Cambridge International A and AS Level Mathematics Pure ...

Cambridge International A and AS Level Mathematics Pure Mathematics 1 Practice Book

University of Cambridge International Examinations bears no responsibility for the example answers to questions taken from its past question papers which are contained in this publication.

Answers

1 Algebra

Exercise 1.1

1 (i) 11a - 9b (ii) -17cd3 - 14cd - 15c4d2 (iii) 5a + 3ab

(vi) x = - 1 or 3

2

(vii) x = 3 or -1

2

(viii) x = - 1 or 2

3

(ix) x = 2 or -3

5

(x) x = 1 (xi) x = ? 1

3

(iv) 2f 3g

(v)

6x y

(vi)

8 x

(vii)

149 60 x

(viii) x + 15 20

2 (i) 3mn2 (4 + 3n)

(ii) (p - 4)(p + 3)

(iii) (3q - 1)(q + 2)

(iv) (t - 2u)(s + p)

(xii) x = 1 or - 3

3

2

(xiii) x = 0 or 2

(xiv) x = - 4 or 1

3

2

2 (i) x = ?1

(ii) x = 1 or 2

2

(iii) x = 4

(iv) x = 1 or x = 2 (v) x = ? 1

2

(vi) x = 4

3 (i) x = -17

(ii)

x

=

2

-12

=

-1

6

4 x = 168km

5 (i)

e

=

v

bd - bc

Exercise 1.3

1 (i) ( x - 3)2 - 8

(ii) ( x + 2)2 - 4

( ) (iii) x - 3 2 - 1

2

4

(ii)

k

=

p-n m2 + w

(iii)

v

=

fu u-f

(iv) ( x + 1)2 + 4 2 (i) x = 3 ? 8

(ii) x = 0 or - 4

(iv)

e

=

d 3

-

p 122w

(iii) x = 2 or 1

3 (i) 2( x - 1)2 + 5

Exercise 1.2

1 (i) x = 0 or -5 (ii) x = 5 or -5 (iii) x = 4 or -2 (iv) x = -7 or 2 (v) x = 8 or - 5

(ii) 2( x + 3)2 - 7

(iii) 3( x + 2)2 - 16

(iv) 5( x - 4)2 - 8

(v) 4( x + 3)2 - 52

( )2

(vi) 9 x - 1 - 1

3

1

P1

Answers

4 (i) a = 19, b = 4

(ii) a = 2, b = 1

5 a = 15, b = 2, c = 2

6 (i)

y 5 4 3 2 1

-7 -6 -5 -4 -3 -2 -1-10 1 2 3 4 5 6 7 x -2 -3 -4 -5

Vertex (?1, 0)

(ii)

y 5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1-10 1 2 3 4 5 6 7 x -2 -3 -4 -5

Vertex (?4, ?2)

(iii)

y

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1-10 1 2 3 4 5 6 7 x -2 -3 -4 -5

Vertex (2, 1)

(iv)

y

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x -1

-2

-3

-4

-5

Vertex (

1 2

,

?4)

(v)

y

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x -1

-2

-3

-4

-5

Vertex(?

1 2

,

1)

(vi)

y

5

4

3

2

1

?7 ?6 ?5 ?4 ?3 ?2 ?1?10 1 2 3 4 5 6 7 x ?2 ?3 ?4 ?5

Vertex (? 2, ?1)

(vii)

y

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x -1 -2 -3 -4 -5

Vertex (0.5, 2.25)

(viii)

y

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1-10 1 2 3 4 5 6 7 x -2 -3 -4 -5

Vertex (1, 1)

2

7 (i) y = ( x - 4)2 - 2 (ii) y = -( x - 1)2 + 5 (iii) y = x( x + 2) = ( x + 1)2 - 1 (iv) y = -( x - 3)2 + 4

Exercise 1.4

1 (i) x = 1.79 or -2.79 (3 s.f.)

(ii) x = 6.14 or -1.14 (3 s.f.)

(iii) x = 0.180 or -1.85 (3 s.f.)

(iv) x = -0.354 or 2.35

2 (i) 3 2

(ii) 5 3 (iii) 3 5

3 a = 3.

4 Using to be the value of the discriminant:

(i) No solutions

(ii) No solutions

(iii) Two solutions

(iv) One solution

(v) No solutions

(vi) Two solutions

5 (i) k = -4

(ii) k = 4 or - 4

(iii) k = 2

(iv) k = 0 or - 4

6 (i)

1> k k 6

(iii) k < 0 or k > 4 (iv) k > -36

24

k > -3

2

7 (i) (ii)

- 2 2 or k < - 2 (iv) k < -1 8 (i) m = -4, n = -12 (ii) p = -16

Exercise 1.5

1 (i) x = 3, y = -1 (ii) x = -2, y = 5 (iii) x = 3, y = 12 (iv) x = 6, y = -3

Exercise 1.6

1 (i) x -9

(ii) x < -8

(iii) x > -2 or

2 (i)

x < 0 or x > 1

-2 < x y 5 4 3 2 1

?5 ?4 ?3 ?2 ?1 0 ?1 ?2 ?3 ?4 ?5

1 2 3 4 5x

(ii) 0 ................
................

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