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Mastering Algebraic Fractions

Mathematics
GCSE Foundation
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About This Worksheet

A worksheet covering Algebraic Fractions for GCSE Foundation students.

Topics covered:

#Mathematics
#Algebraic Fractions

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Mastering Algebraic Fractions

Subject: MathematicsGrade: GCSE Foundation
Name:
Date:

Untitled Worksheet

Grade GCSE Foundation
A

Introduction

Review the key concepts of simplifying and manipulating algebraic fractions. Remember to factor expressions where necessary.
B

Practice Questions

Answer all questions. Show your working in the grid spaces provided.
1.
Simplify the algebraic fraction: 2x2−84x \frac{2x^2 - 8}{4x} .
[2 marks]
2.
Simplify: 3x2+6x9x \frac{3x^2 + 6x}{9x} .
[2 marks]
3.
Express the sum: 1x+2x2 \frac{1}{x} + \frac{2}{x^2} as a single fraction.
[3 marks]
4.
Factor the numerator: 6x2+9x 6x^2 + 9x .
[2 marks]
5.
Simplify: 4x2−92x+3 \frac{4x^2 - 9}{2x + 3} .
[2 marks]
6.
Solve for x x : x+1x−2=34 \frac{x + 1}{x - 2} = \frac{3}{4} .
[3 marks]
7.
If 3xx+2=2 \frac{3x}{x + 2} = 2 , find x x .
[3 marks]
8.
Express 4x2−12x+1 \frac{4x^2 - 1}{2x + 1} as a simplified algebraic expression.
[2 marks]
9.
A rectangle has length x2 \frac{x}{2} and width 2x+4x \frac{2x + 4}{x} . Find an expression for its area.
[3 marks]
10.
A recipe requires 2x+3x+1 \frac{2x + 3}{x + 1} cups of sugar. If x=4 x = 4 , how many cups are needed?
[2 marks]
11.
Challenge: A car's fuel efficiency is given by 100x+2 \frac{100}{x + 2} miles per gallon, where x x is the number of passengers. If the efficiency drops to 25 miles per gallon, how many passengers are on the car?
[4 marks]
12.
Real-world application: An engineer models the stress on a beam with 5xx+4 \frac{5x}{x + 4} . Find the value of x x when the stress is 4 units.
[4 marks]

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Details

Created
12/30/2025
Updated
12/30/2025
Type
worksheet
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