Mastering ax² + bx + c = 0: Problem Solving & Reasoning
Mathematics
Year 9
13 questions
~26 mins
3 views0 downloads
About This Worksheet
A worksheet designed to develop proficiency in solving quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Includes procedural practice, reasoning, real-world contexts, and extension problems.
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Mastering ax² + bx + c = 0: Problem Solving & Reasoning
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Read the introduction carefully before attempting the questions.
1.
The quadratic formula is used to solve equations of the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / 2a. Use this formula to find the solutions to the following quadratic equations.
[2 marks]B
Fluency & Practice
Solve the following quadratic equations using the quadratic formula.
1.
Solve 2x² + 3x - 2 = 0 for x.
[3 marks]2.
Solve x² - 4x + 1 = 0.
[3 marks]3.
Solve 3x² + 0x - 7 = 0.
[3 marks]C
Problem Solving & Reasoning
Apply your knowledge to multi-step problems, explaining your reasoning.
1.
A ball is thrown upwards such that its height after t seconds is given by h = -5t² + 20t + 2. Find the times at which the ball reaches the ground. Explain your steps.
[4 marks]2.
The product of two numbers is 24, and their difference is 2. The numbers satisfy the quadratic equation x² - 4x - 6 = 0. Find the numbers.
[4 marks]D
Real-world Applications
Solve these practical problems involving quadratic equations.
1.
A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 54 m², find its dimensions. (Set up and solve the quadratic equation.)
[4 marks]E
Challenge & Extension
Attempt these more difficult problems for extended understanding.
1.
Given the quadratic equation 4x² + px + 9 = 0, find the value of p such that the roots are real and equal. Show your working.
[4 marks]2.
If the roots of the quadratic equation x² + kx + 16 = 0 are real, find the range of possible values for k.
[4 marks]F
Mixed Review
Solve these questions involving various aspects of quadratic equations.
1.
Factorize the quadratic: x² - 5x + 6. Then, solve for x.
[3 marks]2.
Complete the square for x² + 6x + 5 and find its roots.
[3 marks]G
Error Analysis
Identify and correct the common mistakes made in solving quadratics.
1.
A student solves x² + 4x + 3 = 0 by factoring incorrectly as (x + 2)² = 0. Identify the mistake and solve the equation correctly.
[4 marks]2.
Explain why using the quadratic formula with a negative discriminant results in complex solutions, and give an example.
[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.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet