3. (i) 8 (ii) 625
(iii) 9 (iv) 1
4. (i)
__ 4
__ 8
(ii) 25x2 (iii) 256n4 (iv) 27y3
___ b3
8a3
____ 9y2
_____ 81m4
5. (i) −8a3 (ii) 9x2
____ 8x3
____ b3
___ y2
(iii) n4 6. (i)
(iv) −343y3 8a3
___ m4
______ 27x3
(ii) x2
___ b3
__ y2
(iii) 16x4 (iv) −8a3
____ 81y4
____ 27b3
Practice questions 13.4
1. (i) 5 (ii) 13 (iii) 6
2. (i) x (ii) a (iii) y
3. (i) 135 (ii) 5x (iii) 8y
4. (i) √
(ii) 4 (iii) √
_ 35
_ 21
5. (i) 15√ (ii) 12√ (iii) 2√
7. (i) x (ii) y2
_ 6
_ 65
_ 55
6. (i) b (ii) 25 + b + 10√
8. (i) n (ii) m2
_ b
+ x + 2y√ + n + 2m√
_ x
_ n
9. (i) 7 (ii) 16 + 6√
10.(i) 3√ (ii) 2√ (iii) 5√
11.√
_ 2
12.10√ 13.√
14.9√ 15.√
16.3√
_ 5
_ 10
_ 2
_ 2
_ 7
Practice questions 13.5
1. (i) n = −1 (ii) n = −2 (iii) n = 8
2. (i) x = −3 (ii) x = 1 (iii) x = 2
3. (i) x = 2
(ii) x = −2 (iii) x = 1
__ 3
_ 2
_ 3
_ 3
_ 7
___ 81
4. (i) n = 5 (ii) n = 2
(iii) n = 5
__ 2
Practice questions 13.6
1. (i) 4·56 × 1010 (ii) 6·708 × 1014 (iii) 5·006384 × 106 (iv) 6·89 × 10−5 (v) 5·2672 × 10−2 (vi) 7·0000223 × 10−6
2. (i) 4·6900902 × 10 (ii) 6·729 × 102 (iii) 6·782 × 10−3 (iv) 1·1678 × 10−6 (v) 5·622882 × 10−2 (vi) 6·79679 × 103
3. (i) 5·69 × 107 (ii) 5·47 × 104 (iii) 3·53 × 103 (iv) 5·07 × 104
4. (i) 7·41 × 109 (ii) 1·2963 × 10−3 (iii) 1·016 × 103 (iv) 1·0528 × 10
5. 6·06987 × 1018 6. 1.7638 × 10−14 7. 3·80459 × 1013
9. 4 × 10−6 10.4·8 × 10−15
m
11.(i) 7 × 105 (ii) 20%
12.4·62963 × 103
Revision questions 13A Core skills 1. (i)
__ p
1
(ii) 1 (iii) 1
__ x2
2. (i) n−4 (ii) x−3 (iii) x−4
__ n3
3. (i) −3 (ii) 2
(iii) −5 (iv) 7
__ 33
___ 33
4. (i) 16x4 (ii) −64n3 (iii) −243y5 (iv) 625x4
__ 82
5. (i) −27a3 (ii) 16x4
(iii) −n3
6. (i) p (ii) 5n (iii) 11x
7. (i) n (ii) m2
+ n + 2m√
8. (i) 3√ (ii) 5√ (iii) 4√ (iv) 3√ (v) 6√ (vi) 30√
382 Linking Thinking 2
_ 3
_ 2
_ 3
_ 5
_ 7
_ 2
_ n
b−3 y−4 m−3 (iv) −8yx−3
___ 43
m2 m m2
8. (i) 2·16 × 105 (ii) 4·32 × 105
9. (i) x = −8 (ii) x = 1 (iii) x = 5
10.1·7566 × 10−15 m
11.(i) 5·32 × 104 (ii) 3·12 (iii) 5·12048 × 10 (iv) 1·286471 × 102
13B Taking it further 1. 611
km
2. 60a12 3. 3a12
units3 units3
4. 0 5. (i) 64 heads (ii) 8 192 heads
6. 1 × 104 7. 2·124 × 107 8. 1·006598 × 1021 9. 3·33333 × 105 10.1·5768 × 108 11.7·2576 × 107 12.9.02 × 103
m2 times
bags times
hours
Unit 14 Working with non-linear equations – quadratics
Practice questions 14.1 1. (i) 5x + 20 (ii) 2x + x2 (iii) 6y2
− 6y
(iv) 10ab + 15ac (v) 12ab − 4a2 (vi) st − 2s2
2. (i) a2 (ii) 3x2 (iii) y2
+ 7a + 12 + 7x + 2 + 3y + 2
(iv) 7n2 (v) 16x2 (vi) 4m2
3. (i) 2x2 (ii) 6x2
+ 46n + 24 + 16x + 4
(iii) −3x2 (iv) x2
(v) 49x2 (vi) x2
4. (i) x2 (ii) a2 (iii) k2 (iv) x2 (v) 6x2 (vi) 2b2
+ 20m + 25 − x − 10 − 13x + 6 + 7x − 2
− 1 − 16
5. (i) 7x3 (ii) 15c3 (iii) 2k3
− 12x + 36 + 4x − 5 − a − 6 − 2k − 3 − 4x + 4 − 4x − 2 + b − 3 + 17x2
+ 3k2
(iv) −6y3 (v) 4x3
(vi) −5t3
6. (i) 12x3 (ii) 2t3
+ 15c2 − 8y2
− 23x2 − 26t2 + 40x2
− 3t2
(iii) −5x3 (iv) 10c3
7. (i) −6y3 t3
(ii)
(iii) −6x3 (iv) 4c3 (v) 4p3 (vi) t3
(v) −4p3 (vi) x3
− 2x2 − 2t2
+ 2t2 − 3x2 − y2
+ 55x + 21 − 10c − 20
− k − 12
+ 32y + 16 − 5x + 15
− 59x − 42 + 32x + 4
+ 8x − 12
+ 23c2 − 16p2
− 8x2
− 12c2 + 12p2
+ 13x + 8 + 5c − 2
− 6p + 20
− 4x − 16 + 6y + 1
− 29t + 30
+ 41x + 63 + 16x − 16 − 30p − 20
− 31t − 42
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