First steps for STEM subjects

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

On

Number

 VideoWritten ResourcesExercises

Indices

   
Rules of Indices HELM workbook
Fractional and Negative Indices

Surds

   
IntroductionSee Written Resources
Simplifying SurdsSee Written Resources
Rationalising DenominatorsSee Written Resources

Rational and Irrational Numbers

   
IntroductionSee Written Resources

Logarithms

   
DefinitionSee Written Resources
Multiplication, division, power rulesSee Written Resources

Algebra

 VideoWritten ResourcesExercises

Simultaneous equations

   
Two linear equations (elimination and substitution methods)HELM workbook

Graphical solutions 

One linear and one non-linear equation 

Algebraic fractions

   
Algebraic fractions     HELM workbook

Quadratics

   
Solving by factorising                                       HELM workbook

Solving with the formulaHELM workbook
Completing the squareBooklet
Difference of Two SquaresSee Written Resources

Rearranging formulae

   
Rearranging formulae HELM workbookSee Written Resources

Factor and Remainder Theorem

   
Introduction

Sigma notation

   
Sigma notationBookletSee Written Resources

Sequences

   
Missing terms in Number Sequences 
Arithmetic progressions BookletSee Written Resources
Geometric progressionsBookletSee Written Resources

Coordinate geometry

 VideoWritten ResourcesExercises

Straight line graphs

   
Parallel and perpendicular lines   See Written Resource

Quadratic Graphs

   
Sketching QuadraticsBooklet

Graphical inequalities

   
Linear inequalitiesBooklet 
Curves and linesBooklet 

Circle geometry

   
Equations of circles   

BookletSee Written Resource
Tangents to circles  

Tangents and normals

   
Equations of tangents and normals to curves

BookletSee Written Resource

Trigonometry

 VideoWritten ResourcesExercises

Finding sides and angles in triangles

   
Right-angled triangles         HELM workbook
Sine and cosine rule

BookletSee Written Resource

Area of a triangle formula

   
The formula A = 1/2 absinC  

Introduction to trig functions

   
Trigonometric graphsBooklet
sec, cosec and cot 
Trigonometric identities

Functions

   
Function NotationHELM BookletSee Written Resource
Composite functions
Inverse Functions
Domain and RangeSee Written Resource

Calculus

 VideoWritten ResourcesExercises

Differentiation

   
Definition of a derivative

Introducing differentiation

Differentiation from first principles

 
Differentiating polynomials

Booklet

 
Finding Stationary Points (Maxima and Minima)  

Integration

   
Introduction to IntegrationBookletSee Written Resource
Polynomial IntegrationBooklet 
Areas Under Curves

Booklet 

Mechanics

 VideoWritten ResourcesExercises
Displacement, Velocity, Time Graphs Worksheet 
Constant Acceleration Equations (SUVAT) Worksheet
Resolving forces - Horizontal Problems See written resource
Resolving forces - Inclined PlanesSee written resourceSee written resource
Connected ParticlesSee written resource

See written resource
Moments
ProjectilesSee written resource
Momentum 

Work & Energy See written resource
Centres of MassHELM BookletSee written resource

Related information

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Two people sitting at a table looking at some work together

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