Year 10 - Quadratic equations - Free practice
Year 10 Quadratic Equations Worksheets
Null factor law, factorising, completing the square preview.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 10 quadratic equations expand past null factor law into more varied factorising patterns. These worksheets give your student practice on each method so they're not relying on one approach when the test asks something unfamiliar.
What's covered
Sub-skills your student will practise
- ✓Solving by null factor law from factorised form
- ✓Solving by first factorising a monic quadratic
- ✓Solving simple non-monic quadratics
- ✓Completing the square (preview of Methods)
- ✓Word problems leading to a quadratic equation
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Frequently asked
Questions parents ask about quadratic equations
How does Year 10 quadratic solving differ from Year 9?
Year 10 introduces non-monic quadratics (coefficient of x^2 isn't 1), completing the square as a preview of VCE Methods, and the quadratic formula. Year 9 stayed with monic factorising plus null factor law.
What's the quadratic formula?
For ax^2 + bx + c = 0: x = (-b plus or minus sqrt(b^2 - 4ac)) / 2a. It works for every quadratic, even ones that don't factorise nicely. Most teachers introduce it in Year 10A.
What's the discriminant?
The b^2 - 4ac inside the quadratic formula. If it's positive, the quadratic has two real solutions. If zero, one repeated solution. If negative, no real solutions (the parabola never touches the x-axis).
What real-world problems lead to a quadratic equation?
Anything involving area, projectile motion (h = -5t^2 + vt + s), or revenue / profit modelling. Year 10 introduces a few of each so students see why quadratics show up outside textbook abstractions.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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