Cambridge International AS and A Level Mathematics Pure Mathematics 1

Answers

282

P1^

  8 (i) x = ±1 or x = ±2

(ii) x = ±1 or x = ±3

(iii) x = ±^23 or x = ±1

(iv) x = ±1.5 or x = ±2

(v) x = 0 or x = ±0.4

(vi) x = 1 or x = 25

(vii) x = 1 or x = 2

(viii) x = 9 (Note: 4 means +2)

  9 (i) x = ±1

(ii) x = ±2

(iii) x = ±3

(iv) x = ±2

(v) x = ±1 or x = ±1.5

(vi) x = 1 or x = 32

(vii) x = 4 or x = 16

(viii) x = 14 or x = 9

10 x = ±3

11 (i) w(w + 30)

(ii) 80 m, 380 m

12 (i) A = 2 πrh + 2 πr^2

(ii) 3 cm

(iii) 5 cm

13 (ii) 14

(iii) 45

14 x^2 + (x + 1)^2 = 292 ;

20 cm, 21 cm, 29 cm

●?^ (Page^ 22)

Since ()x+a 2

2

= x^2 + ax + a

2

4 , it

follows that to make x^2 + ax into a

perfect square you must add a

2

4 or

a

2

2

() to it.

Exercise 1E (Page 24)

  1 (i) (a) (x + 2)^2 + 5

(b) x = − 2; (−2, 5)

(c)

(ii) (a) (x − 2)^2 + 5

(b) x = 2; (2, 5)

(c)

(iii) (a) (x + 2)^2 − 1

(b) x = −2; (−2, −1)

(c)

(iv) (a) (x − 2)^2 − 1

(b) x = 2; (2, −1)

(c)

(v) (a) (x + 3)^2 − 10

(b) x = − 3; (−3, −10)

(c)

(vi) (a) (x − 5)^2 − 25

(b) x = 5; (5, −25)

(c)

(vii) (a) (^) ()x+^12 +
2
(^134)
(b) x=–;^12 ()–, 21134
(c)
x
y
(0, 9)
(–2, 5)
O
x
y
(0, 9)
(2, 5)
O
x
y
(0, 3)
(–2, –1)
O
x
y
(0, 3)
(2, –1)
O
x
y
(0, –1)
(–3, –10)
O
x
y
(5, –25)
O
x
y
(0, 2)
O
(– , 1 )^1 – 2 –^34