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100s of Maths Questions on Quadratics
A teacher-ready question bank on quadratics for Years 9-10 (Grades 9-10). Cover factoring, completing the square, the quadratic formula, parabolas, the discriminant, and applied problems — with answers and difficulty tiers built in.
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What’s Included in the Quadratics Question Bank
🔥Progressive Difficulty Levels
Questions across every standard method: factoring monic and non-monic trinomials, difference of two squares, completing the square, and the quadratic formula — sequenced so students build fluency in one approach before mixing them.
🌍 Targeted Practice
Coverage of parabola behaviour: vertex and standard form, axis of symmetry, roots, intercepts, and the discriminant. Includes graph-reading items so students connect algebraic work to the curve.
💡Conceptual Understanding
Applied problems set in projectile motion, area and dimension, profit and revenue, and braking distance — so quadratics earn their place in the unit rather than sitting as isolated algebra.
Practice Questions
Practice Questions
Three tiers per sub-topic: starter items that lock in technique, core items at year-level standard, and extension items pitched at higher-band students or pre-senior preparation. Use them as do-nows, exit tickets, or full lessons.
Engaging Exercises
Engaging Exercises
Every question ships with worked answers, so you can hand the set to a relief teacher, set it for homework, or run it as a self-marking station without a second prep block.
Differentiated Questions
Differentiated Questions
Filter by sub-topic — factoring, quadratic formula, completing the square, graphs, applications — so you can target the specific gap surfaced by a recent assessment instead of reteaching the whole unit.
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What Is Covered in the Quadratics Question Bank
Solving Quadratic Equations
Students work through factoring (monic, non-monic, and difference of two squares), completing the square, and the quadratic formula. The bank sequences items by method first so students build fluency in each technique, then mixes methods so they learn to choose the most efficient route for a given equation. The discriminant is introduced as the tool for predicting how many real solutions exist before any working is shown.
Quadratic Functions and Parabolas
The standard form ax² + bx + c, vertex form, and factored form are treated as three views of the same curve. Students convert between forms, identify the axis of symmetry, find the vertex by completing the square or using -b/2a, and sketch parabolas from key features. Graph-reading items ask students to recover an equation from a labelled diagram — the inverse skill — which is where most students lose marks in end-of-topic assessments.
Applied and Word Problems
Applied questions are set in contexts students actually see in senior maths: projectile motion (maximum height and time of flight), area and perimeter constraints, optimisation of revenue or profit, and braking distance. Each context is paired with a scaffolded version and an unscaffolded version, so you can differentiate without writing two sets of questions.
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