The bridge to university algebra. Partial fractions, the modulus function, e and the natural logarithm, complex numbers, matrices and proof, engineered into 57 pages you can master in one afternoon.
Year 12 · Grade 12Ages 16–18Mathematics · Algebra57 pages
Pages
57
Format
A4 PDF
Access
Lifetime
Delivery
Instant
Overview
This is the whole Year 12 algebra year, rebuilt for revision and pitched as the bridge to university — crossed on proof, not on luck. Fifty-seven pages take a student from algebraic fractions and partial fractions, through the modulus and piecewise functions, into e and the natural logarithm, complex numbers, matrices and the art of proof — 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
Anyone who finished the Year 11 crash course and is ready for the final level
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
Algebraic Fractions, Level Three — heavy simplification, partial fractions and rational graphs
The Modulus & Piecewise Functions — |x| defined, modulus equations and inequalities, and piecewise rules
e & the Natural Logarithm — the number e, ln and its laws, and continuous growth
Complex Numbers — i, conjugates and division, complex roots and the Argand diagram
Matrices — arithmetic, multiplication, the determinant and inverse, systems and transformations
Proof & the Final Toolkit — deduction, counterexample, exhaustion, contradiction and the binomial series
Exam Lab — word problems, a 24-question mixed review and full solutions
What your child will be able to do
Split expressions into partial fractions and graph rational functions
Solve modulus equations and inequalities and work with piecewise functions
Use e and the natural logarithm to model continuous growth
Compute with complex numbers and plot them on the Argand diagram
Multiply and invert matrices, and choose the right method of proof
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.
Numbered key facts
The non-negotiables of the year, numbered in sequence 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 algebra — the bridge to university — 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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