EXERCISE 1A

1.     

2.     

3.     

4.      (i)   46   (ii)   41   (iii)   208

5.      (i)   3   (ii)   5   (iii)   8

6.      8

7.      5

8.      12

9.      2

10.  €2,315.25

11. 

12. 

13.  3

14.  1

 

EXERCISE 1B

1.     

2.     

3.     

4.     

5.     

6.     

7.     

8.     

9.     

10. 

11. 

12. 

13. 

14. 

15. 

16. 

 

EXERCISE 1C

1.      (i) 7   (ii) 12        (iii) 18

2.      (i) 4   (ii) 26        (iii) 10       (iv) 126

3.      (i) 6   (ii) 1          (iii) -4

4.      (i) 8   (ii) 15        (iii) 44

5.      (i) 25 (ii) 83        (iii) 49

6.      (i) 16 (ii) 20        (iii) 48

7.      (i) 24 (ii) 64        (iii) 25

8.      (i) 2   (ii) -4       

9.      (i) -1  (ii) -4       

10.  (i) 2   (ii) 1         

11.  -3

12. 

13.  9

14.  7

15.  -1

16. 

17.  19

18.  -1

19.  -3

20.  30

21.  2

 

EXERCISE 1D

1.     

2.     

3.     

4.      Ann is 7, Bill is 13.

5.      Carl is 26, Dorothy is 6.

6.      16, 17 and 18.

7.      28, 29 and 30.

8.      43, 44, 45 and 46.

9.      68, 69, 70, 71 and 72.

10.  The youngest child is 13.

11. 

12. 
Ann gets €285, Barry gets €255.

13.  Emma is 20.

14. 
Tom catches up 2 hours after Dan has started.

15.  Amy gets €35, Brian gets €45 and Chris gets €90.

 

EXERCISE 1E

1.     

2.     

3.     

4.     

5.     

6.     

7.     

8.      (i) has solution x = 1                (ii) 7

9.      (i)  has solution x = 5         (ii) 2

10.  (i) (ii) 1

11.  (i) 5   (ii) 5

12. 

 

EXERCISE 1F

  1. x = 4, y = 2
  2. x = 3, y = 5
  3. x = , y = 0
  4. x = 3, y = 3
  5. x = 6, y = 4
  6. x = 2, y = 3
  7. x = 3, y = 4
  8. x = 2, y = -1
  9. x = 5, y = -4
  10. x = -3, y = 2
  11. x = 2, y = 4
  12. x = 1, y = 3
  13. x = 5, y = 6
  14. x = 1, y = -2
  15. x = 0, y = 3

 

EXERCISE 1G

  1. x = 2, y = 3
  2. x = 4, y = 6
  3. x = 2, y = 4
  4. x = 1, y = -2
  5. x = 3, y = 1
  6. x = -6, y = 5
  7. x = -1, y = 9
  8. x = 2, y = 1
  9. x = 5, y = -1
  10. x = -4, y = 5
  11. x = 1, y = -4
  12. x = 1, y = -4
  13. x = 15, y = 12

 

EXERCISE 1H

    8. €130
    9. 23
    10. 36
    11. The length is 18 m and the breadth is 12 m.

 

CHAPTER TEST 1

  6. (i) 6               (ii) 19       (iii) 13
  8. 3
  9. The man is aged 42, the son 14.
  10. 12 pages
  11. (i) x =6, y = -5               (ii) x = 2, y = -1         (iii) x = 4, y = 3
  12. 24

 

EXERCISE 2A

  1. e.g. N
  2. e.g.
  3. e.g. N, Z, Q, Z\N, Q\Z, R\Q etc.
  6. (i) 0.6            (ii) 0.55    
    (iii) 0.1234567                (iv) 4.76
  7. (i) 0.142857  (ii) 0.285714             
    (iii) 0.428571 (iv) 0.571428
    (v) 0.714285 (vi) 0.714285
  8. (i) 0.6775      (ii) 0.03     (iii) 0.421875            
  9. (i) 17,300      (ii) 930      (iii) 20      
    (iv) 532,100   (v) 2,600
  10. (i) 3,000        (ii) 2,100   (iii) 1,560 
    (iv) 780          (v) 7,000
  11. (i) 1,600        (ii) 925,400                (iii) 200    
    (iv) 1,920       (v) 4,783,000
  12. (i) 4.5            (ii) 2.5       (iii) 7.5
  13. (i) 2.09          (ii) 4.5       (iii) 6

 

EXERCISE 2B

 

EXERCISE 2C

3.      (i) 81             (ii) 81        (iii) 2         (iv) 2       
(v) 3              (vi) 3         (vii) 10      (viii) 10
(ix) 125          (x) 125

4.      (i) 0.5            (ii) 0.5       (iii) 0.04    (iv) 0.04   
(v) 0.125       (vi) 0.125  (vii) 0.5     (viii) 0.5
(ix) 0.0625     (x) 0.0625

5.     

6.     

7.     

8.     

9.     

10.  n = 2

11. 

12. 

13. 

14. 

15. 

16.  (a) = (iii), (b) = (ii), (c) = (v), (d) = (i), (e) = (iv)

 

EXERCISE 2D

  7. 9.8

 

CHAPTER TEST 2

  1. e.g.
  3. (i)  0.85         (ii) 0.2125
    (iii) 2.046875 (iv) 0.321
  4. (i) 7100         (ii) 4,260
  5. 5,

 

EXERCISE 3A

    1. (i) x = 60            (ii) y = 20  (iii) z = 30
    2. (i) x = 127, y = 53               (ii) w = 72, z = 36
      (iii) p = 30, q = 110             (iv)       r = 15
    4. (i) x = 40            (ii) y = 18  (iii) z = 15
    5. (i) x = 36, y = 36                 (ii) w = 38, z = 84

 

EXERCISE 3B

2.      (i) x = 30, y = 90                 (ii) w = 140, z = 20
(iii) p = 65, q = 65               (iv) r = 60, s = 120

9.      x = 40, y = 100

11. 

13.  x = 70

 

EXERCISE 3C

7.      (i) h = 8 cm        (ii) l = 24 cm

8.      21 cm2

9.      16 cm

10.  (i) 18 cm2           (ii) 8 cm

 

CHAPTER TEST 3

1.      (i) x = 36            (ii) y = 18

2.      (i) x = 22.5, y = 135            (ii) w = 5, z = 45

3.      48˚:60˚:72˚

6.     

 

EXERCISE 4A

1.      (i) 7(x+2)           (ii) 6(a-3)  (iii) 4(y+4)

2.      (i) 3(x+3)           (ii) 10(a-7)                 (iii) 9(y+5)

3.      (i) 5x(2x-3y)      (ii) 4a(2a+5b)            (iii) 3x(2x-3b)

4.      (i) 3c(5b-1)        (ii) 4a(3a+1)              (iii) 2x(2x-1)

5.      (i) (3x+z)(x+2)   (ii) (a+4)(5b+c)

6.      (i) (q-2)(p+3)     (ii) (3c+d)(4a+2) = 2(3c+d)(2a+1)

7.      (i) (2c+d)(3a-5b)                (ii) (3z+4)(7x-2y)

8.      (i) (4c+1)(10a-3b)              (ii) (4z-5)(3x-y)

9.      (i) (n-5)(a+b)     (ii) (2ab-3)(2a+b)

10.  (i) (x+2y)(x-y)(x+y)            (ii) (3a-4b)(2a+c)

11.  (i) (xy-z)(2x-3)   (ii) (3a+b)(3a+4c)

12.  (i) (3a-2)(4ab+3c)              (ii) (x-b)(x+a)

 

EXERCISE 4B

1.                (i) (a-b)(a+b)            (ii) (c-d)(c+d)            (iii) (y-z)(y+z)

  1. (i) (a-3)(a+3) (ii) (b-6)(b+6)            (iii) (y-10)(y+10)
  2. (i) (a-2)(a+2) (ii) (b-7)(b+7)            (iii) (y-8)(y+8)
  3. (i) (a-30)(a+30)             (ii) (b-20)(b+20)        (iii) (y-15)(y+15)
  4. (i) (a-17)(a+17)             (ii) (b-22)(b+22)        (iii) (y-35)(y+35)
  5. (i) (a-16)(a+16)             (ii) (b-41)(b+41)        (iii) (y-19)(y+19)
  6. (i) (a-1)(a+1) (ii) (b-1)(b+1)            (iii) (y-1)(y+1)
  7. (i) (a-15b)(a+15b)         (ii) (b-24c)(b+24c)    (iii) (y-14z)(y+14z)
  8. (i) (a-9b)( a+9b)            (ii) (b-12c)(b+12c)    (iii) (y-13z)(y+13z)
  9. (i) (2a-11b)(2a+11b)     (ii) (5b-19)(5b+19)    (iii) (7y-26)(7y+26)
  10. (i) (8a-30)(8a+30)         (ii) (4b-33)(4b+33)    (iii) (9y-40)(9y+40)
  11. (i) (6a-21)(6a+21)         (ii) (27b-15)(27b+15)                 (iii) (3y-11)(3y+11)
  12. (i) 800  (ii) 160               (iii) 140
  13. (i) 260  (ii) 800               (iii) 80
  14. (i) 320  (ii) 4,000            (iii) 80
  15. (i) 4      (ii) 1
  16. (i) 12    (ii) 18
  17. (i) 33    (ii) 5
  18. (i) 3(a-3)(a+3)               (ii) 2(x-5y)(x+5y)      (iii) 3(10a-1)(10a+1)
  19. (i) 2(x-2)(x+2)               (ii) 2(x-7)(x+7)          (iii) 5(x-2y)(x+2y)
  20. (i) 2(a-4b)(a+4b)           (ii) 3(x-5y)(x+5y)      (iii) 2(2p-1)(2p+1)
  21. (i) 2(5a-1)(5a+1)           (ii) 3(2a-1)(2a+1)      (iii) 6(10a-1)(10a+1)
  22. (i) 7(x-3)(x+3)               (ii) 5(5a-1)(5a+1)      (iii) 3(3a-2)(3a+2)
  23. (3x-y)(3x+y)
  24. (2a-b)(2a+b)
  25. (x-5y)(x+5y)

 

EXERCISE 4C

  1. (i) (2x+4)(x+1)               (ii) (3y+5)(y+1)          (iii) (2x+1)(x+2)
  2. (i) (2x+5)(x+1)               (ii) (3x+3)(x+1)         (iii) (2x+1)(x+1)
  3. (i) (2a-5)(a-2)                (ii) (3x-2)(x-1)           (iii) (2x-7)(x-1)
  4. (i) (2x-2)(x-4)                (ii) (3x-3)(x-2)           (iii) (2p-4)(p-3)
  5. (i) (4x+1)(x+2)               (ii) (6x-1)(x-1)           (iii) (8x+2)(x+1)
  6. (i) (4a-1)(2a-1)              (ii) (3x+4)(x+1)         (iii) (2y-3)(y-5)
  7. (i) (3x-10)(x+1)             (ii) (2x+2)(2x+2)       (iii) (3x-2)(x-3)
  8. (i) (5x+5)(x-4)               (ii) (6x+3)(x-1)          (iii) (7x+1)(x+1)
  9. (i) (2x-2)(x+2)               (ii) (3x-2)(x+8)          (iii) (3x+5)(x-1)
  10. (i) (5a-2)(a-5)                (ii) (2b-10)(b+1)        (iii) (2c-2)(c-3)
  11. (i) (x-25)(x-1)                (ii) (x+12)(x-1)          (iii) (4x+5)(x-2)
  12. (i) (5x+2)(x-2)               (ii) (3x+4)(x-2)          (iii) (5x+2)(x-3)
  13. (i) (x-2)(x+14)               (ii) (y-4)(y-1)             (iii) (z+25)(z-2)
  14. (i) (2x+2)(x+1)               (ii) (2x-5)(2x+3)        (iii) (x-20)(x-1)
  15. (i) (x-5)(x-4)                  (ii) (x+4)(x-3)            (iii) (5x+1)(2x-1)
  16. (i) (3x-4)(x+2)               (ii) (y+5)(y+5)            (iii) (z+3)(z-2)
  17. (i) (x+9)(x+1)                 (ii) (3p+2)(p-12)        (iii) (q+5)(q+2)
  18. (i) (5a+1)(a-2)               (ii) (7b-2)(b+1)          (iii) (3x-1)(8x+3)

 

EXERCISE 4D

  1. (i) 7x2            (ii) -6a      (iii) -3y2     (iv) b
  2. (i) 10x2          (ii) -3a      (iii) -8y2     (iv) 3b
  3. (i) x               (ii) 2a2       (iii) -5y2     (iv) 2b4
  4. (i) x               (ii) 2a2       (iii) -6y3     (iv) 3b2
  5. (i) x2              (ii) -3a      (iii) -11y    (iv) 2b
  6. (i) 4a2+5a+3                  (ii) 2x2+3x+4
  7. (i) 3b2-8                         (ii) 4x3-3x2+2x-6
  8. (i) 2x2-x         (ii) 3x2+x-3
  9. (i) x+4           (ii) x+5
  10. (i) x+2           (ii) 3x+2
  11. (i) 4x+3         (ii) 2x+1
  12. (i) x+5           (ii) a-3

EXERCISE 4E

  1. x2+3x-2
  2. x2+5x-3
  3. 5x2+2x-3
  4. 2x2-3x+4
  5. 3x2+6x+2
  6. 4x2-3x+5
  7. 3x2+x+4
  8. 5x2+2x+2
  9. 4x2+3x+7
  10. 2x2-3x-7
  11. x2-5x+6
  12. 2x2-x+6
  13. 2x2-x
  14. x2+2x
  15. x2+x-3
  16. x2+2x-5
  17. 4x2+4x+1
  18. x2-6x+9
  19. 2x2-x+3
  20. 3x2+x+4
  21. x2-x-1
  22. 3x2+2x+1
  23. 2x2-3x+5
  24. x2+x-12

 

EXERCISE 4F

 

EXERCISE 4G

 

EXERCISE 4H

 

