Volume I, Algebra: The Language
Where symbols stop being decoration and start being arguments. Substitution, the balance method, and the first sequences a child can predict rather than continue.
$79one volume
Volume VIII · Geometry
Volume I
Volume VIII · Geometry: Space and Proof
Circle theorems held to proof standard, tangents and normals by calculus, and vectors in three dimensions: the same mathematics used to put a spacecraft where it needs to be.
Pages
57
Format
2 PDF editions
Access
Lifetime
Delivery
Instant
Overview
This is the whole Year 12 geometry year. Coordinate methods, transformations, trigonometry to exact values, geometric proofs written to standard, circles under calculus, and vectors in three dimensions, then an Exam Lab that rehearses all of it under timed conditions.
It can be read in an evening, or worked through properly across a weekend for a 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 programs.
Look inside
Six pages from the volume. Open the reader to turn between them, and to switch the same page between the Study and Screen editions.
Who it’s for
- Students in Year 12, US Grade 11, ages 16 to 17, who want the whole year in one place
- Parents looking for a rigorous, screen-light revision resource that actually gets used
- Stronger students ready to stretch into Level 3 material such as both-sides equations and midpoints
- Anyone moving between the UK, US, Canada, Australia, New Zealand or Singapore systems
Topics included
- Coordinate Geometry: gradients, midpoints, distance, parallel and perpendicular lines
- Transformations: translation, reflection, rotation, enlargement and combinations
- Trigonometry: the sine and cosine rules, radians, bearings, exact values
- Geometric Proofs: circle theorems held to proof standard, congruence and similarity
- Circle Geometry and Calculus: tangents and normals by differentiation, the circle under calculus
- Vectors in Three Dimensions: components, magnitude, direction, position and displacement
- The Exam Lab: word problems, a 24-question mixed review, the Mistake Museum, exam day, reference plates
What your child will be able to do
- Prove a circle theorem rather than quote it
- Find a tangent or normal to a curve by differentiation
- Use the sine and cosine rules, radians and exact values without a calculator
- Work with vectors in three dimensions, including magnitude and direction
- Recognise the classic mistakes examiners set, and avoid them under pressure
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.
23 numbered key facts
The non-negotiables of the year, numbered 01-23 for fast last-minute review.
The Mistake Museum
A curated gallery of the errors that cost real marks, each one defused.
Exam Lab and reference plates
The LAUNCH method, timed missions, a 24-question mixed review with solutions, and two reference plates.
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?
Two typeset, print-ready A4 PDFs of 57 pages in seven parts: a Study edition for paper and a Screen edition for reading in the dark. Both arrive together in one download and open on any phone, tablet or computer.
Which curriculum does it follow?
It covers the shared core of Year 12, US Grade 11, geometry across the UK, US, Canada, Australia, New Zealand and Singapore systems, cross-checked against Oak National Academy units. No single exam board is assumed.
How do I pay, and in which currency?
Checkout accepts card, PayPal and wallets. Prices display and charge in US dollars.
If it is not what I expected
Write to hello@insightbay.net and I will put it right. Your licence is for your own family: yours to keep and print for your household, not to resell or redistribute.
If it is not what you expected
A Field Guide is delivered as a PDF the moment payment is confirmed. If a volume is not what you expected, write to hello@insightbay.net and I will put it right. Your licence is for your own family: yours to keep and print for your household, not to resell or redistribute. Payments are processed securely by Razorpay and PayPal, and Insight Bay never sees or stores your card details.
Where it stops
This volume assumes the algebra underneath it. Differentiation is used, not taught: if tangents by calculus are new, Volume V comes first.
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