x² + bx + c = 0: Real-world Applications
Mathematics
Grade 6
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the application of solving quadratic equations of the form x² + bx + c = 0 through real-world problems, procedural practice, and reasoning tasks.
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x² + bx + c = 0: Real-world Applications
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Solve the following quadratic equations by factorising. Show all your working in the grid areas provided.
1.
Factorise the quadratic equation x² + 5x + 6 = 0 and find its solutions.
[2 marks]2.
Factorise x² - 7x + 12 = 0.
[2 marks]3.
Solve for x: x² + 3x - 4 = 0.
[2 marks]B
Problem Solving & Reasoning
Read the problem carefully and use your knowledge of factorising quadratics to find the solution. Show your working.
1.
A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, find the dimensions of the garden by setting up and solving a quadratic equation.
[4 marks]2.
A ball is thrown upwards, and its height in meters after t seconds is given by h = -5t² + 10t + 2. When does the ball reach a height of 8 meters? Set up and solve the quadratic equation.
[4 marks]C
Real-world Applications
Solve these contextual problems involving quadratic equations. Show your detailed working.
1.
A toy rocket is launched vertically, and its height in meters after t seconds is given by h = -4t² + 16t + 5. When will the rocket hit the ground?
[4 marks]2.
A farmer wants to build a rectangular pen with an area of 24 square meters. The length of the pen is 2 meters more than its width. Find the dimensions of the pen by solving a quadratic equation.
[4 marks]D
Challenge & Extension
Attempt these more challenging problems to extend your understanding. Show all your working.
1.
The quadratic equation x² + (k)x + 20 = 0 has equal roots. Find the value of k and then factorise the quadratic for that value.
[4 marks]2.
Construct a quadratic equation with roots at x = -2 and x = 3, then factorise it.
[4 marks]E
Mixed Review
Solve these various questions to review your understanding of quadratic factorisation.
1.
Factorise: x² + 2x - 15 = 0.
[2 marks]2.
Solve for x: x² - 4x + 4 = 0.
[2 marks]F
Error Analysis
Below is a student’s solution to factorise x² + 6x + 9 = 0. Read the solution and identify any mistakes, then correct them.
1.
Student’s solution: x² + 6x + 9 = (x + 3)(x + 3) = 0, so x = -3. Is this correct? If not, what is the mistake and what is the correct solution?
[4 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet