Mathematics (Extended) · Revision notes

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Chapter 4 · §4.2

Equations

Definition

Equation

Examiner note

ax + b = c

Worked example

Solve 3x + 5 = 20.

Step 1. 3x + 5 = 20

Step 2. 3x = 15

Step 3. Check: 3(5) + 5 = 20

x = 5

Glide· Chapter 1

Foundations

Every later topic rests on how numbers behave.

In this chapter

Key formulae

a × b = b × a

n(A ∪ B)

Chapter map

Chapter 1 · Quick reference

Quick Reference

Every formula and definition on one card.

Powers

a^m·aⁿ = a^m+n

Coordinates

y = mx + c

Mensuration

A = πr²

Trigonometry

sin θ = o/h

Probability

P = n(A)/n(S)

Statistics

mean = Σx/n

InsideChapter cover, teaching page with margin notes, and the quick reference card.

What you get

The night before

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Each topic is explained step by step, with worked examples using real numbers, from Foundations through to Statistics.

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Every chapter has an exam-advice page that names the errors students most often make and shows a model answer broken down mark by mark.

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A recall checklist closes each chapter, so you can test yourself cold before you move on.

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All 12 topics

01 FoundationsNumber types, primes, sets, powers, fractions and the four operations.
02 Powers, Form & ProportionIndex laws, standard form, estimation, bounds, ratio and rates.
03 Money, Growth & SurdsPercentages, interest, time, currency, exponential growth and surds.
04 AlgebraManipulation, fractions, equations, inequalities, quadratics, sequences and proportion.
05 Graphs, Calculus & FunctionsPractical graphs, function families, sketching curves, differentiation and functions.
06 Coordinate GeometryGradients, straight lines, parallel and perpendicular.
07 GeometryAngles, polygons, similarity and circle theorems.
08 MensurationPerimeter, area, surface area and volume of solids.
09 TrigonometryPythagoras, SOHCAHTOA, exact values, graphs, sine/cosine rules and 3D trigonometry.
10 Transformations & VectorsVector notation, magnitude and the four transformations.
11 ProbabilitySingle and combined events, tree and Venn diagrams.
12 StatisticsAverages, charts, cumulative frequency and correlation.

Checked before it is published

Cross-checked. Every fact and formula is checked against the Cambridge syllabus and at least one further authoritative source.
Diagrams verified. Each diagram is checked against the syllabus and past-paper conventions before the chapter is finalised.
Layout tested. An automated page check runs first, then a manual walkthrough of every page.
Our own words. Every explanation is written from scratch, never adapted from other revision notes.

Glide is an independent publisher and is not endorsed by Cambridge.

Questions

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Strictly the formulas for the subject, and nothing else.

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