GCSE (1 – 9)
Algebraic Fractions
Name: ___________________________
Instructions
• Use black ink or ball-point pen.
• Answer all questions.
• Answer the questions in the spaces provided
– there may be more space than you need.
• Diagrams are NOT accurately drawn, unless otherwise indicated.
• You must show all your working out.
Information
• The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.
• Keep an eye on the time.
• Try to answer every question.
• Check your answers if you have time at the end
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1 Simplify fully
(Total for question 1 is 2 marks)
…..........................
x
2
+ 5
x
x
2
+ 7
x
+ 10
2 Simplify fully
(Total for question 2 is 2 marks)
…..........................
x
2
−
x
− 12
x
2
− 9
x
+ 20
3 Simplify fully
(Total for question 3 is 2 marks)
…..........................
3
x
2
+ 9
x
x
2
− 9
4 Simplify fully
(Total for question 4 is 2 marks)
…..........................
x
+ 4
x
2
− 16
5 Write in the form where a, b, and c are integers.
(Total for question 5 is 3 marks)
…..........................
3
x
2
+ 11
x
− 4
x
2
+ 3
x
− 4
ax + b
x + c
6 Write in the form where a, b, and c are integers.
(Total for question 6 is 3 marks)
…..........................
x
2
+ 7
x
− 18
2
x
2
−
x
− 6
x + a
b x + c
7 Simplify fully
(Total for question 7 is 3 marks)
…..........................
3 x + 6
x − 4
÷
2 x
2
+ 9 x + 10
x
2
− 4 x
8 Simplify fully
(Total for question 8 is 3 marks)
…..........................
2 x − 2
x + 5
÷
x
2
− 4 x + 3
2 x
2
+ 13 x + 15
9 Solve
(Total for question 9 is 4 marks)
…....................................................
8
x + 3
+
3
x + 8
= 1
10 Solve
(Total for question 10 is 4 marks)
…....................................................
8
3 x − 2
+
6
x + 1
= 2
11 Solve
(Total for question 11 is 4 marks)
…....................................................
2
5
−
x
+
3
x
+
7
=
1
12 Solve
(Total for question 12 is 4 marks)
…....................................................
7
x + 1
−
4
3x − 2
= 1
13 Given that
2x + 1 : x + 2 = x + 8 : 3x – 4
Find the possible values of x.
(Total for question 13 is 4 marks)
…....................................................
14 Given that
x – 1 : 2x – 3 = x + 2 : 3x – 2
Find the possible values of x.
(Total for question 14 is 4 marks)
…....................................................
15 Given that
x + 9 : 5x – 1 = x + 7 : 2x – 3
Find the possible values of x.
(Total for question 15 is 4 marks)
..........................…..........................
16 Given that
5 – 3x : 9 – x = 3x + 7 : 4 – x
Find the possible values of x.
(Total for question 16 is 4 marks)
..........................…..........................
