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 University of Leeds videoHELM workbookCorbett maths worksheet on laws of indices
Fractional and Negative IndicesMASH video on Fractional IndicesMathCentre worksheet on negative and fractional powers

Corbett maths worksheet on fractional indices

Corbett maths worksheet on negative indices

Surds

   
IntroductionVideoWebpageSee Written Resources
Simplifying SurdsVideoWebpageSee Written Resources
Rationalising DenominatorsVideoWebpageSee Written Resources

Rational and Irrational Numbers

   
IntroductionVideoWebpageSee Written Resources

Logarithms

   
DefinitionVideoMathCentre booklet on logarithmsSee Written Resources
Multiplication, division, power rulesVideoMathCentre worksheet on the laws of logarithmsSee Written Resources

Algebra

 VideoWritten ResourcesExercises

Simultaneous equations

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

Corbett maths worksheet on solving simultaneous linear equations by elimination

Khan Academy quiz on solving simultaneous linear equations by substitution

Graphical solutionsMASH Video 

Online Exercise

Corbett maths worksheet

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

Algebraic fractions

   
Algebraic fractions     VideoHELM workbook

Worksheet on adding algebraic fractions

Worksheet on dividing algebraic fractions

Worksheet on multiplying fractions

Quadratics

   
Solving by factorising                                       Solving quadratic equations by factorisingHELM workbook

Corbett maths worksheet 1

Corbett maths worksheet 2

Solving with the formulaSolving quadratic equations with the formulaHELM workbookCorbett maths worksheet
Completing the squareCompleting the squareBookletCorbett maths worksheet
Difference of Two SquaresDifference of Two SquaresWebpageSee Written Resources

Rearranging formulae

   
Rearranging formulae VideoHELM workbookSee Written Resources

Factor and Remainder Theorem

   
IntroductionVideoWebpageworksheet

Sigma notation

   
Sigma notationSigma notation for sumsBookletSee Written Resources

Sequences

   
Missing terms in Number SequencesVideo Corbett Maths Worksheet
Arithmetic progressions Definition of sequencesBookletSee Written Resources
Geometric progressionsIntroduction to geometric sequencesBookletSee Written Resources

Coordinate geometry

 VideoWritten ResourcesExercises

Straight line graphs

   
Parallel and perpendicular lines   VideoFinding parallel and perpendicular linesSee Written Resource

Quadratic Graphs

   
Sketching QuadraticsMASH Video on Sketching Quadratic GraphsBooklet

Online Exercise

Corbett maths worksheet

Graphical inequalities

   
Linear inequalitiesVideoBooklet 
Curves and linesVideoBooklet 

Circle geometry

   
Equations of circles   

Circles centred on (0,0)

Circles centred anywhere

Identifying Circle Equations

BookletSee Written Resource
Tangents to circlesVideo: Tangents to circles  

Tangents and normals

   
Equations of tangents and normals to curves

Equations of tangents

Equations of normals

BookletSee Written Resource

Trigonometry

 VideoWritten ResourcesExercises

Finding sides and angles in triangles

   
Right-angled triangles         SIN, COS and TANHELM workbookCorbett maths worksheet
Sine and cosine rule

Sine Rule

Cosine Rule

BookletSee Written Resource

Area of a triangle formula

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

Introduction to trig functions

   
Trigonometric graphsMASH VideoBookletOnline Exercise
sec, cosec and cotMaths Genie VideoIntroduction 
Trigonometric identitiesVideoTrig identities

Addition formulae

Double angle formulae

Functions

   
Function NotationKhan Academy VideoHELM BookletSee Written Resource
Composite functionsVideoComposite FunctionsKhan Academy exercises
Inverse FunctionsVideoInverse FunctionsExercises
Domain and RangeVideoWebpageSee Written Resource

Calculus

 VideoWritten ResourcesExercises

Differentiation

   
Definition of a derivativeFormal definition of the derivative as a limit

Introducing differentiation

Differentiation from first principles

 
Differentiating polynomialsPower rule

Booklet

 
Finding Stationary Points (Maxima and Minima)Video  

Integration

   
Introduction to IntegrationIntroduction to integral calculusBookletSee Written Resource
Polynomial IntegrationReverse power ruleBooklet 
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

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

Ropes & Towbars

Pulleys

See written resource
MomentsVideoIntroduction to momentsExercise
ProjectilesSee written resourceWebpageExercise
Momentum 

Introduction

Collisions

Momentum Exercise

Collisions Exercise

Work & Energy WebpageSee written resource
Centres of MassVideoHELM BookletSee 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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