# First steps for STEM subjects

These resources cover topics that students in STEM courses will find useful.

On

## Number

Video Written Resources Exercises

#### Indices

Rules of Indices

University of Leeds video

HELM workbook

Corbett maths worksheet on laws of indices

Fractional and Negative Indices MASH video on Fractional Indices MathCentre worksheet on negative and fractional powers

Corbett maths worksheet on fractional indices

Corbett maths worksheet on negative indices

#### Surds

Introduction   Webpage See Written Resources
Simplifying Surds   Webpage See Written Resources
Rationalising Denominators   Webpage See Written Resources

#### Rational and Irrational Numbers

Introduction   Webpage See Written Resources

#### Logarithms

Definition   MathCentre booklet on logarithms MathCentre worksheet on logarithms
Multiplication, division, power rules   MathCentre worksheet on the laws of logarithms MathCentre worksheet on the laws of logarithms

## Algebra

Video Written Resources Exercises

#### Simultaneous equations

Two linear equations (elimination and substitution methods) University of Leeds video HELM workbook

Corbett maths worksheet on solving simultaneous linear equations by elimination

Khan Academy quiz on solving simultaneous linear equations by substitution

Graphical solutions MASH Video

Online Exercise

Corbett maths worksheet

One linear and one non-linear equation MASH Video on Substitution method for one linear and one non-linear equation   Corbett maths worksheet

#### Algebraic fractions

Algebraic fractions        HELM workbook

Worksheet on dividing algebraic fractions

Worksheet on multiplying fractions

Solving by factorising                                        Solving quadratic equations by factorising HELM workbook

Corbett maths worksheet 1

Corbett maths worksheet 2

Solving with the formula Solving quadratic equations with the formula HELM workbook Corbett maths worksheet
Completing the square Completing the square Booklet Corbett maths worksheet
Difference of Two Squares Difference of Two Squares Webpage See Written Resources

#### Rearranging formulae

Rearranging formulae    HELM workbook See Written Resources

#### Factor and Remainder Theorem

Introduction   Worksheet on factor and remainder theorem worksheet

#### Sigma notation

Sigma notation Sigma notation for sums Booklet See Written Resources

#### Sequences

Missing terms in Number Sequences Video   Corbett Maths Worksheet
Arithmetic progressions  Definition of sequences Booklet See Written Resources
Geometric progressions Introduction to geometric sequences Booklet See Written Resources

## Coordinate geometry

Video Written Resources Exercises

#### Straight line graphs

Parallel and perpendicular lines    Video Finding parallel and perpendicular lines See Written Resource

Online Exercise

Corbett maths worksheet

#### Graphical inequalities

Linear inequalities   Booklet
Curves and lines   Booklet

#### Circle geometry

Equations of circles

Circles centred on (0,0)

Circles centred anywhere

Identifying Circle Equations

Booklet See Written Resource
Tangents to circles

Video: Tangents to circles

#### Tangents and normals

Equations of tangents and normals to curves

Equations of tangents

Equations of normals

Booklet See Written Resource

## Trigonometry

Video Written Resources Exercises

#### Finding sides and angles in triangles

Right-angled triangles

SIN, COS and TAN

HELM workbook Corbett maths worksheet
Sine and cosine rule

Sine Rule

Cosine Rule

Booklet See Written Resource

#### Area of a triangle formula

The formula A = 1/2 absinC  Area of a triangle Finding the area of a triangle using sine

#### Introduction to trig functions

Trigonometric graphs MASH Video Booklet Online Exercise
sec, cosec and cot Maths Genie Video Introduction
Trigonometric identities

Trig identities

Double angle formulae

See Written Resource

#### Functions

Function Notation Khan Academy Video HELM Booklet See Written Resource
Composite functions

Composite Functions

Inverse Functions   Inverse Functions Exercises
Domain and Range   Webpage See Written Resource

## Calculus

Video Written Resources Exercises

#### Differentiation

Definition of a derivative

Formal definition of the derivative as a limit

Introducing differentiation

Differentiation from first principles

Differentiating polynomials

Power rule

Booklet

Finding Stationary Points (Maxima and Minima)

#### Integration

Introduction to Integration Introduction to integral calculus Booklet See Written Resource
Polynomial Integration Reverse power rule Booklet
Areas Under Curves

Area between a curve and the x-axis (positive area)

Area between a curve and the x-axis (negative area)

Booklet