Playbook
Quadratic Equations
89 q · 24% HARD · about 4.2 a paper, the HARD spread thinly across nine subtopics. Common roots, maximum/minimum and word problems have never set a HARD question.
- Questions in the bank
- 89
- q/paper (21 papers)
- 4.24
- Tagged HARD
- 24%
- Subtopics
- 9
Strand: Selective
When you’ll see it
A quadratic to solve or form, or a question about its roots without solving it.
How this chapter is tested
89 questions, about 4.2 a paper, at 24% HARD spread thinly over nine subtopics. Common roots, maximum and minimum, and word problems have never set a HARD question.
Most questions never need the roots themselves: the sum −b/a, the product c/a and the discriminant answer them.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Sum and product of roots
α + β = −b/a, αβ = c/a, and expressions like α² + β² built from them.
Nature of roots
The discriminant b² − 4ac: positive, zero or negative.
Forming an equation
x² − (sum)x + (product) = 0.
Roots in a relation
One root twice the other, or roots in a ratio.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Sign of the sum
The sum of roots is −b/a, not b/a.
Real and equal
A zero discriminant gives equal roots; 'real' includes equal.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Quadratic Equations notesDrill every Quadratic Equations question
89 questions from the bank, across 9 subtopics.
Drill one subtopic at a time
The 9 subtopics, in teaching order.
- Solving and Forming Quadratic EquationsDrill Solving and Forming Quadratic Equations
- Symmetric Functions of the RootsDrill Symmetric Functions of the Roots
- Roots in a Given RelationDrill Roots in a Given Relation
- Nature of Roots and DiscriminantDrill Nature of Roots and Discriminant
- Perfect Squares, Signs and Location of RootsDrill Perfect Squares, Signs and Location of Roots
- Common RootsDrill Common Roots
- Maximum and Minimum of Quadratic ExpressionsDrill Maximum and Minimum of Quadratic Expressions
- Equations Reducible to QuadraticsDrill Equations Reducible to Quadratics
- Word Problems and ApplicationsDrill Word Problems and Applications
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