📚 What's in here
Two complete units. Year 10 — Parabolas: solving quadratic equations (5G–5J) then sketching parabolas (7A–7G). Year 11 — Counting Methods: the counting principles, arrangements, selections and probability (10A–10D).
Every lesson has worked examples (click Show solution), a video walkthrough, a quick auto-marked quiz, and a Cambridge working program — plus a printable worksheet and answer key.
Year 10 Core · Parabolas — Chapter 5 (solving quadratics) & Chapter 7 (graphs)
Solving by Factorising
The Null Factor Law; solving by taking out a common factor, monic and non-monic factorising, and difference of two squares.
Open online lessonApplications of Quadratics
Setting up and solving worded problems with quadratics, and rejecting answers that don't make sense (like a negative length).
Open online lessonCompleting the Square
Solving a quadratic by turning it into a perfect square, including answers left in exact surd form.
Open online lessonQuadratic Formula & Discriminant
The quadratic formula, and how the discriminant tells you whether there are two, one or no solutions.
Open online lessonExploring Parabolas
The basic parabola and its key features — turning point, axis of symmetry, intercepts — plus dilations and reflections.
Open online lessonSketching using Transformations
Sketching from turning-point form — shifting, stretching and reflecting the basic parabola, and reading off the turning point.
Open online lessonSketching using Factorisation
Finding x-intercepts by factorising, then using them to locate the axis of symmetry and the turning point.
Open online lessonSketching by Completing the Square
Completing the square to find the turning point, then sketching with all key features labelled.
Open online lessonQuadratic Formula & Discriminant
Using the quadratic formula for irrational x-intercepts, and the discriminant to predict how many x-intercepts a parabola has.
Open online lessonApplications of Parabolas
Maximum and minimum problems — projectile paths, areas — using the turning point and intercepts to answer in context.
Open online lessonIntersection of Lines & Parabolas
Solving a line and a parabola together, and using the discriminant to tell whether they meet at two points, touch, or miss.
Open online lessonYear 11 Methods · Counting Methods — Cambridge Methods 1&2 (10A–10D)
Addition & Multiplication Principles
The two counting rules: add the choices when it's "this or that", multiply them when it's "this and then that".
Open online lessonArrangements (Permutations)
Factorials and the permutations rule for putting things in order, including arrangements with restrictions.
Open online lessonSelections (Combinations)
Choosing a group when order doesn't matter — the combinations rule, team-selection problems, and selections of any size.
Open online lessonApplications to Probability
Using arrangements and selections to count outcomes and work out probabilities for equally-likely situations.
Open online lesson