Cambridge International A and AS Level Mathematics Pure ...
[Pages:42]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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