Using Lagrange Multipliers to Maximise a Function

Using a Graph to Solve an Equation

Units of Gravitational Constant

Transforming Equation of Regression Line

Transformation of Linear Coupled First Order Differential Equations Using Eigenvectors

Solving Simultaneous Equations With Three Unknowns

Simple Harmonic Motion for Particle Connected to Two Springs on Horizontal Table

Proof There are an Infinite Number of Primes

Proof of Thin Lens Equation

Proof of Thin Lens Equation

Proof of Center of Mass of Volume of Revolution Formula

Partial Pressures

Partial Pressures

Proof of Acceleration Formula for Circular Motion

Particle Leaving Inner Surface of Sphere

Particle Leaving External Surface of Sphere

Particle in Horizontal Circular Motion Connected to Two Rods

Integration Using Two Substitutions

How Many Times Does a Wheel Turn to Travel 1 km

Homogeneity of Units for Time Constant RC

Energy of Electron in Hydrogen Atom According to the Bohr Model

Effect on Braking Distance of Doubling Speed

Deflection of Charged Particle Suspended on String Between Charged Plates

Condition on Maximum Angular Velocity for Particle in Horizontal Circular Motion on Elastic String

Centre of Mass of Volume of Revolution Rotated About y Axis

Centre of Mass of Volume of Revolution Rotated About x Axis

When Minute and Second Hands Coincide

When Do Clock Hands Coincide Hour and Minute

Using Implicit Differentiation to Find the Turning Point

Terminal Velocity of Sphere in Fluid Using Stokes Law

Taylor Series of Composite Function

Speed of Electrons Accelerated Through a Potential Difference

Rate of Change of Volume of Sphere With Area

Proof of Formula for Curved Surface Area of Cone

Probability of Having a Disease Given a Positive Test

Moment of Inertia of a Compound Pendulum

Long Division of Polynomials 4

Long Division of Polynomials 3

Long Division of Polynomials 2

Kirchoffs Law Example Multiple EMFs 2

Kirchoffs Law Example Multiple EMFs 1

Induced EMF Between Wingtips of Plane Flying in Earths Magnetic Field

Fourier Series for x Between Minus 1 and 1

Fourier Series for Modulus x Between Minus 1 and 1

Finding Percentage Errors in Calculations

Electric Potential Energy of Collection of Charges 2

Electric Potential Energy of Collection of Charges

Elastic Collisions For Particles of Equal Mass Mass Glancing Collision

Elastic Collisions For Particles of Equal Mass Head on Collision

Doppler Effect Observer Moving

Deriving the Equations of Circular Motion

Proof of Fluid Pressure Equation

Wavelengths and Frequencies of String Fixed at Both Ends

Using Hubbles Law to Estimate Distance to Galaxy

The Number of Electrons C Protons and Neutrons in an Atom

Solving Simultaneous Equations Advanced Example

Rotation Plus Reflection Equals Reflection

Proof That Squre Root Function is Continuous on [1,2]

Proof That Square Function is Continuous on [1,2]

Proof That sin x is Continuous on [0, pi over 2]

Proof That Reciprocal Function is Continuous on [1,2]

Overlapping Fringes From Diffraction Grating

Non Uniform Beam Suspended By Two Strings Find Centre of Gravity

Image of a Line After Rotation

Image of a Line After Reflection

Different Electric Power Equations

Image of a Line After a Matrix Transformation

Find Least n For Which Sum of Decreasing Geometric Series is Within 10x5E-5 of Sum to Infinity

Equations of Simple Harmonic Motion

Effect of Extra Length on Mean

Distances of Points on Ground Seen From Top of Pole

Decimal Places and Significant Figures

Centre of Gravity of Lamina With a Hole

Calculating sample Frequencies

Angles and Parallel Lines

border=”1″/> Area of Kite

Dividing a Quantity in a Ratio

Energy Levels and Transitions in Hydrogen Atom

Area Between Curve and Normal to Curve

Value of a Composite Function at a Point

Relationship Between Wavelength and Kinetic Energy of Electron

Relationship Between Electric Force and Eletrostatic Energy

Proof of Area of Surface of Revolution Formula

Proof by Induction 3 To Power n Greater than 3n

Area Between Line, Curve and Axis

Proof of Formula for Length of Arc

Proof of Formula for Area of Sector

Proof of Area of Segment Formula

Linear Inequalities With Fractions

Effect of Extra Member on Mean and Standard Deviation

Sum of Interior Angles of Polygon

Rarranging Equation By Grouping Terms From Both Sides

Proof of Pooled Variance Formula

Proof of Area of Triangle Formula

Rearranging Equation of Line to Find Gradient and Intercepts

Rarranging Equation By Grouping Terms From Both Sides

Proof of Factor and Remainder theorems

Proof of Area of Triangle Formula

Production of Particle – Antiparticle Pairs by Photon Decay

Particle on Table Connected to Hanging Particle By String

Particle on Slope Connected to Particle on Table

Lifetime of Subatomic Particles Travelling Close to Speed of Light

Increase in Entropy as Heat is Transferred From Hot to Cold Body

Finding the Equation of a Perpendicular Line

Estimating the Age of the Universe Using Hubbles Constant

Proof with pure logic that this table is actually a Cow

Estimating the Age of the Universe Using Hubbles Constant

Scaling Force, Cross Sectional Area, Length and Youngs modulus

Proof of Product Formula for Intersecting Chords

Density of Substance When Different Substances Are Mixed

Collisions, Momentum and Restitution 2

Collisions, Momentum and Restitution

Applications of Minimisation and Optimisation 2

Applications of Minimisation and Maximisation

Transforming Graphs – Absolute Value of x

Proof of Diffraction Grating Equation

Object Formed By Diverging Lens Object Between focus and Lens

Maximum Number of Fringes Formed By Diffraction Grating

Image formed By Converging Lens – Object Between Focus and Lens

Finding Vector Equation of a Plane From Three Points

Finding the Vector Equation of a Plane From the Cartesian Equation

Factorising General Quadratics 2

Factorising General Quadratics

Converging Lens – Formation of Image With Object Further Than Focal Length

Average Speed of Electrons Carrying a Current

Laurent Series For Simple Linear Reciprocal

Laurent Series For a Simple Reciprocal Function About a Point

Using Cauchys nth Derivative Formula to Evaluate Integrals 1

Using Cauchys nth Derivative formula to Evaluate Integrals

Using Cauchys Integral Formula to Evaluate an Integral 4

Resistance Between Corners of Cube With Resistance Along One Edge

Equal And Opposite Impulse And Impact

Algrebra – Sides of Isosceles Triangle

Simplifying and Integrating a Quotient

Simplifying and Integrating a Quoitient 2

Simplifying and Integrating a Quotient 3

Integrating a Product of Cosine and Exponential

Integration by Parts x ln Squared x

Integration by Parts x times a Square Root

Integrating Product of Sine and Exponential

Proof of Alternate Segment Theorem

Vertical Circular Motion for Mass on String – Condition on u

Simplifying Algebra – Algebraic Fractions

Proof That Tangents From a Point to a Circle Have the Same Length

Proof That Product of the Parts of a Diameter Bisecting a Chord Equals Half Length of Chord Squared

Proof That Opposite Angles in a Cyclic Quadrilateral Add to 180

Proof That Mass on a Spring Executes SHM

Proof That Angle Subtended By Diameter is a Right Angle

Integration by Parts x squared Times Exponential

Integrating Product of x and Exponential by Parts

Integrate tan Squared sec Squared

Integrating Using Partial Fractions Making y the Subject

Integrating Product of x and log by Parts

Proof That Angles Subtended From the Same Chord Are the Same

Integrating Product of Sin and x

Integrating Product of Sin and x Squared

Integrating Product of Cosine and x

Equation of Perpendicular Line

Standard Deviation of a List of Numbers

Proof by Contradiction That Log Base 3 of 5 is Irrational

Normal Distribution P(X<x) z negative

Normal Distribution P(X>x) negative z

Is This Number Divisible by 11

Proof that Binomial Distribution is a Probability Distribution

Variance of a Uniform Distribution

Proving that the Standard Normal is a Probability Distribution

Proof that Poisson Distribution is a Probability Distribution

Proof that a Geometric Distribution is a Probability Distribution

Expectation Value of Exponential Distribution

Expectation Value of a Uniform Distribution

Calculating Spearmans Rank Correlation Coefficient

Variance of a Poisson Distribution

Functions of Roots of a Cubic 3

Functions of Roots of a Cubic 1

Mean of a Poisson Distribution

Functions of Roots of a Cubic 2

Prove cot x – tan x equals 2 cot 2x

Integrating 1 over square root of a squared plus x squared

Integrating 1 over a squared plus x squared

General Solutions of Trigonometric Equations – Tan

General Solutions of Trigonometric Equations – Sin

General Solutions of Trigonometric Equations – Cos

When to Use the Sine or Cosine Rule

Using the Sine Rule to Find a Side

Binomial Expansion of a Quotient

Bodies in Contact Coming to Thermal Equilibrium

Partial Fractions With Repeated Terms

Partial Fractions With Irreducible Quadratic

Finding Values of Trig Functions Using Compound Angle Formulae

Superfluous Solutions When Solving Absolute Value Equations

Probability Without Replacement

Solving Absolute Value Equations

Sketching Absolute Value Graphs

Proving sin A Plus Sin B Formula

Proving Sin A Minus Sin B Formula

Proving Formula for cos A Plus cos B

Proving Formula for cos A Minus cos B

Solving Simple Trigonometric Equations for Multiple Solutions Tangent

Solving Simple Trigonometric Equations for Multiple Solutions Cosine

Solving Dimple Trigonometric Equations for Multiple Solutions Sine

Quadratic Trigonometric Equations 2

Quadratic Trigonometric Equations 1

Proof That Total Energy of Body in Circular Orbit is Half of GPE

Finding the Closed Form of a Second Order Recurrence Relation

More Advanced Proof by Induction

Proving SUVAT Equation v squared equals u squared plus 2as

Independent Events Very tricky Example

Another Tricky Independent Events Example

Irrational_numbers_that_subtract_to_give_rational_numbers

Difference_in_Weight_Between_Man_at_Poles_and_Equator

Deriving_suvat_equation_s_equals_vt-half_at_squared

Deriving_suvat_equation_s_equals_ut_plus_half_at_squared

Vectors and Dividing Sides in a Certain Ratio

Using Simple Trigonometry to Find a Side

Using Difference Quotients to Differentiate

The Sign Convention for Vertical Motion

The Integrating Factor Method 2

The Curved Paths of an Electron Passing Between Parallel Charged Plates

The Cartesian Equation of a Projectile

The Box Method of Multiplication

Summing a Trigonometric Series With Complex Terms

Summing a Trigonometric Series 2

Summing a Trigonometric Series 1

Solving the Differential Equation for Radioactive Decay

Solving SUVAT Questions With Simultaneous Equations

Solving Simultaneous Inequalities With One a Quadratic

Solving Simultaneous Equations to Find the nth Term of a Geometric Sequence

Solving Simultaneous Equations to Find nth Term for Arithmetic Sequence

Solving Simple Equations With Fractions on Both Sides

Solving Simple Differential Equations

Solving Simple Differential Equations

Solving Quadratic Inequalities

Solving Quadratic Equations by Factorising

Solving More Complex Exponential Equations With Logs

