Answers
Chapter 1: Basic arithmetic
Problem 5
Exercises 1.1
1. (a) Rational (b) Rational (c) Rational (d) Irrational (e) Rational (f) Irrational (g) Irrational (h) Rational (i) Rational (j) Irrational
2. (a) 18 (b) 11 (c) 6 (d) 11 (e) -4 3. (f) −1 (g) 2 15 7 (h) 1 20 19 (i) 2 (j) 3 3 1 3. (a) 16.36 (b) 21.87 (c) 8.80 (d) 22.71 (e) -13 20. (f) 0.17 (g) 0.36 (h) 1.20 (i) -4 27. (j) 8.16 4. 1300 5. 950 6. 3000 7. 11 000 8. 600 9. $8 000 000 10. $34 600 000 11. 844 km 12. 0.73 13. 33 14. 3.248 15. 4.21 16. 1.7 17. 79 cents 18. 2.73 19. 1.1 20. 3.6 m 21. $281.93 22. 1.8 g 23. $3.20 24. (a) 7.95 (b) 30.03 (c) 0.37 (d) 5.74 (e) 0.52 25. 0.2 Exercises 1.2 1. 1 2. -11 3. -56 4. 10 5. -4 6. -1 2. 7. -7 51. 8. -35 52. 9. 6.57 10. 2 15 4 - 11. -7 12. −23 13. 10 14. 1 15. 5 16. 3 17. 1 18. 60 19. −20 20. 9 Exercises 1.3 1. (a) 25 16 (b) 1000 51 (c) 5 20 1 (d) 11 5 4 2. (a) 0.4 (b) 1.875 (c) 0 416. o (d) 0 63.oo 3. (a) 50 1 (b) 8 3 (c) 1000 1 (d) 1 1000 97 4. (a) 0.27 (b) 1.09 (c) 0.003 (d) 0.0623 5. (a) 35% (b) 33 % 3 1 (c) 226 % 3 2 (d) 0.1% 6. (a) 124% (b) 70% (c) 40.5% (d) 127.94% 7. (a) 0 52. ; 25 13 (b) 0 07. ; 100 7 (c) 0 168. ; 125 21 (d) 1 09 1. ; 100 9 (e) 0 434. ; 500 217 (f) 0 1225. ; 400 49 8. (a) 0 83. o (b) 0 07.oo (c) 0 13.oo (d) 0 16. o (e) 0 6.o (f) 0 15.oo (g) 0 142857.o o or 0. 142857 (h) 1 18.oo 9. (a) 9 8 (b) 9 2 (c) 1 9 5 (d) 3 9 7 (e) 99 67 (f) 11 6 (g) 45 7 (h) 60 13 (i) 990 217 (j) 1 495 37 10. (a) 0 5.o (b) 7.4 (c) 0.73o (d) 0 68.oo (e) 1 72.oo 11. (a) 8 5 (b) 2 8 1 (c) 11 8 (d) 2 18 7 (e) 45 4 12. 74% 13. 77.5% 14. 17.5% 15. 41.7% Exercises 1.4 1. 20 3 2. 20 7 3. (a) 20 17 (b) 10 7 (c) 1 20 1 (d) 28 3 (e) 5 3 4. $547.56 5. 714.3 g 6. 24 7 7. $65 8. 179 cm 9. (a) 11.9 (b) 5.3 (c) 19 (d) 3.2 (e) 3.5 (f) 0.24 (g) 0.000 18 (h) 5720 (i) 0.0874 (j) 0.376 10. $52.50 11. 54.925 mL 12. 1152.125 g 13. $10.71 14. 5.9% 15. 402.5 g 16. 41.175 m 17. $30.92 18. 3.2 m 19. 573 20. $2898 Problem 5 11 5
minutes after 1 o’clock.
Exercises 1.5 1. (a) 500 (b) 145 (c) 64 1 (d) 3 (e) 2 2. (a) 13.7 (b) 1.1 (c) 0.8 (d) 2.7 (e) -2 6. (f) 0.5 3. (a) a17 (b) y0 1 = (c) a-4 (d) w (e) x5 (f) p10 (g) y6 (h) x21 (i) 4x10 (j) 81y-8 (k) a (l) y x 45 10 (m) w10 (n) p5 (o) x-3 (p) a b a b or 2 3 2 3 - (q) x y x y or 5 2 5 2 - 4. (a) x 14 (b) a-7 (c) m 4 (d) k 10 (e) a-8 (f) x (g) mn 2 (h) p-1 (i) 9 x 22 (j) x 21 5. (a) p 5 q 15 (b) b a 8 8 (c) b a 64 12 3 (d) 49 a 10 b 2 (e) 8 m 17 (f) x 4 y 10 (g) k 27 2 23 (h) 16 y 47 (i) a 3 (j) 125x-21y18 Answer S1-S5.indd 540 7/31/09 1:35:59 PM
6. 4 2 1 7. 324 8. 2 27 10 9. (a) a 3 b (b) 25 1 10. (a) pq 2 r 2 (b) 32 7 11. 9 4 12. 18 1 13. 27 4 14. 81 1 15. 108 1 16. 12 1 17. 2 5 58 22 18. 3888 49 Exercises 1.6 1. (a) 27 1 (b) 4 1 (c) 343 1 (d) 10 000 1 (e) 256 1 (f) 1 (g) 32 1 (h) 81 1 (i) 7 1 (j) 81 1 (k) 64 1 (l) 9 1 (m) 1 (n) 36 1 (o) 125 1 (p) 100 000 1 (q) 128 1 (r) 1 (s) 64 1 (t) 64 1 2. (a) 1 (b) 16 (c) 1 2 1 (d) 1 25 11 (e) 1 (f) 125 (g) 1 3 1 (h) 49 (i) 3 8 3 (j) 32 (k) 2 3 1 (l) 1 (m) 1 36 13 (n) 1 81 19 (o) 1 (p) 16 (q) 15 8 5 - (r) 23 7 - (s) 1 (t) 25 16 3. (a) m-3 (b) x-1 (c) p-7 (d) d −9 (e) k −5 (f) x-2 (g) 2x-4 (h) 3 y −2 (i) 2 1 z-6 or 2 z-6 (j) 5 3t-8 (k) 7 2x-1 (l) 2 5m-6 (m) 3 2y-7 (n) 3x 4 2 + -] g (o) a b 8 + -] g (p) ]x-2g-1 (q) ^5p+1h-3 (r) 2 4] t-9g-5 (s) 4 1 x 11 + -] g (t) 9 5a 3b 7 + -] g 4. (a) 1 t5 (b) 1 x6 (c) 1 y3 (d) 1 n8 (e) 1 w10 (f) 2 x (g) 3 m4 (h) 5 x7 (i) 8 1 x3 (j) 4 1 n (k) 1 1 x+ 6 ] g (l) 8 1 y+z (m) 3 1 k 2 -] g ( n) 3 2 1 x y9 + ^ h (o) x 5 (p) y 10 (q) 2 p (r) ]a+bg2 (s) x y x y + (t) 2 3 w z x y 7 -+ e o Exercises 1.7 1. (a) 9 (b) 3 (c) 4 (d) 2 (e) 7 (f) 10 (g) 2 (h) 8 (i) 4 (j) 1 (k) 3 (l) 2 (m) 0 (n) 5 (o) 7 (p) 2 (q) 4 (r) 27 (s) 2 1 (t) 16 1 2. (a) 2.19 (b) 2.60 (c) 1.53 (d) 0.60 (e) 0.90 (f) 0.29 3. (a) 3 y (b) 3 y2or_3 yi2 (c) 1 x (d) 2x+5 (e) 3 1 1 x- (f) 6q r 3 + (g) x 7 x 1 7 1 or 2 5 ] + g ^5 + h2 4. (a) 2 t 1 (b) 5 y 1 (c) 2 x 3 (d) 9 x3 1 -] g (e) 2 s 4 +1 1 ] g (f) 2 t 2 +3 -1 ] g (g) -2 x y 5 -3 ^ h (h) 2 x 3 +1 5 ] g (i) 3 x-2 -2 ] g (j) 2 y 2 1 7 + -1 ^ h (k) -3 x 5 +4 1 ] g 2 2 1 -a k 3 4 3 -_ i 5. (a) x2 3 (b) x 2 1 (c) x3 2 (d) x3 5 (e) x4 5 6. (a) x x 2x2 3 + 2+ (b) a3 b 2 3 2 - (c) p p 2p2 1 + -1+ 2 (d) x x 1 2 + - + (e) x 2 3x x 1 2 3 2 5 - + - - 7. (a) 2 1 a b 3 - (b) 3 1 y 2 3 ^ - h (c) 6 1 4 a 4 7 ] + g (d) 3 1 x y5 4 ^ + h (e) 7 3 8 6 x 2 9 ] + g Exercises 1.8 1. (a) 3 8. #103 (b) 1 23. #106 (c) 6 19. #104 (d) 1.2#107 (e) 8 67. #109 (f) 4 16. #105 (g) 9#102 (h) 1 376. #104 (i) 2#107 (j) 8#104 2. (a) 5 7. 10 2 # - (b) 5 5. 10 5 # - (c) 4 10 3 # - (d) 6.2#10-4 (e) 2#10-6 (f) 8 10# -8 (g) 7.6 10 6 # - (h) 2.3 10 1 # - (i) 8.5 10 3 # - (j) 7 10 11 # - 3. (a) 36 000 (b) 27 800 000 (c) 9 250 (d) 6 330 000 (e) 400 000 (f) 0.072 3 (g) 0.000 097 (h) 0.000 000 038 (i) 0.000 007 (j) 0.000 5 4. (a) 240 000 (b) 9 200 000 (c) 11 000 (d) 0.36 (e) 1.3 (f) 9.0 (g) 16 (h) 320 (i) 2900 (j) 9.1 5. (a) 6.61 (b) 0.686 (c) 8.25 (d) 1.30 6. 1.305#1010 7. 6.51#10-10 Exercises 1.9 1. (a) 7 (b) 5 (c) 6 (d) 0 (e) 2 (f) 11 (g) 6 (h) 24
(i) 25 (j) 125 2. (a) 5 (b) −1 (c) 2 (d) 14 (e) 4 (f) −67 (g) 7 (h) 12 (i) −6 (j) 10 3. (a) 3 (b) 3 (c) 1 (d) 3 (e) 1 4. (a) a (b) -a (c) 0 (d) 3 a (e) −3 a (f) 0 (g) a+1 (h) - -a 1 (i) x-2 (j) 2-x 5. (a) |a+b|=6 | |a +|b|=6 `|a+b|#|a|+|b| (b) |a+b|=3 | |a +|b|=3 `|a+b|#|a|+|b| (c) |a+b|=1 | |a +|b|=5 `|a+b|#|a|+|b| (d) |a+b|=1 | |a +|b|=9 `|a+b|#|a|+|b| (e) |a+b|=10 | |a +|b|=10 `|a+b|#|a|+|b| 6. (a) x2=|x|=5 (b) x2=|x|=2 (c) x2=|x|=3 (d) x2=|x|=4 (e) x2=|x|=9
7. (a) x+5forx2-5and- -x 5forx1-5 (b) b-3forb23and3-bforx13 (c) a+4fora2-4and- -a 4fora1-4 (d) 2y-6fory23and6-2yfory13 (e) 3x+9forx2-3and-3x-9forx1-3 (f) 4-xforx14andx-4forx24
(g) 2k 1 k 2k 1 k
2 1
2 1
for 2 and for 1
+ - - - - (h) 5x 2 x 5x 2 x 5 2 5 2
for 2 and for 1
- - +
(i) a+bfora2-band- -a bfora1-b (j) p-qforp2qandq-pforp1q
Test yourself 1 1. (a) 20 9 (b) 0.14 (c) 0.625 (d) 200 157 (e) 1.2% (f) 73.3% 2. (a) 49 1 (b) 5 1 (c) 3 1
3. (a) 8.83 (b) 1.55 (c) 1.12 (d) 342 (e) 0.303 4. (a) 1 (b) 1 (c) 39 (d) 2 (e) -10 (f) -1 (g) 4 5. (a) x9 (b) 25y6 (c) a b11 6 (d) 27 8x18 (e) 1 6. (a) 40 29 (b) 3 7 1 (c) 12 (d) 2 2 1 (e) 12 2 1 7. (a) 4 (b) 6 (c) 19 (d) 64 1 (e) 4 (f) 3 (g) 7 1 (h) 2 (i) 1 (j) 4 8. (a) a 5 (b) x 30 y 18 (c) p 9 (d) 16 b 36 (e) 8 x 11 y 9. (a) 2 n 1 (b) x-5 (c) x y 1 + -^ h (d) 4 x+1 1 ] g (e) 7 a+b 1 ] g (f) 2x-1 (g) 2 1 x-3 (h) 3 x 4 (i) 7 x 5 +3 9 ] g (j) 4 m -3 10. (a) 1 a5 (b) n 4 (c) x+1 (d) x-1y (e) 4 7 1 t 4 -] g (f) 5 a+b (g) 1 x 3 (h) b 3 4 (i) 3 ]2x+3g4 (j) 1 x3 11. |a+b|=2 | | |a + b|=8 `|a+b|#|a|+|b| 12. 1 13. 192 1 14. 689 mL 15. (a) 6 h (b) 12 7 (c) 8 1 (d) 33.3% 16. $38 640 17. 70% 18. 6.3#1023 19. (a) 2 x 1 (b) y-1 (c) 6 x+3 1 ] g (d) 2x 3 11 - -] g (e) 3 y 7 20. (a) 1.3#10-5 (b) 1.23#1011 21. (a) 9 7 (b) 330 41 22. (a) 1 x3 (b) 2 5 1 a+ (c) a b 5 c m 23. 14 500 24. LHS= - + - =| 2 5| 7, RHS= -| 2|+ - =| 5| 7. So |a+b|#|a| |+ b| since 7#7. Challenge exercise 1 1. 4 303 278 2. 1 18 11 3. 0 502 51. , %, , . 99 51 0 5o 4. 53 3 1 % 5. 16 1 6. 3.04#1014 7. 83% 8. 1 9990 3271 9. 18 h 10. 1.98 11. 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1 LHS RHS k k k k k k k k k 1 1 1 1 1 1 1 : ` = - + = - + = -= -= - + = -+ + + + + + + ^ ^ ^ ^ h h h h 12. −2 4
.
3 5 13. 0 34 2 1 5 0. , , . , , 7 3 - o 14. 6 3 2 % 15. , x 1 x x x 1 1 1 1 1 when 2 when 1 - - - - 16. 0.73 17. 0.6% 18 4.54 19. 4.14 10 20 # - 20. | | | | | | , , ; | | | | | | , , ; a b a b a b a b a b a b b a b 0 0 0 0 0 0 0 0 when or whena or 2 2 1 1 1 2 1 1 2 + = + + + `|a+b|#|a+b| for all a , bChapter 2: Algebra and surds
Exercises 2.1 1. 7 x 2. 3 a 3. z 4. 6 a 5. 3 b 6. −3 r 7. -y 8. −5 x 9. 0 10. 3 k 11. 9 t 12. 10 w 13. -m 14. -x 15. 0 16. 5 b 17. 11 b 18. -10x 19. 6x-6y 20. a-3b 21. 4xy+2y 22. -6ab2 23. m2-6m+12 24. p2-2p-6 25. 8x+3y 26. -2ab+10b 27. 2bc-ac 28. 2a5 9x3 1 - + 29. x3-2xy2+3x y2 +2y3 30. 3x3+x2-7x-6 Exercises 2.2 1. 10b 2. 8xy 3. 10p2 4. -6wz 5. 15ab 6. 14xyz 7. 48abc 8. 12d2 9. 12a3 10. -27y3 11. 32x10 12. 6a b2 3 13. -10a b3 2 14. 21p q3 4 15. 5a b3 3 16. -8h10 17. k p3 3 18. t 8112 19. -14m11 20. x y 24 6 3 Exercises 2.3 1. 6 x 2. 2 3. 4a2 4. 8 a 5. 4 a 6. 2 y 7. 3 p 8. 2 ab 9. 3 4 y 10. 3x 3 - 11. 3 a 12. 3 1 ab2 13. 2 qs - 14. 3 2 c d2 15. x z 2 2 2 16. 6p q4 17. 4c a b4 7 18. 2a b6 19. 3y x z3 3 - 20. 2b a 6 13 Exercises 2.4 1. 2x-8 2. 6h+9 3. -5a+10 4. 2xy+3x 5. x2 2x - 6. 6a2 16ab - 7. 2a b2 ab2 + 8. 5n2 20n - 9. 3x y3 2+6x y2 3 10. 4k+7 11. 2t-17 12. 4y2 11y + 13. -5b-6 14. 8-2x 15. -3m+1 16. 8h-19 17. d-6 18. a2-2a+4 19. 3x2-9x-5 20. 2ab-2a b2 +b 21. 4x- 1 22. -7y+4 23. 2b 24. 5t-6 25. 2a+26 Exercises 2.5 1. a2 7a 10 + + 2. x2 2x 3 + - 3. 2y2 7y 15 + - 4. m2-6m+8 5. x2+7x+12 6. y2-3y-10 7. 2x2 x 6 + - 8. h2 10h 21 - + 9. x2 25 - 10. 15a2-17a+4 11. 8y2+6y-9 12. xy+7x-4y-28 13. x3 2x2 3x 6 - + - 14. n2 4 - 15. 4x2 9 - 16. 16-49y2 17. a2-4b2 18. 9x2-16y2 19. x2-9 20. y2 36 - 21. 9a2 1 - 22. 4z2 49 - Answer S1-S5.indd 542 7/31/09 1:36:01 PM
23. x2-2xy+11x-18y+18 24. 2ab+2b2-7b-6a+3 25. x3 8 + 26. a3 27 - 27. a2 18a 81 + + 28. k2-8k+16 29. 4 4 x2+ x+ 30. 14 49 y2- y+ 31. 4x2 12x 9 + + 32. 4t2 4t 1 - + 33. 9a2+24ab+16b2 34. x2-10xy+25y2 35. 4a2 4ab b2 + + 36. a2 b2 - 37. a2 2ab b2 + + 38. a2-2ab+b2 39. a3+b3 40. a3-b3 Exercises 2.6 1. t2+8t+16 2. z2-12z+36 3. x2-2x+1 4. y2 16y 64 + + 5. q2 6q 9 + + 6. k2 14k 49 - + 7. n2+2n+1 8. 4b2+20b+25 9. 9-6x+x2 10. 9y2 6y 1 - + 11. x2 2xy y2 + + 12. 9a2 6ab b2 - + 13. 16d2+40de+25e2 14. t2-16 15. x2-9 16. p2 1 - 17. r2 36 - 18. x2 100 - 19. 4a2 9 - 20. x2-25y2 21. 16a2-1 22. 49-9x2 23. x4-4 24. x4 10x2 25 + + 25. 9a b2 2 16c2 - 26. x 4 4 x 2 2 + + 27. a 1 a 2 2 - 28. x2 y 22 x2 y2 4y 4 -^ - h = - + - 29. a b2 2a b c c2 a2 2ab b2 2ac 2bc c2 + + + + = + + + + + ] g ] g 30. ]x+1g2-2]x+1gy+y2=x2+2x+ -1 2xy-2y+y2 31. 12a 32. 32 z2 - 33. 9x2 8x 3 + - 34. x2+3xy+y2-2x 35. 14n2-4 36. x3 12x2 48x 64 - + - 37. x2 38. x4 2x y2 2 y4 - + 39. 8a3+60a2+150a+125 40. 4x4 16x3 15x2 4x 4 + + - - Problem 2, a= b=7, c=9, d=4, e=3, f=8, g=0, h=6, i=1 Exercises 2.7 1. 2^y+3h 2. 5]x-2g 3. 3]m-3g 4. 2 4] x+1g 5. 6 4^ -3yh 6. x]x+2g 7. m m] -3g 8. 2y y^ +2h 9. 3a]5-ag 10. ab b] +1g 11. 2xy]2x-1g 12. 3mn n^ 2+3h 13. 2xy]4x-zg 14. a]6b+ -3 2ag 15. x^5x- +2 yh 16. q2 3q3 2 -_ i 17. 5b b2 3 + ] g 18. 3a2b2]2b-ag 19. (m+5) (x+7) 20. ^y-1 2^h -yh 21. (7+y) (4-3 )x 22. ]a-2 6g] x+5g 23. ]2t+1g^x-yh 24. ]3x-2]ga+2b-3cg 25. 3x2 2x 3 + ] g 26. 3q3 pq2 2 -_ i 27. 3ab 5a b3 2 1 + ^ h 28. 4x x2] -6g 29. 5m n2 ^7mn3-5h 30. 4ab2^6ab3+4h 31. 2rr r] +hg 32. ]x-3]gx+2g 33. (x 4) (y2 2) + + 34. - +]a 1g 35. (a2+1 4) ( ab-3) Exercises 2.8 1. ]x+4 2g] +bg 2. ^y-3h]a+bg 3. ]x+5]gx+2g 4. ]m-2]gm+3g 5. ]d-c a]g +bg 6. ]x+1g^x2+3h 7. ]5a-3g]b+2g 8. ^2y-x x^h +yh 9. ^y+1h]a+1g 10. ]x+5]gx-1g 11. (y+3) (1+a) 12. (m-2) (1-2 )y 13. ^x+5y^h2x-3yh 14. ^a+b2h]ab-4g 15. ]5-x x]g +3g 16. (x+7) (x3-4) 17. ]x-3 7g^ -yh 18. ]d+3 4g] -eg 19. ]x-4 3g^ +yh 20. ]a+3 2g] -bg 21. (x-3) (x2+6) 22. ^q-3^hp+qh 23. ]x-2 3g^ x2-5h 24. ]a-3bg]4+cg 25. ^y+7h]x-4g 26. (x-4) (x3-5) 27. (2x-3) (2x2+4)=2(2x-3) (x2+2) 28. 3(a+2b a) ( +3) 29. 5 (y-3) (1+2 )x 30. ]r+2]grr-3g Exercises 2.9 1. ]x+3]gx+1g 2. ^y+4^hy+3h 3. ]m+1g2 4. ]t+4g2 5. ]z+3g]z-2g 6. ]x+1]gx-6g 7. ]v-3]gv-5g 8. ]t-3g2 9. ]x+10]gx-1g 10. ^y-7^hy-3h 11. ]m-6]gm-3g 12. ^y+12^hy-3h 13. ]x-8]gx+3g 14. ]a-2g2 15. 2 16 x- x+ ] ]g g 16. ^y+4h^y-9h 17. ]n-6]gn-4g 18. ]x-5g2 19. ^p+9h^p-1h 20. ]k-2g]k-5g 21. ]x+4 ]gx-3g 22. ]m-7]gm+1g 23. ^q+10h^q+2h 24. ]d-5]gd+1g 25. ]l-9 ]gl-2g Exercises 2.10 1. ( a2 +1) (a+5) 2. ^5y+2h^y+1h 3. ( x3 +7) (x+1) 4. ( x3 +2) (x+2) 5. ( b2 -3) (b-1) 6. ( x7 -2) (x-1) 7. ^3y-1^hy+2h 8. ]2x+3]gx+4g 9. ^5p-2^hp+3h 10. ]3x+5 2]g x+1g 11. ( y2 +1) (y-6) 12. ]5x-1 2]g x+1g 13. ( t4 -1) (2t-3) 14. ( x3 +4) (2x-3) 15. ^6y-1^hy+8h 16. ]4n-3]gn-2g 17. ]4t-1 2]g t+5g 18. ^3q+2 4^h q+5h 19. ]4r-1 2g] r+6g=2]4r-1g]r+3g 20. ]2x-5 2]g x+3g 21. ^6y-1^hy-2h 22. ^2p-3 3^h p+2h 23. ( x8 +7) (x+3) 24. ]3b-4 4g] b-9g 25. ( x6 +1) (x-9) 26. ]3x+5g2 27. ^4y+3h2 28. ]5k-2g2 29. ]6a-1g2 30. ]7m+6g2
Exercises 2.11 1. ^y-1h2 2. (x+3)2 3. (m+5)2 4. (t-2)2 5. (x-6)2 6. ]2x+3g2 7. ]4b-1g2 8. ]3a+2g2 9. ]5x-4g2 10. ^7y+1h2 11. ^3y-5h2 12. ]4k-3g2 13. ]5x+1g2 14. 9a-22 ] g 15. ]7m+6g2 16. 2 1 t 2 + d n 17. 3 2 x 2 -d n 18. 3 5 1 y 2 + d n 19. x 1x 2 + c m 20. 5k 2 k 2 -d n Exercises 2.12 1. (a+2) (a-2) 2. (x+3) (x-3) 3. (y+1) (y-1) 4. ]x+5]gx-5g 5. ( x2 +7) (2x-7) 6. ( y4 +3) (4y-3) 7. (1+2 ) (1z -2 )z 8. ]5t+1 5]g t-1g 9. ]3t+2 3]g t-2g 10. ]3+4x]g3-4xg 11. (x+2 ) (y x-2 )y 12. ^6x+y^h6x-yh 13. ]2a+3b ]g2a-3bg 14. ^x+10y x^h -10yh 15. ]2a+9b]g2a-9bg 16. ^x+ +2 y x^h + -2 yh 17. (a+ -b 3) (a- +b 1) 18. ]z+ +w 1]gz- -w 1g 19. 2 1 2 1 x+ x -d nd n 20. 3 1 3 1 y y + -e oe o 21. ^x+2y+3^hx-2y+1h 22. (x2+1) (x2-1)=(x2+1) (x+1) (x-1) 23. _3x3+2yi_3x3-2yi 24. _x2+4y2i^x+2y xh^ -2yh 25. (a4+1) (a2+1) (a+1) (a-1) Exercises 2.13 1. (b-2) (b2+2b+4) 2. ]x+3g^x2-3x+9h 3. ]t+1g^t2- +t 1h 4. (a-4) (a2+4a+16) 5. (1-x) (1+ +x x2) 6. ^2+3yh_4-6y+9y2i 7. (y+2z y) ( 2-2yz+4z2) 8. (x-5 ) (y x2+5xy+25 )y2 9. ^2x+3yh_4x2-6xy+9y2i 10. ]ab-1g^a b2 2+ab+1h 11. (10+2 ) (100t -20t+4 )t2 12. 2 3 4 2 3 9 x x2 x - + + d ne o 13. 10 1 100 10 1 a +b a2 -ab+b2 d ne o 14. ^x+ -1 y xh_ 2+2x+ +1 xy+ +y y2i 15. ^5xy+6zh_25x y2 2-30xyz+36z2i 16. a a 1 9 2- + - ^ h 17. 1 3 1 3 9 x x x2 - + + d ne o 18. ^x+ +y 3h_y2-3y-xy+ +9 6x+x2i 19. ^x+ -y 1h_x2+4x-xy+y2-5y+7i 20. ( a2 + -6 b) (4a2+24a+2ab+6b+b2+36) Exercises 2.14 1. 2]x+3]gx-3g 2. 3^p+3h^p-4h 3. 5^y-1h_y2+ +y 1i 4. 2ab a^ +2b) (2a-1h 5. 5]a-1g2 6. -]2x-3]gx-4g 7. 3z z] +5g]z+4g 8. ab]3+2ab]g3-2abg 9. x]x+1]gx-1g 10. 2 3] x-2]gx+2g 11. ]m-5 3]g +ng 12. -7 2] x+1g 13. ^y+5h^y+4h^y-4h 14. ]x-1g]x+2g^x2-2x+4h 15. ]x+1g^x2- +x 1h]x-1g^x2+ +x 1h 16. x x] +2]gx-5g 17. ]x+3g(x-3)2 18. y 2( xy+1 2) ( xy-1) 19. 3 2] -bg^4+2b+b2h 20. 3 3] x-2 2]g x+5g 21. 3]x-1g2 22. (x+2) (x+5) (x-5) 23. z z] +3g2 24. ]x+1g]x-1 2g] x+3 2g] x-3g 25. 2]x+2g]x-2g^x+y xh_ 2-xy+y2i 26. 4a a( +3) (a-3) 27. 5x 2] -xg^4+2x+x2h 28. (a+2) (a-2) (a+3) (a-3) 29. 4 (k k+5)2 30. 3 (x+1)(x-1)(x+3) Exercises 2.15 1. x2+4x+ =4 ]x+2g2 2. b2-6b+ =9 ]b-3g2 3. x2-10x+25=]x-5g2 4. y2+8y+16=^y+4h2 5. m2-14m+49=]m-7g2 6. q2+18x+81=^q+9h2 7. x2+2x+ =1 ]x+1g2 8. t2-16t+64= -]t 8g2 9. x2-20x+100=]x-10g2 10. w2+44w+484=]w+22g2 11. x2-32x+256=]x-16g2 12. 3 4 9 2 3 y2 y y 2 + + =d + n 13. 7 4 49 2 7 x2- x+ =dx- n2 14. 4 1 2 1 a2+ + =a da+ n2 15. 9 4 81 2 9 x2 x x 2 + + =d + n 16. y 5y y 16 25 4 5 2 2 2 - + =d - n 17. k 11k k 16 121 4 11 2 2- + =d - n2 18. x2+6xy+9y2=^x+3yh2 19. 4 4 2 a2- ab+ b2=]a- bg2 20. p2-8pq+16q2=^p-4qh2 Exercises 2.16 1. a+2 2. 2t-1 3. 3 4y+1 4. 2 1 4 d- 5. 5x 2 x - 6. 4 1 y- 7. a b a 3 2 2 -] g 8. 3 1 s s + 9. 1 1 b b2 b + + + 10. 3 5 p+ 11. 3 1 a a + + 12. 2 4 3 x x y 2+ + + 13. x-3 14. 4 2 1 2 p p p 2- + 15. 2a b a b -+ Answer S1-S5.indd 544 7/31/09 1:36:03 PM
