1
1 Factorise completely.
................................................... [3]
[Total: 3]
2 Expand and simplify .
........................................................................ [3]
[Total: 3]
3 Expand and simplify.
................................................... [2]
[Total: 2]
2
4 Simplify.
................................................... [2]
[Total: 2]
5 Expand and simplify.
................................................... [3]
[Total: 3]
6 (a) Factorise .
................................................... [1]
6 (b) and .
Find the value of p + q.
................................................... [2]
[Total: 3]
3
Find the value of a and the value of b.
a = ...................................................
b = ................................................... [3]
[Total: 3]
8 Complete this statement with an expression in terms of m.
( ................................................... )
[2]
[Total: 2]
The difference between the areas of the two rectangles is 62 cm2.
4
(a) Show that .
[3]
(b) Factorise .
................................................... [2]
(c) Solve the equation to find the difference between the perimeters of the two rectangles.
................................................... cm [2]
[Total: 7]
10 Factorise completely.
(a)
................................................... [2]
5
(b)
................................................... [2]
(c)
................................................... [2]
[Total: 6]
11 The probability that Andrei cycles to school is r.
(a) Write down, in terms of r, the probability that Andrei does not cycle to school.
................................................... [1]
(b) The probability that Benoit does not cycle to school is .
The probability that both Andrei and Benoit do not cycle to school is 0.4 .
(i) Complete the equation in terms of r.
( ................................................... ) × ( ................................................... ) = 0.4 [1]
(ii) Show that this equation simplifies to .
[3]
6
(iii) Solve by factorisation .
r = .............................. or r = .............................. [3]
(iv) Find the probability that Benoit does not cycle to school.
................................................... [1]
[Total: 9]
12 Expand and simplify.
................................................... [2]
[Total: 2]
13 Factorise.
7
(a)
................................................... [1]
(b)
................................................... [2]
[Total: 3]
14 Factorise.
................................................... [2]
[Total: 2]
15 Expand and simplify.
................................................... [2]
[Total: 2]
16 Factorise completely.
8
(a)
................................................... [2]
(b)
................................................... [3]
[Total: 5]
17 Factorise .
................................................... [3]
[Total: 3]
18
9
(a) Find .
................................................... [1]
(b) Find .
................................................... [2]
(c) Find .
................................................... [2]
(d) Find in its simplest form.
................................................... [2]
(e) Find in the form .
................................................... [2]
(f) Find x when .
x = ................................................... [2]
[Total: 11]
10
19 Factorise completely.
................................................... [2]
[Total: 2]
20 Factorise completely.
................................................... [2]
[Total: 2]
21 Expand the brackets and simplify.
................................................... [3]
[Total: 3]
11
22 Factorise.
................................................... [2]
[Total: 2]
23 Factorise.
................................................... [2]
[Total: 2]
24 Factorise.
................................................... [1]
[Total: 1]
25 (a) Factorise .
................................................... [2]
12
25 (b)
The area of the rectangle is 84 cm2.
Find the perimeter.
................................................... cm [3]
[Total: 5]
26 In this question, all measurements are in metres.
The diagram shows a right-angled triangle.
(a) Show that .
[3]
13
(b) Solve .
Show all your working and give your answers correct to 2 decimal places.
x = .............................. or x = .............................. [4]
(c) Calculate the perimeter of the triangle.
................................................... m [2]
(d) Calculate the smallest angle of the triangle.
................................................... [2]
[Total: 11]
27 Factorise completely.
................................................... [2]
[Total: 2]
14
28 Factorise completely.
................................................... [2]
[Total: 2]
29 Factorise.
Answer ................................................... [1]
[Total: 1]
30 Factorise.
Answer ................................................... [2]
[Total: 2]
15
31 Factorise completely.
ax + ay + 3cx + 3cy
Answer ................................................... [2]
[Total: 2]
32 Factorise completely.
3a2 – 12b2
Answer ................................................... [3]
[Total: 3]
33 Factorise 2x2 – 5x – 3.
Answer ................................................... [2]
[Total: 2]
34 Simplify.
Answer ................................................... [2]
[Total: 2]
35 Factorise completely.
16
(a) yp + yt + 2xp + 2xt
Answer(a) ................................................... [2]
(b)
Answer(b) ................................................... [2]
[Total: 4]
36 f(x) =
(a) f(x) can be written in the form .
Find the value of m and the value of n.
Answer(a) m = ...................................................
n = ................................................... [2]
17
(b) Use your answer to part (a) to find the positive solution to .
Answer(b) ................................................... [2]
[Total: 4]
37 Simplify.
................................................... [3]
[Total: 3]
38 Write as a single fraction in its simplest form.
................................................... [3]
[Total: 3]
18
39 Simplify.
................................................... [3]
[Total: 3]
40 Darpan runs a distance of 12 km and then cycles a distance of 26 km.
His running speed is x km/h and his cycling speed is 10 km/h faster than his running speed.
He takes a total time of 2 hours 48 minutes.
(a) An expression for the time, in hours, Darpan takes to run the 12 km is .
Write an equation, in terms of x, for the total time he takes in hours.
................................................... [3]
(b) Show that this equation simplifies to .
[4]
19
(c) Use the quadratic formula to solve .
You must show all your working.
x = .............................. or x = .............................. [4]
(d) Calculate the number of minutes Darpan takes to run the 12 km.
................................................... min [2]
[Total: 13]
