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

Rational and Irrational Numbers

     
Introduction Video Webpage See Written Resources

Logarithms

     
Definition Video MathCentre booklet on logarithms See Written Resources
Multiplication, division, power rules Video MathCentre worksheet on the laws of logarithms See Written Resources

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      Video HELM workbook

Worksheet on adding algebraic fractions

Worksheet on dividing algebraic fractions

Worksheet on multiplying fractions

Quadratics

     
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  Video HELM workbook See Written Resources

Factor and Remainder Theorem

     
Introduction Video Webpage 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

Quadratic Graphs

     
Sketching Quadratics MASH Video on Sketching Quadratic Graphs Booklet

Online Exercise

Corbett maths worksheet

Graphical inequalities

     
Linear inequalities Video Booklet  
Curves and lines Video 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 Video

Trig identities

Addition formulae

Double angle formulae

Functions

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

Composite Functions

Khan Academy exercises
Inverse Functions Video Inverse Functions Exercises
Domain and Range Video 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) Video    

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  

Mechanics

  Video Written Resources Exercises
Displacement, Velocity, Time Graphs   Worksheet  
Constant Acceleration Equations (SUVAT)   Worksheet Exercise
Resolving forces - Horizontal Problems   Worksheet See written resource
Resolving forces - Inclined Planes See written resource Webpage See written resource
Connected Particles See written resource

Ropes & Towbars

Pulleys

See written resource
Moments Video Introduction to moments Exercise
Projectiles See written resource Webpage Exercise
Momentum  

Introduction

Collisions

Momentum Exercise

Collisions Exercise

Work & Energy   Webpage See written resource
Centres of Mass Video HELM Booklet See written resource
Two people sitting at a table looking at some work together
Two people sitting at a table looking at some work together

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