Cambridge International AS and A Level Mathematics Pure Mathematics 1

Exercise 1D

19

P1^

1

3 Factorise the following quadratic expressions.

(i) x^2 + 6 x + 8 (ii) x^2 − 6 x + 8

(iii) y^2 + 9 y + 20 (iv) r^2 + 2 r − 15

(v) r^2 − 2 r − 15 (vi) s^2 − 4 s + 4

(vii) x^2 − 5 x − 6 (viii) x^2 + 2 x + 1

(ix) a^2 − 9 (x) (x + 3)^2 − 9

4 Factorise the following expressions.

(i) 2 x^2 + 5 x + 2 (ii) 2 x^2 − 5 x + 2

(iii) 5 x^2 + 11 x + 2 (iv) 5 x^2 − 11 x + 2

(v) 2 x^2 + 14 x + 24 (vi) 4 x^2 − 49

(vii) 6 x^2 − 5 x − 6 (viii) 9 x^2 − 6 x + 1

(ix) t 12 − t 22 (x) 2 x^2 − 11 xy + 5 y^2

5 Solve the following equations.

(i) x^2 − 11 x + 24 = 0 (ii) x^2 + 11x + 24 = 0

(iii) x^2 − 11 x + 18 = 0 (iv) x^2 − 6 x + 9 = 0

(v) x^2 − 64 = 0

6 Solve the following equations.

(i) 3 x^2 − 5 x + 2 = 0 (ii) 3 x^2 + 5 x + 2 = 0

(iii) 3 x^2 − 5 x − 2 = 0 (iv) 25 x^2 − 16 = 0

(v) 9 x^2 − 12 x + 4 = 0

7 Solve the following equations.

(i) x^2 − x = 20 (ii) 35

3

4

xx^2 +

=

(iii) x^2 + 4 = 4 x (iv) 21 x+=^15 x

(v) x−= (^1) x^6 (vi) 3 x+=^8 x 14
8 Solve the following equations.
(i) x^4 – 5x^2 + 4 = 0 (ii) x^4 – 10x^2 + 9 = 0
(iii) 9 x^4 – 13x^2 + 4 = 0 (iv) 4 x^4 – 25x^2 + 36 = 0
(v) 25 x^4 – 4x^2 = 0 (vi) (^) xx−+ 65 = 0
(vii) x^6 – 9x^3 + 8 = 0 (viii) xx−− 60 =
9 Find the real roots of the following equations.
(i) x
x
2
(^12)
+=^2 (ii) x
x
2
(^12)
=+^12
(iii) x
x
2
(^62)
−=^27 (iv) 1 120 0
+−xx 24 =
(v) 9424 13
xx
+= (vi) x
x
3
3
+=^23
(vii) x
x
+=^86 (viii) 2 +=x^37
x