x=F0},-1~y~1 2 2x2 + 1, (2x- 3)2 , 4x- 9, 8x2 - 24x + 19 3 1' 0, 1 4 (a)3,11 (b)3<x<ll 5 30,55 8 -4 9 3y = 2x + 12, y = 3x - 2, 2y = 3x - 6, y + 3x = 10

10 ot. s), ct. -t>. o. -It), (2f, 2-t>

Check 24

Check 25

Check 26

1x<¥ 2x<l 3 {1, 2, ... , 10} 4 -1 5 -2<x<12 6 7,8 7 -3 <x <4 8 -4.6<x<-2.2 9 {2, 3, ... , 7}

10 -l<x<4 11 2<x<3 12 -.JTS <X <yTI 13 -3 <X <2 14 0 <x < 2t 15 x > 2 or x < -2

1 ( ~), (-:).( ~),( ~}( :} 00, vfs, y'IO +viS

2 b + c, a + b + c, a + b 3 b - a, -b -a, 2b

4 (=~), (_~), (_~) 5 (5, -3), (_~) 6 (6, 4), (18, 8), .;m

1 l( 3 -2) 2 -5 4

2(: ~) 3 impossible

4 _1 (9 -3) 36 6 2

5 ( ~ -~) 1 ( 11 4)

6 78 -3 6

271

Check 27

Check 28

Check 29

Check 30

Exercise 1

272

c ~3) ( -5 1~) (b) 1~ -6 (c) -13 -19;

1 (a) ( 11 5 -41) -4 -1

(e)( ~ ~4 ~8) 4 12 (f) impossible

16 4 24 (d) impossible

2 ( * 1) -1 4

.1. 0) 3 (; -t

4 (a) (10) (b)(~ ~) (c) (-9)

( 92 5) (e) 5 (f) ( -:) (g)(:) (6 9 0)

(h) 3 6 3

(-4 0) 5 -9 -3

(i)(~ 10 3~) 11 17 2 38

6 (a) fi, -M (b)~ -u 37• 37 (c)-!-, 2t (d) lli ~ 147' 147

1 80,80, 70 6 124,28,34 9 37t, 75

4 (a) n 5 (a) -ls

1 fz 4 .l. .l.

2' 9

2 90 3 50,50 7 55, 35, 55, 70

10 120, 120

(b) -t (b) to

(c) n (c) fo

(d) fs

3 1.. .1. g, 2

6 0.14,0.53

4 80 5 30, 110 8 63,31t

(e) t

1D 2C 3D 4B 5C 6A 7A 8A 9C 100 11 (a){3,7} (b){l3,15} 12 (a) {36} (b){6, 12, 18,24,30,42,48,54,60}.

(c) { 4, 8, 16, 26,44} 13 62 14 16

(d) impossible

Exercise 2

Exercise 3

15 (a) (A n B n C') u (A n B' n C) u (A' n B n C) (b) (A U C) n B' (c) ((A u C)' n B) U ((A U B)' n C) U ((B U C)' n A) (d) ((AU B)' n C) U (An B n C')

16 (a) if> (b) cyclic 17 (a) (i) S (ii) if> (b) (i) 6 (ii) 47 18 (a) There are no fast red cars (b) Some red cars are fast

(c) Some red cars are not fast 19 {5, 10, 15, 20, 25},{3, 6, ... , 27},{5, 10, 20, 25} .... 20 (b) {3} (c) {1, 4, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39}. 21 (d) {2, 3, 13, 17, 19} (e) {1, 14, 15, 16, 18, 20}

(f) {1, 6, 8, 9, 12, 14, 15, 16, 18} 22 (a) 19 (b) 32 23 (a) 32 (b) 44 (c) 3 (d) 20 (e) 4 24 (a) {multiples of 70} (b) 83 25 14 26 (a) 10 (b) 3 (c) 15 (d) 59 28 (a) (i) {3} (ii) {1, 2, 3} (iii) {1, 2, 3, 4, 5}

(b) (i) {4, 16, 36} (ii) {25, 36, 49} (iv) {36} 29 (a)34% (b) (ii)24 (iii) 3 30 (b)lOO,n(badsteeringonly)=O

1 C 2 B 3 A 4 D 5 B 6 A 7 B 8 D 9 C 10 B 11 D 12 c 13 c 14 £30.17 15 £288 000,£300, 82p 16(a)9,6 (b)3n+4 170.02 18£87.72 19(a)l01010 (b) 110 (c) 111000011 (d) 100011 21 (a) 6 (b) 4 (c) 8 22 7.44 X 105 , -2.08 X 105 23 (a) 0.0025 (b) (i) 0.05263 24 2 25 (a) 2.4393 (b) 0.141 (c) 22.41 or 22.28 26 9% 26 (a) 300 (b) lOp (c) llp (d) 31.4% (e) £141.45 27 £120 33.10, 9% 28 (a)£75000 (b)(i)3.2p (ii)£17.28 (c) (i)£230 (ii)2.7% 29 (a)(i)£159 (ii)£223 (iii)£205 (b)£624 (c)£245.30 30 (a) £104.13 (b) £178.50 (c) 6.25% (d) £233.50 31 (a) 2361.6 (b) 85000 (c) 125 (d) 1676 32 (a) 2660 (b) 9.5, £434, 2.2, £84 33 (a) 31 (b) 17 (c) 0 (d) R, U 34 (a) 300 (b) £25 320 (c) £410.64

1D2C3D4B5C 13 ±6 14 by2 /(x- 1)

6 B 7 C 8 A 9 C 10 B 11 D 12 A 15 (x- 3) (2x + 1) (x- 1)

16 (2a+4b+5c)(2a+4b-5c) 19 -1

17 (v2 - u2 )/2s 18 (a) y'29 (b) t

20 (a) 200.016 (b) 1.96 (c) )r _\oon 21 (a) (x + 1) (4x + 1) (b) 4(3a +b) (2b- a) (c) x(x + 3) (x- 2) 22 (a) if>, (b) t, (c)y'2 (d)V2,i 23 (a) 2p2 (b) 8x (c) 18x4

24 (a) x- 1 (b) x, 1 (c) 1.62 (x- 1)

25 (a) R- (b) -(k~+m) (c) 4~k 26 (a) (i) 17-!- (ii) 2 (b) 1.77

27 (a) i (b) -2, 11- (c) 0, -3 (d) 2-t (e) 1 (f) ±5 (g) -i (h) -1

273

Exercise 4

Exercise 5

274

(i) ±3 (j) 2 28 (a) q- 4y (b) (4- 2T2)/T2 (c) t/(y- 4) (d) J_r2 - y 2 (e) J4 + y 2

(f) jA2 t2 ~616y2 (g)- (by+ c)/a (h)~ (i) F!- 1

29 (a) '2t(q- 3) (q + 3) (b) 4t(q + 2t) (c) (2t 3) (x + y)

(d) (8x + 11) (4x- 9) (e)(x- 1) (x2 + 2x + 2)

30 (a) 4 (b) 13 (c) 9 (d) -38

31 (a) 2, -1 (b) vf/(v- f) (c) (x + 4)2 + 9 32 (wy +(52- w)r)/52 33 6.52 34 (a) 1600 (b) 8 35 366 36 (a)(ii)(A+b2 )/2b (b)4l 37 (a)137 (b)51,52,53,61,70 38 (b) correct to 2 d.p. 39 (a) (ii) x 3 = 12 41 1.74 x 1.74 x 4.74 42 240, 2 h 5 min 43 (a)0,1,3,6,10 (b)1,2,3,4 (c)n (e)99 44 (a) (i) 4 (ii) 49 (iii) 484 46 (b) 58 (c) 48 (d) W = 2R + 4 (e) 44 (f) 5t (g) not possible

1 B 2 A 3D 4 A 5 C 6 B 7 A 8 D 9 B 10 D 11 D 12 64 cm2 13 (a) 8.8 x 105 (b) 2.72 x 10-2 14 (a) 90 (b) 90 15 £982 600, 520 km 16 (a) £6000,£360~£2400 (b)370,£4500,75% 17 (a) 2240 m3 (b) 1640 cm3 (c) -i 18 (a) 5960 mm (b) £178.80 (c) £208.60 (d) £47.25 (e) £434.65

(f) £43.46-!- (g) £23.91 19 (c) 52 20 48m3 , 5 min, 384m3 , 37.5 em 21 (c) (i) 64 m/s (ii) 8 m/s2 (iii) 672 m 22 (a) 60 (b) 11.3 (c) 3{ m/s2

23 3t min, 6 7 min 25 (b) 160° (c) 7.8 km (d) 0.7 km (e) 50 min (f) 9.4 km/h 26 (b) 11.25 27 (a) 0.5 h (b) 1 h 30 min (c) 180 km (d) 2 h

(e) 90km/h (f) 13.15 28 (a) 1054 (b) 1 h 54 min (c) 14 min (d) 47 km (e) 47 km/h (f) 18 km

1D 2B 3B 4A 5C 6D 7B 14(a)2 (b)(-11-,3) (c)(3,-6) 15 (a) (ii)Jf (b)y+2x+3=0 17 (a) x = 2.24 (b) 3.3 or 1.5

8 C 9 D 10 D 11 C

16 x 3 + 1.6x2 + x + 1 = 0 18 (c)(i) 0.81 (ii) -4.1 (iii) 11.3

(d) -2.4 (e) 1, -2t 19 (a) 6 (b) 6V3, 2VJ 20 (a) (10, 0) (0, 5) (b) -0.5 (c) y = 2x (d) (2, 4) (e) (4, 8) (f) (5, 2-!-)

(g) 5vfs/2 23 (a)- to (b) 0, (-4, -5) (c) 1.93 21 (a)(i)x142 (ii)x144 (b)gh (c)x143(x-1) 22 (a) 2 (b) 0, 1, 2 (c) 0 23 (a) (3 - x)/2 (b) 2/3x (c) 3yx (d) 3.yx=-'2 (e) (1 - x)/2x

(f) (b- dx)/(cx- a) 25 4 solutions, 2.65 26 (a) -22 (b) -2 (c) -22 (d) -4, 9 (e) 9.92, -1.92 27 (a) 18.8 (b) ±5.29 (c) --i (d) y ~ 6 28 (a)2.5 (b)3.6 (c)2.5<x<4.1 29 (b) 100 (c) A= 170- lOt (d) between 6.30 and 8.30 Sunday 30 (b) (ii) 2 (c) 2.73, -0.73 31 (a) 175,315 (d) 46 mile/h (e) 30 mile/h 32 (a) (x- 3) (x- 2) (b) x = 3, 2 (c) (0, 6) (2, 0) (3, 0) (d) -4, -5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

1D 2C 3A 4D SA 6D 7C 8B 9D 10C 118,9,10 12 (a) 24 (b) (i) 2t (ii) 0 13 £4.80 14 X+ y ~ 1000, y ~ 2x, X~ 100, y ~ 800,333,667 15 (a) h~15 (b)p>25 (c)45~h+p<60;25.30

1D 2B 3C 4B SC 6C 7C 8B 9A 100 ll(a)34 (b)26 --+

12 7, 4 13 5PT 14 6, 0 ~ 15 (a) (i) 2v (ii) 3v + 2u (iii) -2v- 2u (b) QN 16 (a) q- p, t(q- p), ¥P + q) (b) t(p + q), tq- i-P (c) tq- P (d) i 17(d)5.1km (e)12.14 18h=k=t,1:3 19(b)t (c)ft (d)~ 20 (c)(a+b+c+d)/4 21 (a) lOa- 2b (b) 2b+ k(lOa- 2b) (c) lOrna+ (2b- lOa) 22 (a) (i) -x (ii) 2x (iii) y- x (iv) x + y (v) 2x- y (b) (i) 3x (ii) 4x- 2y

(c) (i) 2 (ii) 6 24 (a) (i) 2n + 2e (ii) 2-J2 (b) k = f 25 (a) (i)(-6 .!.) (ii) 13 (b) 3a + 3b, -a+ 3b, m = 4, n = 3

-22 26 (a) tb, fb, -b +a (b) f(a- b), fa (c) trapezium (d) 2i (e) 27 cm2

27 (a) equal (b) C!) (=:) (d)(_!) (e) returns to A

1B 2D 3C 4A SD 6D 7B 81:8 12(1,3),(2,3)

13 (6, 4),H 14 (a)(!), 4-y'3" (b) (10, 8) (c) -1-!

15 90° anticlockwise about k 16 (b) -90° ( _ ~ b) (c) (_~) (d) -90° about (0, -2)

17 (a)D(-2,-2) (d) (4,-4),-! 18 (a) similar (b) equal (c) t (d) 1: 16 (e) 1:4 (f) 15 cm2

19 (a) straight line (b) parallel line x 2 (c) translation, parallel! : 2, enlargement x 4 20 (a) 4, 6 (b) If (c) (i) 9 (d) AQB

1A 2C 3D 4D SA 6D 7D 8A 9D 10C 11 Jf,y'-t,3

12 (1) (_~ -~) 14 C~) 16 18, -11

17 8, 24 19 (2, 1), (3t, -t), (--!, --t)

21 (a)(iv) S = T' (b) (li)G 0

18 rotation 53° clockwise 20 (6, 4), H

22 (a) (i) (: _ ~) (ii) (_ 1 ~ -~~) (b) rotation 90° about 0, (~ ~)

24 (a) (i) (3, 9) (ii) (14, 8) (iii) (2, - 7) (b) (i) -3 (ii) -1, 2 25 90° (6, 0)

275

Exercise 10

Exercise 11

Exercise 12

276

26 S, 5, 90°, 25,-l- 27 (b) (ii) shear (c) (ii) (~ ~) (d)(~ ~) 28 (c) (i) ( -1, 0), ( -3, 0), ( -1, 1) (d) (ii) reflection in Oy (iii) T = SR

1 (a) 20° (b) 10.3 em (c) 20.3 em 2 52-! 0 , 82t0 , 127t0 , 97t 0

3 13 em 5 140° 6 (a) 60° (b) 240° (c) 30° 7 (a) 64° (b) 107° 8 100° 9 POT, AQO, QTC 10 (a) 180- x (b) 360/x (c) 360/x (d) 360/x

11 2 12 (a) (i) 40, 50, 35, 45 (ii) 10n, IOn- 5, 9 (b) (i) 90 em (iii) 5

lB 2C 3B 4C 5D 6B 7B 8A 9C lOC 11·t,t,fo 12 c 13 533t 14 To 15 ~ 16 6 17 t 18 i' ·t to 19 ~ ' ~ 20 ~~, 4~0 21 (a) 1- (b) (i) t (ii) t 22 (a) 6 (b) 12 (c) 12 (d) £5600 23 (a) 0.343 (b) 0.1029 (c) 0.3087 (d) 0.6517 24 0.24, 600 25 (a) (i) !6 (ii) t (b) (i) is (ii) Tfo (c) 0.202 26 (b) 114° (c)(i)0.316, (ii)0.673 (d) 2~3~0 x 1\3~~9 27 (a)t (b)(i)% (ii)i 28 (b)48,49 (d)49.1 29 (a)5.09% (b)(ii)233°,102° 30 (a)3,2 (b)(i)£114 (ii)£3.80 31 (a)(i)40.5-45.5 (b)(i)43.5 (ii)8 (c)70 32 (a) t (b) f (c) U (d) 221 (e) ~~ (f) 1cis, ~i 33 (a) (i) 1440 (ii) 3760 (b) 20 per cent 34 (a)8 (b)30 (c)81 (d)2.7

1 B 2A 3C 4C 5D 6D 7C 8D 9C 10 7.38 em, 49.5°, 14.9 em 11 20.5 em, 6.43 em, 2, 63.4° 12 (a) 7.2, 10.8 (c) 56.3° (d) 55.3° 13 25.1 m, 65° 14 144.76 , 60.2 n miles, 78.3° 15 (a) (i) 254.8 m (ii) 27° (b) 711.3 m, 331.7 m 16 (a) 4.8 em (b) 9.6 km (c) 45.4° 17 (a) 33.4°, 146.6° (b) (i) 4.76 miles (ii) 3.14 miles 18 (a) 173.8 m (b) 337° 20 (a) 14° (b) 4.84 m 21 (a) 10 em (b) 200 cm3 22 (a) 84.3° (b) 151.4 em (c) 82° 23 (a)3119m (b)3589m (c)3569m 24 6.4m,9.38m2

25 (a) 8.29 em (b) 14.9 em (c) 17.4 cm2 (d) 2.34 em 26 (a) 14.4 (b) 133.8° (c) 0.87 km 27 190.4 m, 248m, 13.5° 28 8.65 em, 5.47 em, 30.6 cm2

29 5.45 em 30 (a) 8.38 (b) 25.13 (c) 17.73 (d) 7. 71 31 (a)2.24m (b)2.84m (c)120° (d)4.1m 32 (56° S, 143° E) 33 75.5° 34 (a) 2751 km (b) 8642 km, 3070 n miles 35 (a) 7440 n miles (b) 9536 n miles, (28° N, 21.6° W) 36 (a) (i) 37° (ii) 53° (iii) 106° (iv) 74 (b) (i) f= 180 - 2x, (ii) g = 2x

(iii) all values

Exercise 13

Test 1

Test 2

Test 3

Test 4

1 (a) perpendicular line (b) parallel line, 4.5 em 3 CQ = 8.1 em 6 3.5 em 9 10 em 10 126 cm3 12 275m2 13 8.7 em, 23.3 em

15 (a) 5.2 m (b) 22m 16 (a) GCE (c) 5, 8, 5 (d) rectangle 17 (a) (i) 6 (ii) 3 (b) 5, 1, 4

1 5 2 1600 3 13 4 10.07 5 24 6 £1.16 7 5 February 9 8 10 £2.70 11 120 805

12 89 13 78 8 4.38 p.m.

14 £7.28 20 £1.60

15£140 168kg 1787.5rniles 18 t 19 12t%

1 £42 2 48 3 8 4 6.5 - 7 m 5 27 6 5 1b 8 8 9 192 cm2 10 £1.60 11 1505 12 8x2

14 12 cm2 15 t 16 65 17 45 s 18 29000 20 9.21 p.m.

1 28 cm2

7 21 °C 13 0314

2 37 3 £200 4 £2.40 5 105 008 11 54.7 8 32cm 9 61 10 18cm2

14 £4.88 15 59p

7 5 13 2t h

19 12 cm3

1 3600 2 £2.64 3 240 cm3 4 5 ft 5 96 cm2 6 l6

7 1000 cm2 8 £96 9 151 miles 10 8 em 11 56 rnile/h 12 250° 13 1230 14 3.99 15 30 g

277

acceleration 86 algebraic expressions 49 algebraic fractions 48 alternate angles 172 angle of elevation/depression 216 approximations 31 area 75 array 153 associative 41, 153 assumed mean 199 aural tests 253

bar chart 194 base 21 bearing 216 binary numbers 21

chord 179 circle theorems 1 79 circumscribing circle 239 codomain 97 coefficient 44 commutative 41, 98, 153 complement 4 composition of functions 98 cone 77 congruent 140 constructions 23 7 corresponding angles 172 cosine ratio 210 cosine rule 222 coursework 261 cuboid 78 curve sketching 1 06 cylinder 77

decimal places 20 De Morgan's laws 7 density 78 determinant 155 difference of two squares 46 dilatation 138 directed numbers 40 disjoint 4 distance-time graph 86

Index

distributive 7,41 domain 97

element 3 enlargement 139, 163 equations

construction of 53 linear 50 quadratic 51 simultaneous 52, 60, 103, 156

equilateral triangle 175 errors 115 Euler's theorem 160 exchange rates 26 exponential graph 106

factorisation 45 Fibonacci sequence 19 flow chart 61 formulae - change of subject 55 fractions 23, 48 frequency 196 function 97

glide reflection 138 gradient 101 great circle 226

highest common factor 4 7 histogram 200 hyperbola 107

image 97 indices 43 inequalities 114 inequations 114 infinite set 3 inscribing circle 240 integers 17 interest 27 interquartile range 199 intersection 4 invariant 139

279

280

inverse function 98 irrational numbers 17 isometry 138 isosceles triangle 175,218 iteration 61

kite 177

latitude and longitude 226 like terms 44 linear programming 11 7 locus 121,247 logic 6 lowest common multiple 4 7

map scales 27 mapping 97 matrix 153

identity 155 inverse 155

mean 196 median 196 member 3 metric system 74 mid-point 102 mirror line 136 mode 196 modulus 125 mortgages 34

nautical mile 226 net 246 network 158 node 158 null set 4

Ogive 198 order of matrix 153

parabola 106 parallelogram 176 Pascal's triangle 19 percentages 25 pictogram 196 pie chart 195 plan and elevation 244 point symmetry 139 polygon 173, 1 78 prime number 17 prism 78 probability 188 proportion 25, 59, 107 pyramid 78 Pythagoras' theorem 211

quadrant 209

range 97 rate 25, 75

domestic 32 ratio 24 rational number 17 rectangle 176

reflection 136, 161 regions 116 remainder theorem 57 retardation 86 rhombus 177 rotation 137, 162 route-matrix 158

sample space 188 scalar 124 secant 181 sector 83 segment 83 semi-interquartile range 198 sequence 18 set 3 shear 139, 163 significant figures 20 similar 140, 145 sine ratio 210 sine rule 220 singular 15 5 speed 86 sphere 77 square 176 standard form 29 straight line 101 stretch 140, 164 subset 5 substitution 42 supplementary angles 172 surd 17, 32, 215 surface area 78 symmetry 174

tangentratio 210 testellation 178 transformation 161 translation 161 transpose 160 trapezium 177 trapezium rule 83 traversable 160 tree diagram 191

union 4 units 74 universal set 4 unlike terms 44

variation 59 vector 124 velocity 86 velocity-time graph 86 Venn diagram 5 vertically opposite angles 1 72 volume 77

wages 33