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LearnCambridge97092026–2027Paper 1 · Pure Mathematics 1Quadratics

Paper 1 · Module

Quadratics

5 subtopics≈ 205 min in total

Start the module: Completing the square and the vertex Open graphing calculator

Completing the square and the vertex
Rewrite $ax^2+bx+c$ as $a(x+p)^2+q$ , read off the vertex, line of symmetry and least or greatest value, and use it to sketch parabolas and solve real problems about maximum height or area.
≈ 45 min
Solving quadratic equations
Three ways to solve $ax^2+bx+c=0$ (factorising, completing the square and the formula), choosing the quickest, giving exact answers, and spotting quadratics in disguise such as $x^4-5x^2+4=0$ .
≈ 45 min
The discriminant and the nature of roots
How $b^2-4ac$ tells you whether a quadratic has two, one or no real roots without solving it, how to find unknown constants from that, and how to show an expression is always positive.
≈ 40 min
Linear and quadratic inequalities
Solve linear inequalities, then quadratic ones using critical values and a sketch, write the answer correctly (and, or, set notation), and combine two conditions.
≈ 35 min
Simultaneous equations and lines meeting curves
Solve one linear and one quadratic equation together by substitution, find the points where a line meets a curve, and use the discriminant to decide whether a line crosses, touches or misses a curve.
≈ 40 min