CHAPTER TEST 4

  1. (i) 4(2x+5)     (ii) 3a(3a-4)               (ii) 5p(5p+2q)
  2. (i) (x+y)(a+6)                 (ii) (r-2s)(4p+3q)       (iii) (5x-2y)(3z-4w)
  3. (i) (x-2y)(x+2y)              (ii) (3a-6)(3a+6) or 9(a-2)(a+2)
    (iii) 2(b-2)(b+2)
  4. (i) 5200         (ii) 3
  5. (5a-4b)(5a+4b)
  6. (i) (3x+4)(x+2)               (ii) (4y-1)(y-5)           (ii) (2a-3)(a+3)
  7. (i) x+5           (ii) 10x2+5x-3

 

EXERCISE 5A

  1. (i) €0.36        (ii)  €4.80  (iii) €0.20
  2. 28
  3. 23.04            
  4. 85.5%          
  5. 96%             
  6. 20%             
  7. 86%             
  8.  €520            
  9.  €13,600       
  10. 12.50%        
  11. 15%             
  12. 60%             
  13.  €25.25         
  14.  €15,600       
  15. 75%             
  16.  €899            
  17.  €24.00         
  18.  €4,530.50    
  19.  €270            
  20. 8%               
  21.  €15,000       
  22. $864.80         $622.66
  23.  €6,372          $6720.05

 

EXERCISE 5B

  1. (i) 57:76:95    (ii) 108:135:162         (iii) 3:18   
    (iv) 39:104     (v) 111:185:259
  2.  €80
  3.  €176
  4.  €684
  5.  €754
  6.  €15:€20.
  7. 10:6
  8. 70 m
  9. 3:2
  10. 5:4
  11. 4:6
  12. 10:35
  13. 77
  14. 168
  15. 216
  16. (i) 12             (ii) 4.5       (iii)1.5
    (iv) 4              (v) 12        (vi) 7

 

EXERCISE 5C

  1. €3.80
  2. 240 km
  3. 76.2 cm
  4. 122 m
  5. 15 cm
  6. 285 km
  7. 27 minutes
  8. 60 hours
  9. 5 hrs 12 mins
  10. 25 sheep
  11. 5 days
  12. (i) 5 m/s         (ii) 125 m/s               
    (iii) 40 m/s      (iv) 3.75 m/s
  13. (i) 126 km/hr (ii) 900 km/hr            
    (iii) 261 km/hr                 (iv) 18 km/hr

 

EXERCISE 5D

  1. 2.5 hrs or 2 hrs 30 mins
  2. 7.5 m/s
  3. 72 km/hr
  4. 42 km/hr
  5. 6.25 m/s
  6. 9.14 a.m.
  7. 135.3 km
  8. 0.032 seconds
  9. (i) 8760 or 8766 hours (taking 1 year to be 365 days or 365.25 days)
    (ii)171,233 km/hr or     171,116 km/hr
  10. 124 km
  11. 10 seconds
  12. 2.22 km/hr

 

EXERCISE 5E

  1. (i) €1,349.84                  (ii) €149.84
  2. (i)  €983.45                    (ii)  €83.45
  3. (i)  €2,153.78                 (ii) €153.78
  4. (i)  €1,663.08                 (ii) €163.08
  5.  (i) €4,049.51                 (ii) €449.51
  6. €4,058.08
  7.  €1,853.67
  8.  €4,514.06
  9. (i) €2,080.00                  (ii) 4%
  10. (i) €618.00    (ii) 3%
  11. (i) €997.50    (ii) 5%
  12. (i) 4%            €800.00
  13. (i) 3%            €600.00
  14.  (i) €4,600.00                 (ii) 19.05% (to two decimal places)
  15.  €11.00         
  16.  (i) €48,400.00               (ii) 6.75%
  17. (i) €22,950.00                (ii) 3%
  18. €2,597.00
  19.  €5,873.92

 

EXERCISE 5F

  1. €900.00
  2.  €15,997.54
  3.  €3,059.52
  4.  €33,647.90
  5.  €8,104.00
  6.  €6,359.72
  7.  €1,460.00
  8. (i) €15,213.00                (ii) €266.21
  9. 19%
  10. 24%
  11.  €1,875.00
  12.  €33,284.00
  13.  €1,816.20
  14.  €19,026.38

 

CHAPTER TEST 5

  1. €1.50
  2.  €1,250.00
  3. 125%
  4. 189                216           324
  5. €119.00
  6. 22.5 and 37.5
  7. 3
  8.  €542.50
  9. 15 days
  10. (i) 17.5 m/s    (ii) 9km/hr
  11. 2.4 m/s
  12.  (i) €2,625.00                 (ii) €2,500.00
  13.  (i) €3,540.00                 (ii) 12%
  14.  €2,375.40
  15. 21

 

EXERCISE 6A

1.      (i) A = {11, 13, 17, 19}      (ii) B = {m, a, t, h, e, i, c, s}
(iii) C = {1, 2, 3, 4, 6, 12}   (iv) D = {3, 6, 9, 12, 15, 18}

2.     

3.     

4.     

5.     