Solving More Complex Exponential Equations

Sketching Absolute Value Graphs

Simultaneous Equations With One a Quadratic 2

Simplifying and Integrating Qoutients

Sequences Defined by Recurrence Relations

Reduction Formulae for cos^n x n odd

Proving the Set of Real Numbers is Not a Group Under Multiplication

Proving Set of 2×2 Rotation Matrices is a Group

Proof of Resistance Formula for Resistors in Series

Proof of Parallel Plate Capacitor Equation

Proof of Inverse Formula For Product of Matrices

Proof of Formula for Resistors in Parallel

Proof of Capacitance Formula for Capacitors in Series

Proof of Capacitance Formula for Capacitors in Parallel

Product of Binomial Expansions

Problem Solving Given Relationship Between Radii and Volumes of Cone and Sphere

Power Used in Each Resistor in a Series Circuit

Particle on Rough Slope Just Stopped By Moving By Horizontal Force

Power Used in Each Resistor in a Parallel Circuit

Particles on Pulleys Height and Speed With Which They Hit the Ground

Operators in Quantum Mechanics

Normalization for Free Particles

Newtons Third Law for a Book on a Table

Motion of a Weight on a String in a Horizontal Circle

Motion Between Three Points Using SUVAT

Minimizing the Distance From a Point to a Curve

Minimizing Surface Area Subject to a Given Volume

Implications of High Taxes for the Economy

Half Life of Radioactive Material

Given a Velocity in 2D Find Displacement

Given a Displacement Vector in 2D Find Velocity and Acceleration

Given Acceleration in 2D Find Velocity

Finding the Gradient and y Intercept of a Given Line

Finding Tensions in Strings Holding a Weight

Finding if Two Particles Moving With Constant Velocity Collide

Finding Centre of Gravity and Weight of a Rod

Finding an Upper Bound for Solution of Travelling Salesman Problem

Finding an Expression for the Bohr Radius

Finding a Lower Bound for the Solution of the Travelling Salesman Problem

Expectation Value of Momentum for Particle in Ground State of Simple Harmonic Oscillator

Expectation Value of Position for Particle in Ground State of Simple Harmonic Oscillator

Cumulative Distribution Function for Probability Distribution Defined Piecewise

Congress in the US Constitution

Checks and Balances in the US Constitution

Binding Energy and Binding Energy Per Nucleon

Asymptotes x Divided by a Quadratic

Asymptotes for a Constant over a Quadratic

Writing Sums and Differences of Logs as Single Logs

Proof that Z6 is Not a Group Under Multiplication

Proof of Newton Raphson Formula

Proof That The Set of Integers 1, 2, 3, 4 is a Group Under Multiplication Mod 5

Expansion and Convergence of Binomials 2

Proof of Energy Per Unit Volume Equals Half Stress Times Strain

Finding Cumulative Distribution Function for Probability Distribution in Two Parts

Solving Equations With Algebraic Fractions

Square Root of a Complex Number

Why is Golbal Warming Called the Greenhouse Effect

Reduction Formulae for sin^n x, n odd

Solving Constant Coefficient Second Order Linear Homogeneous Differential Equations

Solving Constant Coefficient Second Order Homogeneous Equations With Repeated Roots

Relative Position Vector of Particles That Start To Move At Different Times

Reduction Formula for I_n in Terms of I_n-2

The Chi Squared Test for Two By Two Contingency Tables

When a Particle Moving Relative to Another Particle is South of That Particle

When a Particle Moving Relative to Another Particle is North West of That Particle

When a Particle Moving Relative to Another Particle is North East of That Particle

When a Particle Moving Relative to Another Particle is East of That Particle

Transforming Variance and Mean 2

Finding Floats of an Activity Network

Ratio of Consecutive Fibbonacci Numbers

Particle on Rough Slope Subject to Horizontal Force Just About to Move up Slope

Problem Solving With Probability Tables

Prims Table Algorithm to Find a Minimum Spanning Tree

Performing a Forward Pass on an Activity Network

Particle on Smooth Slope Held in Equilibrium by Horizontal Force

Gantt Charts – Activity Networks

Finding Quadratic Expressions By Transformation of Roots 2