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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. Focus on common denominators and simplifying expressions.
B

Practice Questions

Answer all questions. Show your working in the grid spaces provided.
1.
Simplify the algebraic fraction: 2x4 \frac{2x}{4} .
[2 marks]
2.
Simplify the expression: x2−9x−3 \frac{x^2 - 9}{x - 3} .
[2 marks]
3.
Factorise the numerator: x2+5x+6 x^2 + 5x + 6 .
[2 marks]
4.
Solve for x: x+1x−2=3 \frac{x + 1}{x - 2} = 3 .
[3 marks]
5.
Express 3xx2 \frac{3x}{x^2} in simplified form.
[2 marks]
6.
Simplify x3−8x−2 \frac{x^3 - 8}{x - 2} .
[2 marks]
7.
A robot moves in such a way that its position p p in meters is given by p=4xx+1 p = \frac{4x}{x + 1} . For x=2 x = 2 , find the position of the robot.
[3 marks]
8.
A car's fuel efficiency is modeled by 120x \frac{120}{x} miles per gallon, where x x is the number of gallons used. If a car uses 4 gallons, how many miles can it travel?
[3 marks]
9.
The sum of two algebraic fractions is 3x+2x+x−1x \frac{3x + 2}{x} + \frac{x - 1}{x} . Simplify the sum.
[3 marks]
10.
Challenge: A swimming pool is being filled with water at a rate modeled by 5xx+2 \frac{5x}{x + 2} liters per minute, where x x is the number of minutes. How long will it take to fill 50 liters?
[4 marks]

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Details

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