Power of Maths Paper 1 OL

Power of Maths: Paper 1 – Answers Revision Questions

1. (a) 30 – 5i (b) (ii) 5 (c) (i) 7 + 2i (ii) 90 2. (a) 3 – 4i; 5 (b) (ii) 7 – 2i (c) –i 3. (a) (i) √

(ii) √

____ 136 = 2 √

___ 34 (iii) √

____ 136 = 2 √

___ 68 = 2 √

___ 34 (iv) √

(b) (i) 0° (ii) 90° 4. (a) –12 + 5i (b) (i) 2 + 8i (ii) 0 – 6i (iii) √

___ 17 (iv) 6 (c) (i) 6 + 2i

(ii) c = 2, d = 3 5. (a) 3 – 3i (b) x = 0, y = 3 (c) 3 + 4i, 5 + 12i (i) 126 (ii) 18 > 8 √

_ 2 (ii) s = 8

__ 25 , t = − 6

__ 5 6. (b) (i) 1 – 2i

(ii) No (c) (i) 1 + 3i (ii) k = –3, t = –5 7. (a) –13 – i (b) (i) 5 + 5i (ii) –2 + 5i (iii) 5 – 5i (c) 50 (d) (i) x = − 4, y = − 1

__ 25 8. (b) (i) 5 + i (ii) 1

(c) (i) P(1, 1); Slope of OP = 1 (ii) 1 _

2 − 1 _

(ii) −2 − 3i, Q(−2, −3); Slope of OQ = 3 _

10. (b) (ii) 5 (iii) 4 __

Section 7 Chapter 15

Exercise 1

1. (i) (a) S = {(2, 1), (4, 5), (6, 7), (8, 3)} (b) D = {2, 4, 6, 8}, I = {1, 3, 5, 7} (c) It is a function (ii) (a) S = {(3, a), (3, b), (2, c)} (b) D = {2, 3}, I = {a, b, c} (c) It is not a function (iii) (a) S = {(1, 5), (2, 5)} (b) D = {1, 2}, I = {5} (c) It is a function (iv) (a) S = {(1, a), (1, b)} (b) D = {1}, I = {a, b} (c) It is not a function (v) (a) S = {(a, d ), (b, e), (c, f )} (b) D = {a, b, c}, I = {d, e, f } (c) It is a function 2. (a) It is a function; D = {a, b, c}, I = {1} (b) It is not a function; D = {1, 2}, I = {a, b} (c) It is a function; D = {1, 2, 3, 4}, I = {1, 4, 9, 16} (d) It is not a function; D = {1, 4}, I = {−2, −1, 1, 2} (e) It is a function; D = {1, 2, 3, 4}, I = {0} 3. (a) (i) −1 (ii) −9 (iii) −6 (b) (i) 4 (ii) 9 (iii) 0∙25 (c) (i) −10 (ii) −20 (iii) 50 (d) (i) −10 (ii) −14 (iii) −7 (e) (i) 8 (ii) −8 (iii) 125

___ 8

(d) 3 (e) 11 __

(b) 1, 1 _

2 , 2, –3 (c) 8, 1 _

(e) 0, 0, 4 (f ) 1 __

2 , 17 __

4. (a) 17 (b) – 4 (c) 3 _

2

2 (f ) –3 (g) 2·5 (h) 1 5. (a) 5, 9, – 4 8 (d) (i) 44 (ii) 9

6. (a) 11, 2x + 9, 13 – 4x (b) 0, 4 − 4t 2 (c) 1, 3 4 , 12p2 − 8p + 2

54 , −4 (g) 5, 5, 5, 5 (h) 1, 3

13, s + 4, s 2 − 2s + 5 (e) 3 _

_____ x + 4 (d)

(f ) 12, 3 × 23x − 1 7. (a) 1 (b) 15 (c) 1, 6 (d) 4 (e) 4

25 − 3 __

2 25 i (c) 4225 2 i; Q

___ 10 (c) (i) P(−9, 6); Slope of OP = − 2

_ 3

( 1 _

__ 13 + 5

2 , − 1 _

2 ) ;

Slope of OQ = −1 (iii) 2 9. (a) k = ± 8 (b) (i) –1 + 3i (ii) √

__ 13 i

____ 136 = 2 √

___ 34

___ 34

(f ) 4 (g) – 4, 2 (h) –2, 0, 1 8. (a) –20 (b) –3 (c) 4 (d) –3, 1 (e) a = –1, k = –2 (f ) a = 5, b = 2

Exercise 2 1. (a) 15 (b) –7 (c) –1 (d) 2 2. (a) −4x2 − 12x − 8, 5 − 2x 2 (b) 4 √

______ 2x + 4 , 2 √

(d) 3 √

__ x , 3

__ 2

x

(e) x 2 − 1 ______

(g) x, x 3. (a) 11 __

Exercise 3

1. 9 2. –2 3. 37 4. 0 5. 6 6. 2 7. 0 8. 2 9. 2 _

3 10. 3

Chapter 16 Exercise 4 2. (a) y = −x + 7

______ 2x + 1 (c) 1

3 , x 2 − 2x + 1 __________

9 3 (b) k = 2, b = 3

______ 2x + 5 , 2

(f ) 1 __

x 3 , 1

__ x + 5

__ x 3

(d) y = 0x + 5 (e) y = –x + 8 3. (a) Linear f (x) = y = − 2

_ 3 (b) y = 4

(b) Linear h(x) = y = 3 _

5 x + 4

(c) Linear C(r) = y = 2πr + 0 (d) Non-linear (e) Linear F( p) = y = − 1

(b) y = −2x + 10 (c) y = − 2 _

_ 5 T + 32 (c) y = − 3

2 (c) 2 (d) –3

3. Linear, y = 1 _

(c) 12 1 _

2 years 2. s = –300t + 6000; 20 mins

_ 2 years

5 x + 19 __

(e) y = –7x + 11 5. (a) V = –180t + 500 (b) θ = 9

6. (a) 3 _

2 (b) 1 _

Exercise 5 1. (a) V = – 4000t + 50 000 (b) 7 1

(ii) 24·4 million (c) 0·334 million/yr = 334 000/yr 5. (a) Membership fee = €250; Cost per round = €30 (b) C = 30n + 250 (c) €1750 (d) 25 6. (b) 500; n = –5t + 200; 40 days

Chapter 17 Exercise 6

2. (a) x: (–1, 0), (1, 0); y: (0, –1) (b) x: Does not cross; y: (0, 1) (c) x: (2, 0), (3, 0); y: (0, 6) (d) x: (1, 0), (2, 0); y: (0, –2) (e) x:

y: (0, 2) (f ) x: 3 , 0 ) , (2, 0); y: (0, –4) (g) x: (–1, 0),

( 2 __

( 1 __

2 , 0 ) ; 349 8 x + 1 4. (a) B (b) (i) P = 0·24t + 7·6

__ 64 p + 13 4. (a) y = 3x – 2

5 (d) y = − 1 _

_ 2 x + 6 (d) P = 3

3 x + 7 _

3

_ 2 t + 5

_ 3 x − 3 (c) y = 7x – 0·5

_ 3 x − 1

_ 3

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