Cambridge Additional Mathematics

Answers 481 h i j k l 2aa=4, b=3,c=¡ 1 ba=3, b=5,c=3 3ay= 2 cos 2x by= cos ¡x 2 ¢ +2 4aa=5, b=1, c=1 b 5aa=^32 , b=6,c=¡^32 b cy ...

482 Answers f 2ab=^32 ,c=2 bb=2,c=¡ 3 3 p=^12 , q=1 EXERCISE 9E.1 1ax¼ 0 : 3 , 2 : 8 , 6 : 6 , 9 : 1 , 12 : 9 b x¼ 5 : 9 , 9 : 8 ...

Answers 483 c 3aminimum=0, maximum=2 bminimum=¡ 2 , maximum=2 cminimum=¡ 3 , maximum=3 dminimum=¡ 2 , maximum=0 4a 2 ¼ b ¼ 2 c ¼ ...

484 Answers 10 acosμ b¡sinμ c 5 cos^2 μ d¡cosμ 11 a4 sin^2 ®¡4 sin®+1 b 1 ¡2 sin®cos® EXERCISE 10A 1 18 2a 4 b 8 c 24 3 6 4 42 5 ...

Answers 485 5a1 6 15 20 15 6 1 bix^6 +12x^5 +60x^4 + 160x^3 + 240x^2 + 192x+64 ii 64 x^6 ¡ 192 x^5 + 240x^4 ¡ 160 x^3 +60x^2 ¡ 1 ...

486 Answers c ³ 0 ¡ 5 ́ d ³ 4 ¡ 2 ́ 5a ³ ¡ 1 ¡ 4 ́ b ³ 2 ¡ 3 ́ c ³ ¡ 5 2 ́ d ³ 0 6 ́ EXERCISE 11B 1a 5 units b 5 units c 2 units ...

Answers 487 3a 24 : 6 km h¡^1 b¼ 9 : 93 ±east of south 4a 82 : 5 m b 23 : 3 ±to the left of directly across c 48 : 4 s 5aThe pla ...

488 Answers b¡BC and! ¡CA.! Each vector has components of the same magnitude, but differing signs (which do not affect the lengt ...

Answers 489 EXERCISE 12B.3 1a 3 A b O c ¡C dO e 2 A+2B f¡A¡B g ¡ 2 A+C h 4 A¡B i 3 B 2aX=A¡B bX=C¡B c X=2C¡ 4 B dX=^12 A eX=^13 ...

490 Answers c^1 (k+ 2)(k¡1) ³k ¡ 2 ¡ 1 k+1 ́ , k 6 =¡ 2 or 1 d^1 k(k+1) ³ k ¡k 3 k¡ 2 ́ , k 6 =0or¡ 1 e 1 k(2¡k) ³ 11 ¡k ¡ 2 kk^ ...

Answers 491 2a x Point B Gradient of AB 0 (0,0) 2 1 (1,1) 3 1 : 5 (1: 5 , 2 :25) 3 : 5 1 : 9 (1: 9 , 3 :61) 3 : 9 1 : 99 (1: 99 ...

492 Answers EXERCISE 13G 1af^0 (x)=2x¡ 1 bf^0 (x)=4x+2 c f^0 (x)=2x(x+1) (^12) +^12 x^2 (x+1) ¡^12 2ady dx =2x(2x¡1) + 2x^2 b dy ...

Answers 493 3a 2 xcos(x^2 ) b¡^1 2 p x sin( p x) c ¡ sinx 2 p cosx d2 sinxcosx e¡3 sinxcos^2 x f¡sinxsin(2x) + 2 cosxcos(2x) gsi ...

494 Answers 3 y=21andy=¡ 6 4 (^12 , 2 p 2) 5 k=¡ 5 6 y=¡ 3 x+1 7 a=¡ 4 , b=7 8 a=2,b=4 10 ax¡ 3 y=¡ 5 bx¡ 9 y=¡ 4 c x¡ 16 y=3 dy ...

Answers 495 e 11 Hint: Find dy dx , then determine the nature of the stationary points. 12 Hint: Show that as x! 0 ,f(x)!¡1, and ...

14 1.m 707 .m 843 .cm^422 .cm 562 .cm t dV dt 80 -1250 O 496 Answers f dP dt ̄ ̄ ̄ t=4 =4 Profit is increasing at $ 4000 per yea ...

1_Qw t 0 a(t) -5 -1 0 s t=0 t=2 t=1 1 2 3 4 4 3 2 1 x y y=Rv O x + 0 f'(x) t v(t)ms-1 -48 -40 O Answers 497 5 decreasing a ...

28 0.m 56 0.m 1 1.0 08. 06. 04. 02. x y O y = ~`x 498 Answers 15 av(t)=3¡^1 2 p t+1 a(t)=^1 4(t+1) (^32) bx(0) =¡ 1 , v(0) = 2: ...

Answers 499 3a bupper¼ 1 : 2506 , lower¼ 1 : 2493 cupper¼ 1 : 2506 , lower¼ 1 : 2493 d R 3 ¡ 3 e ¡x 22 dx¼ 2 : 4999 compared to ...

500 Answers 3af(x)=^13 x^3 +^12 x^2 +x+^13 bf(x)=4x (^52) +4x (^32) ¡ 4 x+5 c f(x)=¡cosx¡x+4 df(x)=^13 x^3 ¡^163 x+5 EXERCISE 15 ...