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studyAlgebra
CoreMaths revision

Quadratic Expressions

Analyse quadratics through expansion, factorisation, completing the square and coefficient relationships.

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Focus points
✓Move between quadratic forms.
✓Complete the square.
✓Use roots and coefficients strategically.
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The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · expansion
Expand and simplify (x−4)(x+7).
Question 2FluencyCore
Original practice · Free Online Revision
Skill · factorisation
Factorise x²−2x−35.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · completing the square
Write x²+8x+3 in the form (x+a)²+b.
Question 4FluencyCore
Original practice · Free Online Revision
Skill · vertex form
Find the minimum value of x²−6x+11.
Question 5ReasoningCore
Original practice · Free Online Revision
Skill · Vieta relations
The roots of x²−9x+14 are α and β. Find α+β and αβ.
Question 6FluencyCore
Original practice · Free Online Revision
Skill · forming quadratics
Form a monic quadratic whose roots are 4 and −3.
Question 7ReasoningStretch
Original practice · Free Online Revision
Skill · algebraic identities
If x+1/x=5, find x²+1/x².
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · coefficient structure
Find all k for which x²+kx+9 is a perfect square trinomial.