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 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

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  

Related information

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Two people sitting at a table looking at some work together

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