Power of Maths: Paper 1 – Answers
Exercise 7 1. (a) 2 √
(f ) 5 √ (l) 3 √
___ 5
__ 2
__ 3 (g) 4 √
(m) √ (b) – 4 + 15 √
__ 3 (b) 3 √
__ 3 (n) 7 √
(g) 0 3. (a) 2 √ (e) 4 + 2 √
(i) – 6 4. (a) √ (f ) √
___ 14 (g) x √
___ 42
___ y
__ y
__ 2 (h) 7 √
__ 3 (c) 3x − 7 √
__ 3 (f ) 2 (g) ab( √
__ 2 (b) √
__ 5 (b) − √
__ 5
(h) √ (c) 0·53 (d) 0·59
Revision Questions 1. 9x + 7 2. (a) (8x + 4) cm (b) 6(2x + 1) cm2 3. 2
_ 3 x; 3x
5. (a) 1 _
(b) 2 (d) 8
__ 2
4. (a) 6x2 + 25x + 24 __________
2x + 3 x m−1 (b) − 1
(d) Power = 8 _
5 m −1 ; f = 5 _
____ x + 2 m−1 (c)
______ x(x + 2) m−1
8 m 6. (a) 2
____ x2 − 4 (e) 206 s 7. (a) A
__ 3
2 = ( 3 √
____ x − 2 hours
____ x + 2 hours (c) The man’s speed is greater
__ A ) 2 (b) 4
(c) 1·368 m2 8. (b) 6 g (c) Fraction left after n half-lives = 1
(c) 12π(4 – x)(4 + x) cm3 (d) 84π cm3 10. (a) 3200 (b) 100 (c) 2t __
(d) Number in B is less than in A for t < 5; Numbers equal for t = 5; Number in B is greater than in A for t > 5
32 (i) 1 _
8 (ii) 1 (iii) 32
Section 3 Chapter 5
Exercise 1 1. (a) 9 (b) – 4 (c) 2 (d) 3 (e) 3 (f ) 3 (g) –2 (h) 3
( j) 1 2. (a) –2 (b) –7 (c) 1 (d) − 50 __
(g) 14 __
(e) 7 (f ) 4 (g) 16 (h) 8 (i) 3 ( j) 4 4. (a) 5 (b) 2 (c) 7 (d) 5 (e) − 23
3 (h) 8 (i) 1 ( j) 9 _
69 cm (b) l = 13·75 m, b = 8·25 m, A = 113·4375 m2 (c) 15 cm, 20 cm, 25 cm (d) 12, 8 (e) 15, 16, 17 (f ) Sandra = 14 yrs, Anna = 12 yrs (g) 15 yrs (h) 16 at €1∙50, 9 at €1 (i) 360 units ( j) 7, 8, 9, 10, 11 (k) 80 km (l) 120 weeks (m) 414 (n) Man = 40 yrs; Son = 20 yrs
__ 7 (f ) − 7
4 3. (a) 2 (b) − 1 _
4 (c) 14 (d) 7
_ 4 5. (c) –5 (d) Yes 6. (a) 23 cm,
9 (e) − 1 _
_ 2 (i) 2
2 (f ) 5
Chapter 6 Exercise 3 1. (a) 16 (b) 1
_ 4 (c) 10 000 (d) a (e) e2 (f ) 2 (g) 4
(h) (a – 1)2 = a2 – 2a + 1 (i) 4 _
Exercise 4 1. (a) y – 4 (b) y
(g) S − 2πr2 ______
2πr
(m) 2D 2 ___
3 (n) ±
_____ M + 1
2. s = (q − p)2 ______
4. 500D2 _____
t = 16 yrs h
(q) 3P + b (r) 5Q + 3l ______ (v) ± √
√ 9
__ 3
2 = 3 √
___ 16
(c) 7 (d) 5 (e) 24 (f ) 12 (g) –3 (h) 13 (i) 2, 4 ( j) 5 (k) 3 _
_ 3 (c) y − 4
(h) mV ____
___ 2H
a − V (i) ±
___ g (o) ±
____ z (w) b2 − A2
_____ 4c
____ 3
(d) 100 I ____
√ √
__ A
___ 2A
(s) 6 4 ; 1·69 3. r =
