Maths topics links and summaries

Maths topics links and summaries

Key: Recommended = ★★★ Excellent = ★★ Good = ★

Toggle section visibility: Section R: Formulae and algebra Section 1: Trigonometry Section 2: Differentiation Section 3: Integration

Expanding brackets
e.g. \(4(3x-3)\)

HELM course notes (Helping Engineers Learn Maths ^††)

No specific recommendation

Khan Academy notes and videos

Mathcentre notes and videos ^†

Expanding brackets

Summary Page

Linear equations
e.g. \(4x+7=-3x+21\)

HELM course notes

Solving linear equations

Khan Academy notes and videos

Solving equations and inequalities

Mathcentre notes and videos ^†

Simple linear equations

Summary Page

Indices (powers)
e.g. \(x^2, y^{-1/3}\)

HELM course notes

Notes on indices

Khan Academy notes and videos

No specific recommendation

Mathcentre notes and videos ^†

Indices or Powers

Summary Page

Algebra: working with equations
e.g. rearranging (transposition)

HELM course notes

Formulae and transposition

Khan Academy notes and videos

Multipart lesson: solving basic equations

Mathcentre notes and videos ^†

Transposition of formulae

Summary Page

Simplification and factorisation

HELM course notes

Simplification and factorisation

Khan Academy notes and videos

Mathcentre notes and videos ^†

No specific recommendation

Summary Page

Trigonometric functions
e.g. \(\sin\), \(\cos\) and \(\tan\)

HELM course notes

Khan Academy notes and videos

No specific recommendation

Mathcentre notes and videos ^†

Summary Page

Reciprocal trigonometric functions
(\(cosec\), \(sec\) and \(cot\))

HELM course notes (Helping Engineers Learn Maths ^††)

Background only

Khan Academy notes and videos

5 part lesson

Mathcentre notes and videos ^†

Cosec, sec, cot

Summary page

Compound angle formulae and Trigonometric identities

HELM course notes

Trig identities

Khan Academy notes and videos

Mathcentre notes and videos ^†

Summary Page

Hyperbolic functions and hyperbolic identities

HELM course notes

Hyperbolic functions and identities

Khan Academy notes and videos

Video on YouTube

Mathcentre notes and videos ^†

Summary Page

Differentiation first principles

HELM course notes

Differentiation: a first principles introduction

Khan Academy notes and videos

Lesson with many sections
(skip Estimating and Differentiability sections)

Mathcentre notes and videos ^†

Introduction handout

Summary Page

Differentiation of standard functions

HELM course notes

Using tables of standard derivatives with engineering examples

Khan Academy notes and videos

No specific recommendation

Mathcentre notes and videos ^†

Summary Page

The chain rule (for differentiation)

HELM course notes

No specific recommendation

Khan Academy notes and videos

Video and interactive lessons (fairly long)

Mathcentre notes and videos ^†

Summary Page

Second derivatives and rates of change

HELM course notes

Khan Academy notes and videos

Modelling rates of change (see HELM links for definitions)

Mathcentre notes and videos ^†

No specific recommendation. See optimisation section instead

Summary Page

Optimisation using differentiation

HELM course notes

Using higher derivatives: for engineering optimisation

Khan Academy notes and videos

Mathcentre notes and videos ^†

Mathematical introduction to optimisation

Summary Page

Integration: indefinite and definite integrals

HELM course notes

Khan Academy notes and videos

No specific recommendation

Mathcentre notes and videos ^†

Summary Page

Integration of standard functions

HELM course notes

No specific recommendation

Khan Academy notes and videos

Multipart lesson

Mathcentre notes and videos ^†

Table of standard integrals

Summary Page

Applications of integration

HELM course notes

Finding areas between curves

Khan Academy notes and videos

Mathcentre notes and videos ^†

No specific recommendation

Summary Page

^† The Mathcentre and Mathtutor websites contain the same content and some content is still in Adobe Flash Player, those elements will be updated eventually.
^†† The 'Helping Engineers Learn Mathematics' (HELM) resources are excellent, links above have been carefully selected to align with the syllabus. The full set can be found at the HELM homepage.