8.      50

9.      3

10.  3

11.  (i) 7   (ii) 9

12.  (i) 12 (ii) 12

13.  7

14.  13

15.  (ii) 3   (iii) 9

16.  (ii) 2   (iii) 3

17. 

 

EXERCISE 6B

1.      (i) 7+5+4+3 = 19                (ii) 4+3+2+6 = 15
(iii) 5+3+2+4 = 14              (iv) 7+6+4 = 17
(v) 4+5+2 = 11  (vi) 3

5.      (i) {6, 12)           (ii) {8, 9, 10}            
(iii) {1, 3, 5, 7, 9, 11}          (iv) {1, 2, 4}

6.      (i) {b, c, d, f, g, h, e, a}      (ii) {a, b, f, g, h}
(iii) {f, g, j}                         (iv) {c, d, e}

7.     

8.      (i) {1, 4, 3, 6}    (ii) {6}      (iii) {4, 5, 6}

 

EXERCISE 6C

1.      (i) 20                  (ii) 65        (iii) 80

2.      (i) 3  (ii) 5          (iii) 1

3.      (i) 3  (ii) 13

4.      (i) 68                  (ii) 6

5.      (i) 12                  (ii) 7          (iii) 4

6.      4

7.      2 play all three. 8 play exactly two.

8.      (i) 4  (ii) 37

 

CHAPTER TEST 6

1.      (ii) {c, a, g, e, f, d}              (iii) {c, a, e}
(iv) {g, f, d}}     (v) {b, h}

3.     

4.      3 like both, 12 like neither.

5.      2

 

EXERCISE 7A

  1. (i) 5               (ii) 9          (iii) 4         (iv) €4       (v) 1          (vi) 0
  3. 28
  4. (ii) 2.5            (ii) 2.5       (iii) 3.5      (iv) 3.5      (v) 5.5       (vi) 5.5
  5. mean =50.5   sum =5050
  1. (i) 5.80,         7,              6
    (ii) 10,            11,            11
    (iii) 4.5,          7,              4
    (iv) 6,             5 and 9,    5
    (v) 1.2,          1.3,           1.3
  2. 4
  3. 6
  4. €4.50
  5. 0.043
  6. 855
  7.  
  8. 8
  9. 16
  10. 15
  11. 13
  12. 5
  13. 10
  14. 8
  15. 8
  16. 5
  17. 8
  18. 7

 

EXERCISE 7B

  1. 6,  4,              6
  2. (i) 3,              3
    (ii) 12,            10
    (iii) 5,             7
    (iv) 32,           40
    (v) 9.5,          8
  3. Given

Number

1

2

3

4

5

Frequency

4

x

5

6

3

then x = 4

  1. 5
  2. 2
  3. 5
  4. 7
  5. 3

 

EXERCISE 7C

  1. (i) 24             (ii) 2
  2. (i) 80             (ii) 30

 

EXERCISE 7D

    1. (i) 10-20             (ii) €33.05
    2. (i) 40-60             (ii) 50
    3. (i) 20-30             (ii) €31.25
    4. (ii) 30-50            (iii) 45       (iv) 14
    5. (i) 60-100           (ii) 51 minutes
    6. (i) 30-40             (ii) 70        (iii) 44       (v) 18
    7. (ii) 49.6              (iii) 54
    8. (i) 10-15             (ii) 10
    9. 17
    10. 5
    11. 2, 5, 3, 3
    12. 8, 12, 4
    13. 4.5, 12, 3, 13.5
    14. 30, 50, 60
    15. 8, 9, 20, 10, 3
    16. 4, 18, 20, 6

 

EXERCISE 7E

  1. (i) 26, 59, 71, 81, 90
  2. (i) 4, 10, 16, 24, 40
  3. (i) 17, 32, 46, 50
  1. (iii) 3, 39, 4
  2. (ii) €10.67      (iii) 18, 40, 68, 88, 90
  3. (ii) €21.50      (iii) 22, 73, 88, 100

 

CHAPTER TEST 7

  2. €12.07
  3. 7 years 3 months
  4. 2
  5. 5
  6. 30, 21, 22
  7. 30                 
  8. (i)  48             (ii)14
  9. (i) 80-100      (ii) €72.40
  10. 8, 9, 5, 10, 4
  11. 6, 24, 44, 70, 88, 100

 

EXERCISE 8A

1.     

2.     

3.     

4.     

5.     

6.     

7.     

8.     

9.     

10. 

11. 

12. 

