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
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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