Volume V, Algebra: The Function
The discriminant with parameters, tangency to the circle, and the moment logarithms stop being a button. Where algebra becomes a way of asking questions about whole families of equations at once.
$79one volume
Volume IV · Algebra
Volume V
Volume IV · Algebra: The Curve
Every quadratic, by every method: factorising, completing the square, the formula, and the judgement to know which one the question is actually asking for. The volume that decides the examination year.
Pages
61
Format
2 PDF editions
Access
Lifetime
Delivery
Instant
Overview
This is the whole Year 10 algebra year. Surds and fractional indices, quadratic equations by every available method, algebraic fractions, functions and their inverses, coordinate geometry and curve sketching, 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 10, US Grade 9, ages 14 to 15, 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
- Surds and Fractional Indices: simplifying, rationalising, fractional and negative powers
- Quadratic Equations: factorising, completing the square, the formula, and choosing between them
- Algebraic Fractions: simplifying, the four operations, equations with fractions
- Functions: notation, composite functions, inverse functions
- Coordinate Geometry: gradients, midpoints, distance, parallel and perpendicular lines
- Sketching Curves: quadratics, cubics, reciprocals, transformations of graphs
- 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
- Solve any quadratic by factorising, completing the square or the formula, and justify the choice
- Simplify surds and work fluently with fractional and negative indices
- Handle algebraic fractions in all four operations and in equations
- Use function notation, compose functions and find inverses
- Sketch a curve from its equation and read an equation from a sketch
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?
A typeset, print-ready A4 PDF of 57 pages in seven parts. 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 10, US Grade 9, 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 is the examination year rebuilt, not a paper drill. It will show a student what they do not understand, but it cannot mark a mock paper or tell them which of three correct methods is faster under pressure. That is what the classes are for.
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