 

EXERCISE 8B

 

EXERCISE 8C

  1. -0.4, -1.4
  2. -0.3, -1.7
  3. -0.54, -2.46
  4. -0.4, -3.6
  5. 1.58, 0.42
  6. 1.8, 0.4
  7. 2.9, -0.4
  8. 0.65, -0.22
  9. 1.2, -5.2
  10. 0.7, -2.2
  11. 0.6, -1.4
  12. 0.8, -0.6
  13. -0.28, -2.39
  14. -1.4, 3.4
  15. -0.8, 1.3
  16. 0.18, -1.43
  17. 0.6, -1.6
  18. -0.4, -0.8
  19. 0.8, -2.0
  20. 0.19, -2.69
  21. 0.7, -0.2
  22. -0.4, -1.8
  23. -0.26, -2.74
  24. -0.6, -2.0

 

EXERCISE 8D

  1. , 0.4, -2.4
  2. , 0.2, -4.2
  3. , 4.65, -0.65
  4. , 4.45, -0.45
  6. , 2.73, -0.73
  8. , 2.74, -1.74
  9. (i) 2.4, -0.9    (ii) -0.6, -3.9
  10. 1.22, -0.55, 1.1, 0.2
  11. 2.4, -0.4, 7.4, 4.6
  12. -0.9, -4.4, -1.9, -5.4
  13. -4.2, 1.2, -2.6, 0.1

 

EXERCISE 8E

 

EXERCISE 8F

  1. -4, 8
  2. -3, 6
  3. -2, 4
  4. , -2, 1
  5. , -4, 6
  6. , -3, 6

 

EXERCISE 8G

 

EXERCISE 8H

  1. {0, 1, 2, 3, 4, 5}
  2. {0, 1, 2, 3, 4}
  3. {0, 1, 2, 3, 4, 5, 6}
  4. {0, 1, 2, 3}
  5. {0, 1, 2, 3, 4, 5, 6}

 

CHAPTER TEST 8

 

EXERCISE 9A

  1. (i) 50º            (ii) 35º       (iii) 130º
    (iv) 90º          (v) 240º
  2. (i) 65             (ii) 16        (iii) 23       (iv) 16
  3. (i) x = 60       (ii) p = 20, q = 40, r = 120
    (iii) y = 48
  4. (i) x = 36       (ii) y =17   (iii) z = 76
  6. (i) 97º            (ii) 62º       (iii) 118º
  1. 63º
  1. 40

 

EXERCISE 9B

  1. (i) x = 40       (ii) y = 45  (iii) z = 10
  2. (i) x = 105     (ii) y = 20, z = 10       (iii) w = 43
  3. (i) 112º          (ii) 28º
  1. 120º
  1. (i) 30º            (ii) 52º       (iii) 77º

 

EXERCISE 9C

  1. (i) x = 55       (ii) y = 9    (iii) z =51
  2. 70º
  1. 60º
  2. 52º
  1. (i) 42º            (ii) 96º       (iii) 48º      (iv) 70º

 

EXERCISE 9D

  1. (i) x = 6         (ii) y = 12  (iii) z =3
  2. (i) x = 6         (ii) y = 9    (iii) z = 12
  3. (i) 10             (ii) 6
  4. (i) 27             (ii) 16
  5. (i) 24             (ii) 33
  6. 1.9
  7. 14.4
  8. (i) 9               (ii) 3
  9. 16
  10. (i) 11.5          (ii) 11
  11. (i) 12             (ii) 16
  12. (i) 48             (ii) |qx| = 10
  13. No
  1. 8.75

 

EXERCISE 9E

  1. (i) 13             (ii) 17        (iii) 10       (iv) 29
    (v) 7              (vi) 24       (vii) 33      (v) 65
  5. 24 cm
  6. 16 cm
  7. 29
  8. 14
  9. 112
  10. 31.3

 

CHAPTER TEST 9

  1. 67º
  2. (i) x = 40, y = 26, z = 132               (ii) p = 90, q = 10
    (iii) r = 160, s = 100, t = 80
  1. (i) 4.5
  1. (i) 4

 

EXERCISE 10A

  1. (i) P = 720, A = 35,000
    (ii) P = 288, A = 2409.75
    (iii) P = 216, A = 1764
  2. (i) 2058         (ii) 525
  3. (i) A = , P = 27.4
    (ii) A = , P = 110.8
    (iii) A = , P = 48.8
  4. (i) 72             (ii) 220.5   (iii) 15
  5. 56
  6. (i) 25             (ii) 12
  8. 7000
  9. 16
  10. (i) 10             (ii) 20        (iii) 1.5
  12. 693
  13. 346.5
  14. (i) 7               (ii) 21
  15. (ii) 21            

 

EXERCISE 10B

  1. (i) A = 348 cm2, V = 360 cm3
    (ii) A = 124 cm2, V = 90 cm3
    (iii) A = 284 cm2, V = 210 cm3
  2. (i) A = 54, V = 27
    (ii) A = 96 ,V = 64
    (iii) A = 150, V = 125 cm3
  3.  (i) CSA = 528 cm2, TSA = 1760 cm2, V = 3696 cm3
    (ii) CSA = 314 cm2, TSA = 471 cm2, V = 785 cm3
  4. (i) A = 1386, V = 4851 cm3
    (ii) A = 2826, V = 14,130 cm3
  5. 16 cm2
  6. 10 cm
  7. (i) 198 cm3     (ii) 504 cm3
  8. (i) 1760 cm2   (ii) 70.4 cm
  9. (i) 9261 cm3   (ii) 4851 cm3
  11. (i) 600 litres   (ii) 160 cm
  12. (i) 19.25 m2   (ii) 16 m
  13. (i)  cm3               (ii) 30 cm
  14. 10 cm
  15. 1.5 m

