467·Mathematics · GCSE
The Graph and the
Algebra Are One Thing
Algebra and graphs knowledge mat for secondary schools (PDF)
Where on a curve the answer to x² − 2x − 3 = 0 sits — and why that makes the graph a way of checking. Expressions, equations and identities; factorising, rearranging and simultaneous equations; a quadratic read both ways, roots to vertex; indices, inequalities and quadratic sequences with a second-difference figure; the three results you must know unprompted; a quadratic solved by factorising and checked on its graph. Eleven terms to define, a model answer on a perpendicular line, and the misconceptions that cost marks.
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One purchase covers the school that buys it. Print it, copy it, hand it round your department. Not for passing to other schools or uploading anywhere.
One landscape A4 page on one topic, built around one idea a class can hold onto. It carries expressions and identities, factorising and simultaneous equations, a quadratic read both ways, indices, inequalities, quadratic sequences and a quadratic solved and checked on its graph — then the vocabulary, a worked exam-style answer and the misconceptions that cost marks.
No photographs, on purpose: there is no archival photograph of a percentage, and a stock image of a calculator would make the sheet worse. Every figure is drawn in code for the sheet — a bar model, a graph, a tree diagram — so nothing on it is licensed from anybody and nothing is AI-generated. Every claim is sourced to the DfE subject content and its Appendix of formulae, and nothing is reproduced from a past paper, a textbook or a specification.
Sold by subject: all four mathematics sheets for one price. A knowledge organiser stores a unit and is revised from afterwards; this is meant to be on the table while the work is happening.
- Written to The DfE GCSE mathematics subject content (DFE-00233-2013) and its Appendix of formulae. No photographs: every figure is drawn in code for the sheet, so nothing on it is licensed from anybody
- Intended for mathematics teachers — on the desk during the lesson, not a student revision guide
- Extent 1 page · 8 sections
—·Look inside
Real pages, straight from the PDF
Click any page to see it full size.
—·Contents
All 8 sections
Taken from the booklet’s own contents page, so the page numbers are the real ones.