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    HELM workbook See Written Resources

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

     
Simultaneous equations    HELM workbook See Written Resources

Algebraic fractions

     
Algebraic fractions        HELM workbook See Written Resources

Quadratics

     
Solving by factorising                                        Solving quadratic equations by factorising HELM workbook See Written Resources
Solving with the formula Solving quadratic equations with the formula HELM workbook See Written Resources
Completing the square Completing the square Booklet 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

     
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

     
Finding maxima and minima of quadratic graphs   Booklet See Written Resource

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 See Written Resource
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   Booklet See Written Resource
Trigonometric identities  

Trig identities

Addition formulae

Double angle formulae

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  
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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