 

EXERCISE 10C

    1. (i) 1100 cm3       (ii) 1386 cm3              (iii) 88 cm3
    2. (i) 87.92 cm2      (ii) 282.6 cm2             (iii) 62.8 cm2
    3. (i) 2.5 cm            (ii) 10 cm 
      (iii) 16.5 cm        (iv) 48.5 cm
    4. 21 cm
    5. 12.5 cm
    6. 10 cm
    7. 7 cm
    8. 24 cm
    9. (i) 58 cm             (ii) 40 cm
    10. (i) 24 cm             (ii) 1232 cm3
    11. (i) 20.5 cm          (ii) 1287.4 cm2
    12. (i) 14 cm             (ii) 9856 cm3
    13. (i) 6.5 cm            (ii) 70.69 cm2
    14. 288 cm3
    15. 1:8

 

EXERCISE 10D

  1. (i)  cm3   (ii) 3 cm
  2. (ii) 3072 cm3                  
  3. (i) 180 cm3 (ii) 144 cm3            (iii) 55.6%
  4. (i) 160 cm3 (ii)  cm
  5. 126 cm3,    5 cm        
  6. (i) 800 cm3     (ii) 3.74 cm               
  7. 36 cm
  8. 2880 cm3,  144 cm3,                20
  9. (i) 1.5 cm       (ii) 2 cm3                2.5+1.5 = 4 cm
  10. 5 cm
  11. (i) 486 cm3 (ii) 243 cm3            (iii) 18 cm
  12. 36 cm3       4 cm         1.4 cm
  13. (i) 1 cm          (ii) 52.6 cm3
  14. 100 cm2     15 cm       14.1 cm

 

CHAPTER TEST 10

  1. (i) 6               (ii) 63 cm2 (ii) 21.4%
  2. 774 cm2
  3. (i)  cm3 (ii) 1000 cm3              (iii)
  4. 2 cm
  5. 24 cm
  6. (i) 72             (ii) 6912 cm3              (i) 74%

 

EXERCISE 11A

  2. (i) Q, R          (ii) A, C    (iii) H, X
  3. X, I, S (the last only in some fonts)
  2. (i) axial symmetry            (ii) translation
    (iii) rotation of 45º           (iv) central symmetry

EXERCISE 11B

  4. (i) yes            (ii) no
  5. No,
  8. Yes,

 

EXERCISE 11C

  1. (ii) (2, 3)
  2. (ii) (3, 2)
  3. (ii) (8, 1)
  5. (ii) (1, 7)
  6. (i) 6               (ii) 5          (iii) 6         (iv) 7
  1. (i) 9               (ii) 4          (iii) 5         (iv) 4
  2. (i) 2x-y+1 = 0                (ii) 3x+y-1 = 0           (iii) x-2y-6 = 0
    (iv) 3x-4y+26 = 0           (v) 6x+5y-3 = 0         (vi) 17x-7y = 0
  3. (i) 2x-y-3 = 0                                  (ii) 3x+y-4 = 0           (iii) 5x-y-7 = 0
    (iv) 2x-3y+13 = 0           (v) 3x-4y-4 = 0         (vi) 9x-5y-8 = 0
  4. (i) 2x+y-7 = 0                (ii) 3x-y+4 = 0           (iii) 4x-y-5 = 0
  5. 7
  6. (i) a(8, 0), b(0, 6)           (ii)
    (iii) 4x-3y-7 = 0              (iv) p(4, 3)
  10. (i) p(4.5, 0), q(-3, 0)       (ii) 6.75
  12. k = 8

EXERCISE 11D

  1. (i) (3.5)          (ii) (8,1)    (iii) (0.7)
    (iv) (-77, 39)  (v) (0.05, 0.01)          (vi) (5, 0)
  2. (i) (4,10)        (ii) (-1, 4)  (iii) (2, 5)
    (iv) (89, -13)  (v) (0.038, 0.007)      (vi) (4, 10)
  3. (ii) x-2y-4 = 0
  4. (ii) the image of L: x+3y-14 = 0 is x+3y-13 = 0
  5. x+y-1 = 0
  6. (ii) 3x+4y-13 = 0            (iii) (-5, 7)
  7. (i) t = 2          (ii) 2x+3y-7 = 0         (iii) (-1, 3)
  8. (i) h = -6        (ii) 4x+5y+2 = 0        (iii) (12, -10)
  9. (h, k) = (3, 3)
  10. (i)              (ii) (-1, 4)  (iii) 3x+4y-13 = 0      (iv) k = 7
  11. x+2y-12 = 0
  12. x+2y-4 = 0

