Mastering Quadratic Equations
Mathematics
GCSE Foundation
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A worksheet covering Quadratic Equations for GCSE Foundation students.
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Mastering Quadratic Equations
Subject: MathematicsGrade: GCSE Foundation
Name:
Date:
Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Review the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a. Use this formula to solve quadratic equations, and practice factoring and reasoning with quadratic expressions.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Factorize the quadratic expression: x² + 5x + 6.
[2 marks]2.
Solve for x: x² - 4x - 5 = 0.
[3 marks]3.
Calculate the roots of 2x² + 3x - 2 = 0 using the quadratic formula.
[3 marks]4.
Factorize: 3x² + 12x.
[2 marks]5.
Solve for x: 4x² = 25.
[3 marks]6.
Factorize: x² - 9.
[2 marks]7.
Determine whether x = 2 is a root of x² - 4x + 4 = 0.
[2 marks]8.
Find the value of x: x² + 6x + 9 = 0.
[2 marks]9.
Complete the square to solve: x² + 4x - 5 = 0.
[3 marks]10.
A ball is projected such that its height h(t) = -16t² + 32t + 5, where t is in seconds. Find the time when the ball hits the ground.
[4 marks]11.
A rectangular garden's length and width are modeled by the quadratic equations x² + 3x - 4 and 2x - 1 respectively. Find the value of x when the area is maximized.
[4 marks]Quick Actions
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet