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1 Simplify
(Total for question 1 is 2 marks)
125 x
6
1
3
( 2 x
1
2
3
4 x
2
2 Simplify
(Total for question 2 is 2 marks)
4 Express 9
3 x + 2
in the form 3
y
, giving y in the form ax + b, where a and b are constants.
(Total for question 4 is 2 marks)
5 Express 8
2 x โ 5
in the form 2
y
, giving y in the form ax + b, where a and b are constants.
(Total for question 5 is 2 marks)
6 Given y = 2
x
(a) Express 4
x
in terms of y.
(b) Hence, or otherwise, solve 4
x
- 6(
x
) โ 16 = 0
(Total for question 6 is 5 marks)
7 Solve: 2
2 x + 1
- 5(
x
) โ 12 = 0
(Total for question 7 is 5 marks)
216 x
6
27 y
3
โ
2
3
3 Simplify
(Total for question 3 is 2 marks)
(Total for question 8 is 3 marks)
8 Solve the equation 8
2 x โ 5
= 2
x + 1
AS Level Maths: Algebraic Expressions
15 Find the value of x such that
1 + x
x
Giving your answer in the form a + b 5 where a and b are rational numbers.
(Total for question 15 is 4 marks)
(Total for question 16 is 3 marks)
16 Show that can be written as
(Total for question 17 is 3 marks)
17 Show that can be written as
(Total for question 10 is 3 marks)
11 Factorise completely: x โ 16 x
3
(Total for question 11 is 2 marks)
12 Factorise completely: 75 x โ 12 x
3
(Total for question 12 is 2 marks)
10 Find the value of x such that
x + 1
= 4
3 x โ 1
13 Expand and Simplify: (2 x โ 1)( x + 2)( x โ 3)
(Total for question 13 is 2 marks)
14 Expand and Simplify: (3 x โ 2)( x โ 5)
2
(Total for question 14 is 2 marks)
9 (a) Solve the equation: x
2
(b) Hence solve the equation: y
3
- 9 y
3
2
(Total for question 9 is 4 marks)
26 In this question you must show detailed reasoning.
(i) Express in the form , where a is an integer and b is a prime number.
(ii) Express in the form , where c and d are integers and e is a prime number.
(Total for question 26 is 5 marks)
a
2 b
9
2
c + d
e (3)
27 In this question you must show detailed reasoning.
Solve the equation , giving your answer in the form where a and
b are positive integers.
(Total for question 27 is 3 marks)
x ( 3 โ
a + b
31 Given that k is an integer, express in the form where a and b are rational
expressions in terms of k.
(Total for question 31 is 4 marks)
18 โ k
a + b
28 Find, using algebra, all the real solutions to the equation
(i) a
2
= 8โa
(ii) b
4
2
(Total for question 28 is 7 marks)
30 (i) Solve the equation
x + โ12 = x โ 3
writing the answer as a surd in its simplest form.
(ii) Solve the equation
3x โ 1
= 3โ 3
(Total for question 30 is 6 marks)
29 Solve the equation
(Total for question 29 is 4 marks)
x
3
3
2