Exercises 2.17 1. (a) 4 5x (b) 15 13y+3 (c) 12 8 a+ (d) 6 4p+3 (e) 6 13 x- 2. (a) 2a 1 b - (b) 1 2 1 q p q2 q + - - + ^ h_ i (c) b x y b 2 1 2 10 2 -+ ] ^ g h (d) ab x2-xy+y2 (e) 5 2 3 1 x x x x - -- -] ] ] ] g g g g 3. (a) 5 x (b) x x x 1 2 -- + ] g (c) 3 a b a b + + + (d) 2 2 x x + (e) p q p q p q p q p q 1 1 2 2 + + -= -++ + ^ h^ h (f) x x x 1 3 1 2 + -] ] ] g g g (g) 2 2 3 8 x x x + -- + ] ]g g (h) 1 2 a a 2 + + ] g (i) y y y y y 2 3 1 3 14 13 2 2 + + -+ + ^ ^ ^ _ h h h i (j) x x x x 4 4 3 5 22 + - + + -] ] ] ] g g g g 4. (a) y y x x 3 9 2 8 2 2- + + _ ] i g (b) 15 2 1 y y+ y+ ^ ^h h (c) x x x x 2 3 4 2 10 4 2 - -+ ] ]g g (d) b b b b 1 3 5 10 2 2 + - -] g (e) x 5. (a) 5 2 3 3 13 x x x x - - + -] g] g] g (b) 2 2 3 5 x x x + -] ]g g (c) p q p q p pq q pq 3 2 5 2 2 + -+ -^ h^ h (d) 2 1 a b a b a2 ab b2 + -- - + ] ]g g (e) x y x y x y y 1 + -+ -+ ^ ^ ^ h h h Exercises 2.18 1. (a) -7.1 (b) -6.9 (c) 48.1 (d) -37.7 (e) 0.6 (f) 2.3 (g) -5.3 2. 47 3. -7 4. 375 5. -196 6. 5.5 7. 377 8. 284 9. -40 10. 51.935 11. 1 4 3 - 12. 22.4 13. 1838.8 14. 4 3 15. 15 16. 10 17. 12=2 3 18. 23.987 19. 352.47 20. 93 21. 4 Exercises 2.19 1. (a) 2 3 (b) 3 7 (c) 2 6 (d) 5 2 (e) 6 2 (f) 10 2 (g) 4 3 (h) 5 3 (i) 4 2 (j) 3 6 (k) 4 7 (l) 10 3 (m) 8 2 (n) 9 3 (o) 7 5 (p) 6 3 (q) 3 11 (r) 5 5 2. (a) 6 3 (b) 20 5 (c) 28 2 (d) 4 7 (e) 16 5 (f) 8 14 (g) 72 5 (h) 30 2 (i) 14 10 (j) 24 5 3. (a) 18 (b) 20 (c) 176 (d) 128 (e) 75 (f) 160 (g) 117 (h) 98 (i) 363 (j) 1008 4. (a) x=45 (b) x=12 (c) x=63 (d) x=50 (e) x=44 (f) x=147 (g) x=304 (h) x=828 (i) x=775 (j) x=960 Exercises 2.20 1. 3 5 2. 2 3. 6 3 4. 3 3 5. -3 5 6. 3 6 7. -7 2 8. 8 5 9. -4 2 10. 4 5 11. 2 12. 5 3 13. - 3 14. 2 15. 5 7 16. 2 17. 13 6 18. -9 10 19. 47 3 20. 5 2-2 3 21. 7-5 2 22. -2 3-4 5 23. 7 6+3 5 24. - 2-2 3 25. -17 5+10 2 Exercise 2.21 1. 21 2. 15 3. 3 6 4. 10 14 5. -6 6 6. 30 7. -12 55 8. 14 9. 60 10. 12=2 3 11. 2 48=8 3 12. 15 28=30 7 13. 2 20=4 5 14. -84 15. 2 16. 28 17. 30 18. -2 105 19. 18 20 . 30 50=150 2 21. 2 6 22. 4 3 23. 1 24. 6 8 25. 2 3 26. 3 10 1 27. 2 5 1 28. 3 5 1 29. 2 1 30. 2 2 3 31. 2 3 32. 2 5 9 33. 2 2 5 34. 3 2 35. 7 5 Exercises 2.22 1. (a) 10+ 6 (b) 2 6- 15 (c) 12+8 15 (d) 5 14-2 21 (e) - 6+4 18= - 6+12 2 (f) 5 33+3 21 (g) - -6 12 6 (h) 5-5 15 (i) 6+ 30 (j) 2 54+ =6 6 6+6 (k) - +8 12 12= - +8 24 3 (l) 210-14 15 (m) 10 6-120 (n) - 10-2 2 (o) 4 3-12 2. (a) 10+3 6+3 5+9 3 (b) 10- 35- +2 14 (c) 2 10- +6 10 15-15 6 (d) 12 18 8 12 24 36 8 12 20 60 10 30 5 15 10 30 + - - = + - - (e) 52-13 10 (f) 15- 15+18 10-6 6 (g) 4 (h) -1 (i) -12 (j) 43 (k) 3 (l) -241 (m) -6 (n) 7+2 10 (o) 11-4 6 (p) 25+6 14 (q) 57+12 15 (r) 27-4 35 (s) 77-12 40=77-24 10 (t) 53+12 10 3. (a) 18 (b) 108 2 (c) 432 2 (d) 19+6 2 (e) 9 4. (a) a=21,b=80 (b) a=19,b= -7 5. (a) a-1 (b) 2p- -1 2 p^p-1h 6. k=25 7. 2x-3y-5 xy 8. a=17,b=240 9. a=107,b= -42 10. 9+ 5 units2
Exercises 2.23 1. (a) 7 7 (b) 4 6 (c) 5 2 15 (d) 10 6 14 5 3 14 = (e) 3 3+ 6 (f) 2 12-5 2 (g) 5 5+2 10 (h) 14 3 14-4 7 (i) 20 8 5+3 10 (j) 35 4 15-2 10 2. (a) 4 3-4 2= ^4 3- 2h (b) 47 6+7 3 -^ h (c) 19 2 15 4 18 19 15 6 2 2 -= --^ h - ^ h (d) 13 19 8 3 13 8 3 19 - = --^ h (e) 6+ +2 5 3+5 2 (f) 2 6 15-9 6+2 10-6 3. (a) 2 2 (b) -^2+ 6-3 2+3 3h= - -2 6+3 2-3 3 (c) 39 22 5+14 2 (d) 10 6 6 16 3 84 8 14 6 21 14 5 3 8 3 4 - - - + =- + + -^ h (e) -4 (f) 4 2 (g) 15 20 12 19 6 25 3 6 15 19 6 65 3 6 + + - = + - (h) 6 6+9 2+2 3 (i) 21 4 6+9 3 (j) 15 4 30 3 30-30 5- (k) 13 28-2 6-7 3 (l) 2 2 15+2 10-2 6- 3-5 4. (a) a=45,b=10 (b) a=1,b=8 (c) 2 1 , 2 1 a= - b= (d) 1 9 5 , 9 8 a= - b= - (e) a=5,b=32 5. 