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.
$79one volume
Volume VII · Algebra
Volume VIII
Volume VII · Algebra: The Complex Plane
Complex numbers, matrices, and the art of proof: the point at which mathematics stops being calculation and becomes argument. The most demanding volume in the library, and the one written for the student who is already ahead.
Pages
57
Format
2 PDF editions
Access
Lifetime
Delivery
Instant
Overview
This is the whole Year 12 algebra year. Heavy algebraic fractions and partial fractions, the modulus and piecewise functions, e and the natural logarithm, complex numbers and the Argand diagram, matrices and their transformations, and four methods of proof, 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
- Algebraic Fractions, Level Three: heavy simplification, partial fractions, improper fractions, rational graphs
- The Modulus and Piecewise Functions: the modulus defined, modulus equations and inequalities, piecewise rules
- e and the Natural Logarithm: the number e, ln and its laws, solving with e and ln, continuous growth
- Complex Numbers: the number i, conjugates and division, complex roots, the Argand diagram
- Matrices: arithmetic, multiplication, determinant and inverse, systems, transformations
- Proof and the Final Toolkit: deduction, counterexample, exhaustion, contradiction, the binomial series
- 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
- Split a rational expression into partial fractions and integrate or expand the result
- Work with the modulus function in equations, inequalities and sketches
- Use e and the natural logarithm in growth and decay problems
- Add, multiply and divide complex numbers, and place them on an Argand diagram
- Choose the right method of proof, and write an argument that would survive marking
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, algebra 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 sits at Further Mathematics level. It is not a first pass at Year 12 mathematics and does not pretend to be: it assumes the syllabus and goes past it.
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