PR (e) 2πlp ___
__ πh ( j) ±
__ x (p) ±
; 6366·8 km 5. A = 17C ____
(x) ± √ √
___ 2E
____ L − 9 (t) dt + s (u) ± √
√ √
__ V
__ C (y) ± √
__ πh ; 2 cm
t + 1 ; A = 68 mg;
___ 3V
____ r − a
____ b
w (f ) v2 − u2 _____
2S
__ πh (k) v2
__ 5g (l) 4π2k
___ H T 2
_______ v2 − 2as
______ Q − 3f
9 ( j) 1∙44 2. (a) 5 (b) 11 2
__ 2 n 9. (a) 192π cm3 (b) 12πx2 cm3
___ y
__ xy
__ 2 (c) 2 √
__ 2
___ 10 (o) 5 √
__ 3
__ 3 (c) 5 √
__ 2 (i) 6 √
___ 6
__ 3
__ 2 (d) 3 √
__ 2 ( j) 16 √
__ 6 (c) 60 √
__ a + √
___ 3
__ 3
__ 5 (e) 11 √
__ y (d) 0 (e) 0 (f ) 5 √
2. (a) 3 √
___ 11
__ b ) (h) 20 + 2 √
__ 3 (d) 6 √
(d) 2 √
___ 5 (e) − √
__ 2
__ 2 (k) 2 √
___ 10
___ 3
__ 2
__ 3 + 6 √
__ 2 + 5 √
___ 91
__ 2
__ 3
5. 11 6. (a) 0·56 (b) 0·03
__ 2 + 6
__ 3
Exercise 2 1. (a) –2, 1 (b) 3, − 1
(g) 0, 3 (h) 0, 1 _
(h) − 8 _
_ 2 (c) 7
_ 2 , 7
_ 2 (d) 0, 3 (e) 0, 7
9 (i) 3, –3 ( j) 0, 1 _
(c) –3, 5 (d) –11, 3 (e) −1, − 1 _
(d) −1, 4 _
7 (e) − 1 _
______ 4 ; 3·39, −0·89 (f ) 4 ± √
___ 73
(g) −4 ± √ (i) ± √
(b) 3x + 8 (c) 10x + 22 2
_______ 7
___ 30
__ 3 ; 1·73, −1·73 ( j) ± √
5. (a) 1 ± √
___ 31 ; 6·57, −4·57 (b) 1 ± √
3 , 3 4. (a) − 3 _
4·16, −2·16 (c) 19 ± √ (e) 5 ± √
_______ 8
____ 345
______ 3 ; 2·90, − 0·23
___ 22
; 0·21, −1·35 (h) −4 ± √
__ 8 = ± 2 √
_______ 2
___ 22
(e) 4x2 – 8x + 3 = 0 9. (a) − 1 _
_ 3 , 5
_ 2 ; t = 1
_ 3 , 7
3 , 5 _
_ 2 (c) x = 1, 4
; 0·35, −4·35
__ 2 ; 2·83, −2·83
6. (a) 2 equal real roots; 2, 2 (b) 2 real roots; 0, 3 (c) 2 real roots; –1, 5 7. –3 8. (a) x2 – 3x + 2 = 0 (b) x2 – 6x + 9 = 0 (c) x2 + 3x + 2 = 0 (d) x2 + x – 30 = 0
2 (b) –1, 3 (c) 2, 3
(d) 2, 6 (e) 0∙3, –3∙3 10. (a) x = 2, 5; y = 4, 7 (b) x = − 2
_ 3 ; y = 6, 7
(d) x = 3, 7 ; x = –3, 6, –2, 9 (e) x = 3 _
| QR | = 13 cm | PQ
5 , 4; y = 13 __
11. (a) 12 (b) 4 (c) 50, 190 (d) 3 Ω (e) 2 s, 14 s (f ) l = 24·05 m, b = 11·10 m (g) l = 10∙8 m, w = 7∙8 m (h) 2 (i)
| = 5 cm, | PR | = 12 cm, 5 , 6
2 (f ) 5 _
4 , 2 _
_ 3 (f ) 0, 2
4 2. (a) 5, –5 (b) 2, –2 3
3 (g) − 6, 2 _
7 , 1 (i) 2, 3 3. (a) –25, 1 (b) – 4, –3 (c) –1, 2 2 (c) Yes, it is a solution
___ 10 ;
; 4·70, 0·05 (d) 1 _
2 , − 2 _
3
343
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