2 2 3 2 2 3 2 1 2 1 2 4 2 1 2 1 2 1 2 1 2 4 2 2 2 1 2 1 2 1 2 4 2 2 1 2 2 2 1 2 1 3 2 2 2 2 2 2 2 # # + -+ = + -- + = -- -+ = -- - + + = - + = - + = ^ ^ ^ h h h So rational 6. (a) 4 (b) 14 (c) 16 7. 3 3 5- 2- 15- 3 8. 3 2 2 2 2 8 3 2 2 2 3 2 2 3 2 2 2 8 2 2 3 2 2 2 3 2 2 2 8 2 9 4 2 6 4 2 4 2 1 6 4 2 4 2 6 4 2 4 2 6 2 2 # # # + + = + -- + = -+ = -- + = - + = - + = ^ ^ h h So rational 9. x= -^ 3+2h 10. 4 4 4 b b b -+ + Test yourself 2 1. (a) -2y (b) a+4 (c) -6k5 (d) 15 5x+3y (e) 3a-8b (f) 6 2 (g) 4 5 2. (a) ]x+6]gx-6g (b) ]a+3]ga-1g (c) 4ab b] -2g (d) (y-3) (5+x) (e) 2^2n- +p 3h (f) (2 x) (4 2x x2) - + + 3. (a) 4b-6 (b) 2x2+5x-3 (c) 4m+17 (d) 16x2-24x+9 (e) p2-25 (f) - -1 7a (g) 2 6-5 3 (h) 3 3- +6 21-2 7 4. (a) a a b 3 9 8 2 2^ + + h (b) 2 15 m- 2 ] g 5. V=157.464 6. (a) 17 (b) 17 6 15-9 7. 3 2 4 5 x x x + -+ ] ]g g 8. (a) 36 (b) -2 (c) 2 (d) 216 (e) 2 9. (a) 5 1 (b) 8 10. d=11.25 11. (a) 15 2 3 (b) 2 2+ 6 12. (a) 3 6- -6 4 3+4 2 (b) 11+4 7 13. (a) 3 (x-3) (x+3) (b) 6]x-3]gx+1g (c) 5^y+2h_y2-2y+4i 14. (a) 3y x 4 3 (b) 3 1 1 x- 15. (a) 99 (b) 24 3 16. (a) a2-b2 (b) a2+2ab+b2 (c) a2-2ab+b2 17. (a) ]a-bg2 (b) ]a-b ag^ 2+ab+b2h 18. 2 3 3+1 19. (a) 4 3 ab b+ a (b) 10 3x-11 20. 7 21 5-46- 2 Answer S1-S5.indd 546 7/31/09 1:36:05 PM
21. (a) 6 2 (b) -8 6 (c) 2 3 (d) 3 4 (e) 30a b2 (f) 3n m 4 (g) 2x-3y 22. (a) 2 6+4 (b) 10 14-5 21-6 10+3 15 (c) 7 (d) 43 (e) 65-6 14 23. (a) 7 3 7 (b) 15 6 (c) 5 1 2 + (d) 15 12-2 6 (e) 53 20+3 15+4 10+3 6 24. (a) 10 10 x+ (b) 21 17a-15 (c) (x 1) (x 1) x 3 2 + -- (d) 1 1 k- (e) 3 15- 6-15 3-15 2 25. (a) n=48 (b) n=175 (c) n=392 (d) n=5547 (e) n=1445 26. 3 121 71 27. (b), (c) 28. (d) 29. (a), (d) 30. (c) 31. (c) 32. (b) 33. (a) 34. (d) 35. (b) Challenge exercise 2 1. (a) 2a b2 -8ab2+6a3 (b) y4-4 (c) 8x3 60x2 150x 125 - + - 2. 17 17 3+2 5+20 3. 2 2 1 4 2 or 4. a b x a b x a b x 4 2 2 2 2 2 + + = d + n 5. (a) ]x+4]gx+9g (b) _x2-3y xi_ 2+2yi=(x+ 3y x) ( - 3y x)_ 2+2yi (c) ]5x+7 25g^ x2-35x+49h (d) ]b-2g]a+2g]a-2g 6. 4x2+12x+ =9 ]2x+3g2 7. x y 1 1 2 -+ ] g 8. 2 5 9. 1 1 a a a 2 2 - + + ] g 10. 2 2 x b a x b a + -d nd n 11. x x x x x x xy y 3 3 2 3 3 6 2 3 4 6 - + -- + + -] g] g] g 12. (a) 8x3 12x2 6x 1 - + - (b) 2 1 3 4 x x 2 -+ ] g 13. x3 7x2 15x 9 + -- 14. 13 66 6 4 2 15 4 5 65 3 - + - + 15. x x x 3 2 9 1 3 1 2 2 + + =d + n 16. x=2 17. 10 400-59 5 18. (a) 3 121 71 (b) , a b 23 17 23 14 = = - 19. 1 2 1 i = 20. 4 r 4 3 3 r r r = = Chapter 3: Equations Exercises 3.1 1. t= -5 2. z= -5.6 3. y=1 4. w=6.7 5. x=12 6. x=4 7. 15 1 y= 8. b=35 9. n= -16 10. r=4 11. y=9 12. k=6 13. d=2 14. x=5 15. y=15 16. x=20 17. m=20 18. x=4 19. a= -7 20. y=3 21. b= -4 22. x=3 23. 1 3 2 a= - 24. t= -4 25. x=1.2 26. a=1.6 27. 8 1 b= 28. t=39 29. p=5 30. xZ4.41 Exercises 3.2 1. 3 3 1 b= 2. x=35 3. 4 9 4 y= 4. 1 35 9 x= 5. 5 8 5 k= 6. x=36 7. t=0.6 8. x= -3 9. y= -1.2 10. x=69 11. w=13 12. t=30 13. x=14 14. x= -1 15. x= -0.4 16. p=3 17. t=8.2 18. x= -9.5 19. q=22 20. x= -3 21. b=0.8 22. a= -0.375 23. x=3 24. y=1 25. 1 3 2 t= - Exercises 3.3 1. t=8.5 2. l=122 3. b=8 4. a=41 5. y=4 6. r=6.68 7. x=6.44 8. n=15 9. 3 3 2 y1= 10. h=3.7 11. (a) BMI=25.39 (b) w=69.66 (c) h=1.94 12. r=0.072 13. x1= -9 14. t=2.14 15. x=!2 16. r=2.12 17. r=10.46 18. x=1.19 19. x=5.5 20. r=3.3 Exercises 3.4 1. (a) x23 -4 -3 -2 -1 0 1 2 3 4 (b) y#4 -4 -3 -2 -1 0 1 2 3 4 2. (a) t27 (b) x$3 (c) p2 -1 (d) x$ -2 (e) y2 -9 (f) a$ -1 (g) y 2 2 1 $ - (h) x1 -2 (i) a# -6 (j) y112 (k) b1 -18 (l) x230 (m) x 3 4 3 # (n) m 14 3 2 2 (o) b 16 4 1 $ (p) r# -9 (q) z28 (r) w 2 5 4 1 (s) x$35 (t) t$ -9 (u) q 6 5 2 2 - (v) x 1 3 2 2 - (w) b 11 4 1 # -
3. (a) 11 1x 7 0 1 2 3 4 5 6 7 8 (b) -2#p15 -3 -2 -1 0 1 2 3 4 5 (c) 11 1x 4 -3 -2 -1 0 1 2 3 4 5 (d) -3# #y 5 -3 -2 -1 0 1 2 3 4 5 (e) y 6 1 1 3 2 1 1 -3 -2 -1 0 1 2 3 4 5 Exercises 3.5 1. (a) x=!5 (b) y=!8 (c) -41 1a 4 (d) k$1,k# -1 (e) x26,x1-6 (f) -10# #p 10 (g) x=0 (h) a214,a1 -14 (i) -121 1y 12 (j) b$20,b# -20 2. (a) x=5,-9 (b) n=4,-2 (c) a22,a1-2 (d) 4# #x 6 (e) x=3,-6 (f) x 5, 4 7 5 = - (g) 3 y 2 2 1 1 1 - (h) x$9,x# -6 (i) x=!12 (j) 2# #a 10 3. (a) 1 4 1 x= (b) a 3, 3 1 = - (c) 2 3 1 b= (d) No solutions (e) 2 7 2 y= - (f) x=7 (g) m 5 1, 3 2 = (h) d 2 , 2 1 1 4 3 = - (i) y , 5 4 2 = - (j) No solutions 4. (a) x 2, 2 1 = - (b) 3, 2 3 1 y= (c) 10, 1 5 3 a= - (d) x 4, 7 3 1 = - (e) d=4,-5 5. (a) t 3, 1 5 2 = - (b) 1 t 3 5 2 1 1 - -3 -2 -1 0 1 2 3 4 5 Exercises 3.6 1. (a) x=3 (b) y=!8 (c) n=!2 (d) x=!2 5 (e) p=10 (f) x=!5 (g) y=!3 (h) w=2 (i) n=!4 (j) q= -2 2. (a) p=!6.71 (b) x=4.64 (c) n=2.99 (d) x=!5.92 (e) y=1.89 (f) d=!2 55. (g) k=!4.47 (h) x=2.22 (i) y=!3 81. (j) y=3.01 3. (a) n=27 (b) t=16 (c) x=32 (d) t=8 (e) p=243 (f) m=625 (g) b=216 (h) y=27 (i) a=128 (j) t=81 4. (a) 5 1 x= (b) 2 1 a= (c) 2 1 y= (d) x 7 1 ! = (e) 3 2 n= (f) a=2 (g) x=!2 (h) b=9 (i) x 3 2 ! = (j) b 1 2 1 ! = 5. (a) x 512 1 = (b) 6 4 1 x= (c) 81 1 a= (d) 625 1 k= (e) x 8 1 ! = (f) x=4 (g) y=!8 (h) n 7 32 19 = (i) b=8 (j) 1 216 127 m= 6. (a) n=4 (b) y=5 (c) m=9 (d) x=5 (e) m=0 (f) x=3 (g) x=2 (h) x=2 (i) x=1 (j) k=2 7. (a) x=2 (b) x=1 (c) x= -2 (d) n=2 (e) x=0 (f) x=6 (g) y 3 1 = (h) x=2 (i) x=2 (j) a=0 8. (a) 2 1 m= (b) 3 1 x= (c) 3 1 x= (d) 2 1 k= - (e) 3 2 k= - (f) 4 3 n= (g) 1 2 1 x= (h) 3 2 n= (i) 6 1 k= - (j) 1 3 2 x= 9. (a) x= -1 (b) x 1 3 1 = - (c) k= -4 (d) n=3 (e) x 21 2 = - (f) x 3 2 = - (g) x 4 2 1 = - (h) x 1 11 7 = - (i) x 1 5 4 = (j) x=18 10. (a) 4 1 m= (b) 2 4 3 k= - (c) 2 8 3 x= (d) 1 2 1 k= (e) 18 1 n= (f) 2 1 n= - (g) 5 4 x= (h) 3 6 1 b= - (i) 1 7 1 x= - (j) m=5 Puzzle
1. All months have 28 days. Some months have more days
as well. 2. 10 3. Bottle $1.05; cork 5 cents
4. 16 each time 5. Friday
Exercises 3.7
1. y=0,-1 2. b=2,-1 3. p=3,-5 4. t=0 5,
5. x= - -2, 7 6. q=!3 7. x=!1 8. a=0,-3
9. x=0,-4 10. x 2 1 ! = 11. x 1, 1 3 1 = - - 12. y 1, 1 2 1 = - 13. b , 4 3 2 1 = 14. x=5,-2 15. x 0, 3 2 = 16. x 1 2, 2 1 = 17. x=0, 5 18. y= -1, 2 19. n=3,5 20. x=3, 4 21. m= -6, 1 22. x=0,- -1, 2 23. y=1,- -5, 2 24. x=5,-7 25. m=8,-1 Exercises 3.8 1. (a) x=! 5-2 (b) a=! 7+3 (c) y=! 23+4 (d) x=! 13-1 (e) p=! 44- =7 !2 11-7 (f) x=! 28+ =5 !2 7+5 (g) y=! 88-10=!2 22-10= ^2 ! 22-5h (h) x=! 2+1 (i) n=! 137-12 (j) y 3 2 5 ! = + 2. (a) x=3 45. ,-1 45. (b) x= -4 59. ,-7 41. (c) q=0 0554. ,-18 1. (d) x=4 45. ,-0 449. (e) b= -4 26. ,-11 7. (f) x=17 7 6 34. , . (g) r=22 3. ,-0 314. (h) x= -0 683. ,-7 32. (i) a=0 162. ,-6 16. (j) y=40 1. ,-0 0749. Exercises 3.9 1. (a) y= -0 354. ,-5 65. (b) x=1 1 5, . (c) b=3 54. ,-2 54. (d) x=1,-0 5. (e) x= -0 553 0 678. , . (f) n=0 243. ,-8 24. (g) m= - -2, 5 (h) x=0 7, (i) x=1,-6 (j) y=2 62 0 382. , . 2. (a) x 2 1! 17 =- (b) x 6 5! 13 = (c) q 2 4 28 2 7 ! ! = = (d) h 8 12 128 2 3 2 2 ! ! =- =- (e) s 6 8 40 3 4 10 ! ! = = (f) x 2 11! 133 =- (g) d 12 5! 73 =- (h) x 2 2 32 1 2 2 ! ! = = (i) t 2 1! 5 = (j) x 4 7! 41 = Exercises 3.10 1. -31x10 2. 01 1y 4 3. n#0,n$1 4. x#-2,x$2 5. n1-1,n21 6. -5# #n 3 7. c1-1,c22 8. -4# #x -2 9. 41 1x 5 10. b#-2,b$-1 11. a1-1,a21 12. y 1 ,y 2 1 2 1- 2 13. x ,x 3 2 1 # $ 14. b 3,b 5 2 1- 2 15. 1 x 2 1 3 1 # # - - 16. -4# #y 3 17. x1-4,x24 18. -1# #a 1 19. -21x13 20. x#-1,x$3 21. 01 1x 2 22. 1 a 1 2 1 # # 23. y 2,y 5 4 #- $ 24. m 1 ,m 3 2 1 2 1 1- 2 25. 1 x 1 3 1 # # Exercises 3.11 1. a=1,b=3 2. x=2,y=1 3. p=2,q= -1 4. x=6,y=17 5. x= -10,y=2 6. t=3,v=1 7. x= -3,y=2 8. x= -64,y= -39 9. x=3,y= -4 10. m=2,n=3 11. w1= -1,w2=5 12. a=0,b=4 13. p= -4,q=1 14. x1=1,x2= -1 15. x= -1,y= -4 16. s=2,t= -1 17. a= -2,b=0 18. k= -4,h=1 19. v1= -2,v2=4 20. x=2,yZ1 41. Problem
23 adults and 16 children.
