The geometry that closes school mathematics. Coordinate methods, transformations, trigonometry, watertight proofs, circles under calculus and vectors in three dimensions, engineered into 57 pages you can master in one afternoon.
Year 12 · Grade 12Ages 16–18Mathematics · Geometry57 pages
Pages
57
Format
A4 PDF
Access
Lifetime
Delivery
Instant
Overview
This is the geometry that closes school mathematics, rebuilt for revision. Fifty-seven pages take a student from the coordinate plane — distances, ratios, gradients and perpendicular gaps — through transformations with every invariant tracked, into the sine and cosine rules with radians running the arcs, congruence and the circle theorems argued to proof standard, the circle equation handed to calculus for tangents and normals, and a final ascent into three dimensions with dot products, lines in space and cross products — then straight into an Exam Lab that rehearses it all under pressure.
It is designed to be skimmed in thirty minutes the night before a test, or worked through properly in two to four hours for a genuine, lasting grip on the year. Every calculation and worked solution has been verified, and the coverage is checked against the shared core of the UK, US, Canadian, Australian, New Zealand and Singapore programmes.
Look inside
A few pages from the book — tap any page to enlarge.
Who it’s for
Students in Year 12 / Grade 12 (ages 16–18) preparing for A-level, IB and equivalent exams
The natural companion to the Year 12 Algebra crash course — the two books shelve as a pair
Parents looking for a rigorous, screen-light revision resource that actually gets used
Anyone moving between the UK, US, Canada, Australia, New Zealand or Singapore systems
Topics included
Coordinate Geometry — distance and midpoint, ratio division, gradient and inclination, line laws, bisectors and point-to-line distance
Transformations — translations, reflections, rotations, enlargements and combined moves, with every invariant tracked
Trigonometry — radians, exact values, the sine rule, the cosine rule and area, and bearings
Geometric Proofs — congruence tests, proof writing, similarity and circle theorems I & II
Circle Geometry & Calculus — the circle equation, implicit slopes, tangents and normals, and related rates
Vectors in Three Dimensions — components and magnitude, the dot product, lines in space and the cross product
Exam Lab — word problems, a 24-question mixed review and full solutions
What your child will be able to do
Measure any segment, cut it in any ratio and drop a perpendicular distance in one formula
Crack any triangle with the sine and cosine rules, with radians running arcs and sectors
Prove congruence, similarity and the circle theorems the way examiners mark them
Differentiate the circle implicitly for tangents, normals and related rates
Compute with 3D vectors — dot products, lines in space and cross products
What’s inside
Formula library
Glowing formula cards: the rule, what it means, when to use it, why it works, and a worked example.
3-level worked examples
Every method shown at three levels of difficulty, so the step up is never a cliff.
Trap-and-fix pairs
The wrong working beside the right working, so misconceptions get corrected on sight.
32 numbered key facts
The non-negotiables of the year, numbered 01–32 for fast last-minute review.
The Mistake Museum
Twelve exhibits of the errors that cost real marks, each one defused.
Exam Lab + cheat sheets
Word problems, worked missions, a 24-question mixed review with solutions, and two cheat sheets.
Frequently asked questions
Is this an instant download?
Yes. The moment your payment is confirmed, your PDF unlocks on the confirmation screen and a secure download link is emailed to you. No waiting, no manual approval.
What format is the file?
A print-ready A4 PDF of 57 pages. It opens on any phone, tablet or computer and prints cleanly at home if your child prefers paper.
Which curriculum does it follow?
It covers the shared core of Year 12 / Grade 12 geometry — coordinate methods, trigonometry, proofs, circles and vectors — across A-level, IB and equivalent programmes. No single exam board is assumed.
How do I pay, and in which currency?
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