 

CHAPTER TEST 11

  1. (i) (2, 6)         (ii) (-7, 16)
  2. t = 7
  3. 9x+5y-35 = 0
  4. |pq| = |pr| = 10 but |qr| =
  5. k = 4,
  6. (i) h = 4         (ii) 3x+4y-24 = 0       (iii) (0, 6)   (iv) 5
  7. (1, -4)
  8. (ii) (2, 3)
  9. If a(1, 3), b(1, -1), c(5, -1), then
    (i) p(3, 1)                     
    (iii) |ab|=|bc| = 4            (iv) (5, -5)
  12. (i) axial symmetry            (ii) central symmetry
    (iii) a rotation of 90º        (iv) translation

 

EXERCISE 12A

  1. (i) 6.55          (ii) 8.96     (iii) 8.63   
    (iv) 2.92         (v) 15.69   (vi) 2.93
  2. (i) 34.3º         (ii) 53.3º    (iii) 39.0º  
    (iv) 47.7º       (v) 60.0º   (vi) 45.0º
  3. (i) 8.3            (ii) 10.5     (iii) 7.5      (iv) 6.9
  4. (i) 42º21’       (ii) 51º19’ (iii) 32º13’ (iv) 39º35’
  5. (i) 39º31’       (ii) 54º47’ (iii) 0º0’    
    (iv) 20º42’     (v) 45º0’
  6. (i) 7.0º           (ii) 11.3º    (iii) 4.3º     (iv) 29.5º
  7. 117 cm
  8. 6.4
  9. 1.63 m to two decimal places
  10. 3.63 m to two decimal places
  11. 79.67 m to two decimal places
  12. 62.5º
  13. 53.4 km
  14. 138 m to the nearest metre

 

EXERCISE 12B

  1. 23º33’
  2. (i) 5.8            (ii) 11.5     (iii) 20.0
  3. 27.5
  4. 10.9              
  5. (i) 34º52’       (ii) 4.5       (iii) 5.8
  1. 1.4
  5. (i) 13             (ii) 11º19’
  6. 58 m

 

EXERCISE 12C

  1. sin 45º =                  cos 45º =            tan 45º = 1
  2. sin 30º =    cos 30º =            tan 30º =
  3. sin 60º =                  cos 60º =               tan 60º =
  4. sin 30º = , x = 9
  5. tan 60º = , x = 5
  6. (i) 1               (ii)
  7. A = 30º
  8. (i) 2         (ii) 5
  9. (i)                   (ii)

 

EXERCISE 12D

  1. (i)         (ii)      (iii)      (iv)
  2. (i)         (ii)      (iii)   (iv)
  3. (i)           (ii)    (iii)       (iv)
  4. (i)             (ii) 0          (iii)       (iv) 0
  5. (i) 30º, 150º   (ii) 45º, 225º              (iii) 30º, 330º
  6. (i) 120º, 240º (ii) 120º, 300º
  7. 135º, 315º
  8. (i) 180º          (ii) 270º

 

EXERCISE 12E

  1. (i) 23 cm2       (ii) 254 cm2                (iii) 59 cm2                 (iv) 514 cm2
  4. |pq| = 7, |qr| = 6,
  5. (i) 80º            (ii) 5 cm
  6. (i) 76º            (ii) 8 cm
  7. (i) 40º            (i) 12 cm
  8. 55º
  9. 48º
  10. 277 square units
  11. |op| = 4          |<rop| = 160º
  12. 15.6 cm2

 

EXERCISE 12F

  1. (i) 8.6            (ii) 13.8     (iii) 18.9    (iv) 13.0
  2. (i) 32º            (ii) 59º       (iii) 32º     
    (iv) If the adjacent to A is 26, then A = 56º
  3. (i) 6.3            (ii) 8.7       (iii) 71.5
  4. (i) 25º44’       (ii) 87º02’ (iii) 16º58’
  5. (i) 9.1 cm       (ii) 62º       (iii) 11.4 cm
  6. (i) 54º53’       (ii) 63º22’ (iii) 7.1 cm
  7. c = 12.8 cm
  8. 179 m
  9. 4 m
  10. (i) 17 m          (ii) 30º
  11. (i) 122 m        (ii) 132 m
  12. (i) 4.3 m         (ii) 5.0 m

 

CHAPTER TEST 12

  1. 80º32’
  2. 17º57’
  3. (i) 18º26’       (ii) 15º15’
  4. sinA =
  5. (i) 60º            (ii)
  7. sinA =
  8. 9
  9. 28.25º
  10. (i) 8.29 cm     (ii) 15.39 cm              (iii) 18.65 cm2