EDEXCEL O/L 4PM1 (Further Pure Maths) - Unit 1 Questions Tute

FURTHER PURE MATHEMATICS
EDEXCEL IGCSE
TUTE 1 – INDICES, SURDS & QUADRATICS
Prepared by Mr. Vijith Fernando


1. Simplify fully
( x 3 y 2 ) 2 ( x 1 y 4 )
x 2 y 3

2. Given that
2 a  4 b  8c

Find the ratio a : b : c.


3. Find the exact solution of
4 ( x  2 )  8( 3 x 1)


4. Simplify completely
2
(27 x ) ( x  2 ) 2
3 3


3x

5. Solve for x
9 x  32 x 1


6. Simplify fully
50  3 8  2 18

a 3
7. Given that  11  b 3 Where a and b are integers,
2 3
find the value of a and the value of b.


42 3 ab 3
8. Given that can be written in the form where a and b are integers and c is prime,
52 3 c
find the value of a, the value of b and the value of c.


9. Simplify fully
12  27
3



1

, 10. Given
x 6 3

Find the exact value of
1
x
in surd form.


11. Let
1
x
2 3

(a) Express x in the form a  b 6 .

(b) Hence find the exact value of
1
x
x


12. The quadratic equation

3(k  2) x 2  (k  5) x  k  0

has real roots.

Find the set of possible values of k.


13. The quadratic equation

2 x 2  kx  12  0

can be factorised into two linear factors with integer coefficients.

(a) Find the possible values of k.

For one of these values of k, the equation has two distinct real roots that are not integers.

(b) Using the quadratic formula, find the exact roots for this value of k, giving your answers in surd
form.


14. Here is a quadratic equation 3 x 2  px  4  0 where p is a constant.

(a) Find the set of values of p for which the equation has two real distinct roots.

(b) List all the possible integer values of p for which the equation has no real roots.




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