Exercises 3.12 1. x=0,y=0 and x=1,y=1 2. x=0,y=0 and x= -2,y=4 3. x=0,y=3 and x=3,y=0 4. x=4,y= -3 and x=3,y= -4 5. x= -1,y= -3 6. x=3,y=9 7. t= -2,x=4 and t=1,x=1 8. m= -4,n=0 and m=0,n= -4 9. x=1,y=2 and x= -1,y= -2 10. x=0,y=0 and x=1,y=1 11. x=2,y=1 and x= -1,y= -2 12. x=0,y=1 13. x=1,y=5 and x=4,y=11 14. x ,y 4 1 4 = = and x= -1,y= -1 15. t ,h 2 1 4 1 = - = 16. x=2,y=0 17. x=0,y=0 and x= -2,y= -8 and x=3,y=27 18. x=0,y=0 and x=1,y=1 and x= -1,y=1 19. x ,y 2 1 2 4 3 = = 20. 13 5 , 13 12 x= - y= - Exercises 3.13 1. x= -2,y= -8,z= -1 2. a= -2,b= -1,c=2 3. a= -4,b=2,c=7 4. a=1,b=2,c= -3 5. x=5,y=0,z= -2 6. x=0,y= -5,z=4 7. p= -3,q=7,r=4 8. x=1,y= -1,z=2
Test yourself 3 1. (a) b=10 (b) a= -116 (c) x= -7 (d) p#4 2. (a) A=1262.48 (b) P=8558.59 3. (a) x2-8x+16=]x-4g2 (b) k2+4k+ =4 ]k+2g2 4. (a) x= -2,y=5 (b) x=4,y=1 and x ,y 2 1 8 = - = - 5. (a) x=2 (b) 4 1 y= 6. (a) b 2, 1 3 1 = - (b) g 2, 4 1 = (c) x$4,x#3 7. (a) A=36 (b) b=12 8. x , 2 1 1 = 9. -11 #y 3 10. (a) x= -0 298. ,-6 70. (b) y=4 16. ,-2 16. (c) n=0 869. ,-1 54. 11. (a) V=764.5 (b) r=2.9 12. x 71 4 1 2 13. x12,x29 14. x=2 4. ,y=3 2. 15. (a) V=2100 (b) r=3.9 16. (a) ii (b) i (c) ii (d) iii (e) iii
17. a=3,b=2,c= -4 18. n 0,n 3 3 1 2 1 - 19. x= -4 20. x= -2 21. (a) y23 (b) -3# #n 0 (c) x=2 (d) x=2 (e) x 3, 1 5 2 = - (f) t$1,t# -2 (g) -4# #x 2 (h) x= -3 (i) y22,y1 -2 (j) x#-1,x$1 (k) 6 5 x= (l) 2 1 2 b # # - (m) No solutions (n) 2 3 1 , 5 3 t= (o) -11 1x 3 (p) m#-3,m$2 Challenge exercise 3 1. y=1 2. x1-a x, 2a 3. a=3,b=!2 4. x=2 56. ,-1 56. 5. ]x+3g]x-3g]x-2g^x2+2x+4h;x=!3 2, 6. x=1,y=2 and x= -1,y=0 7. b=4;x=! 17+4Z8 12. ,-0 123. 8. x=!1 9. -11 1t 1 10. -3# #x 8 11. 4 1 x= 12. r=2.31 13. No solutions 14. x=! b+a2+a 15. P=2247.36 16. x 3 4 10 2 ! = ^ h 17. y 1,y 5 3 1- 2 Chapter 4 : Geometry 1 Exercises 4.1 1. (a) y=47c (b) x=39c (c) m=145c (d) y=60c (e) b=101c (f) x=36c (g) a=60c (h) x=45c (i) y=40c (j) x=80c 2. (a) 121c (b) 72 29c l (c) 134 48c l 3. (a) 42c (b) 55 37c l (c) 73 3c l
4. (a) (i) 47c (ii) 137c (b) (i) 9c (ii) 99c (c) (i) 63c
(ii) 153c (d) (i) 35c (ii) 125c (e) (i) 52c (ii) 142c
(f) (i) 15c7l (ii) 105c7l (g) (i) 47c36l (ii) 137c36l (h) (i) 72c21l (ii) 162c21l (i) (i) 26c11l (ii) 116c11l (j) (i) 38c51l (ii) 128c51l 5. (a) x=49c (b) 41c
(c) 131c 6. (a) y=15c,x= =z 165c (b) x=142c,y=48c,z=28c (c) a=43c,b=137c,c=101c (d) a=97c,b= =d 41c, c=42c (e) a=68c, b=152c, c=28c (f) a=10c,b=150c 7. x x x x 0 x x 8 10 2 10 10 7 10 36 18 360 20 - + - + + + + = = = (angle of revolution) ( ) ( ) ABE x EBC x ABE EBC 8 10 8 20 10 150 2 10 2 20 10 30 150 30 180 c c c c c + + + + = -= -= = -= -= + = + = ABC ` + is a straight angle ( ) DBC x DBC EBC 7 10 7 20 10 150 150 30 180 c c c c + + + = + = + = + = + = DBE ` + is a straight angle
` AC and DE are straight lines
8. AFC x CD bisects ` ` + = AFE + ( ) ( ) ( ) ( ) DFB x x CFE x x x AFC CFE AFB AFB 180 180 180 180 2 is a straight angle
(vertically opposite angles) is a straight angle ` c c c c + + + + + + = - -= = - + -= = 9. +ABD++DBC 110 3 3 70 180 x x c = - + + =
So +ABC is a straight angle. AC is a straight line.
10. +AEB++BEC+ +CED
50 8y 5y 20 3y 60
90c
= - + - + +
=
So +AED is a right angle. Exercises 4.2 1. (a) a= = = =b e f 148c,c= = =d g 32c (b) x= =z 70c,y=110c (c) x=55c,y=36c,z=89c (d) y=125c,x= =z 55c (e) n= = = = = = =e g a c z x 98c, 82 o=m= = = = = =h f b d y w= c Answer S1-S5.indd 550 8/1/09 6:50:34 PM
