A-Level Maths

Differentiation

• What is Differentiation? 

• Differentiation from First Principles

• Finding the Tangent & Normal to a Curve 

• Stationary Points, Maximum & Minimum

• Chain Rule for Differentiation

• Product Rule for Differentiation

• Proof of Product Rule

• Quotient Rule for Differentiation

• Differentiating ln(x)

• Differentiation a^x

• Differentiating e^x

• Implicit Differentiation

• Finding Derivatives of Inverse Trig Functions Using Implicit Differentiation

• Finding Derivatives of Sec(x), Cot(x) & Cosec(x)

• Differentiating Parametric Equations

• Chain Rule Worked Practise Questions

• Product Rule Worked Practise Questions

• Quotient Rule Worked Practise Questions

• Implicit Differentiation Worked Practise Questions

• Introduction to Differential Equations

• Separation of Variables to Solve Differential Equations

Integration

• What is Integration? 

• Finding the Value of the Constant of Integration

• How to Calculate Definite Integrals

• Finding the Area Under a Curve by Integration

• Integration by Substitution (Indefinite Integrals)

• Integration by Substitution (Definite Integrals)

• Integration by Parts

• Integrating ln(x)

• Integration by Substitution Worked Practise Questions

• Integration by Parts Worked Practise Questions

• Introduction to Differential Equations

• Separation of Variables to Solve Differential Equations

Trigonometry

• What are Radians? 

• Arc Length & Sector Area

• Proving sin^2(x) + cos^2(x) = 1

• Proving tan(x) = sin(x)/cos(x)

• Introduction to Solving Simple Trig Equations

• Solving Trig Equations of the Form sin(kx), cos(kx) & tan(kx)

• Double Angle Formulas

• R-Addition Formulas

• Proving Sin, Cos & Tan Angle Addition Formulae 

Sequences & Series

• What is an Arithmetic Progression?

• What is an Arithmetic Series? 

• What is a Geometric Progression? 

• What is a Geometric Series? 

• What is a Recurrence Relation? 

• Binomial Expansions of the form (1+x)^n, n∈N

• Binomial Expansions of the form (a+b)^n, n∈N

• Binomial Expansions of the form (1+x)^n, n∈R

• Range of Validity of Binomial Expansion 

• Binomial Expansion Example Questions

Algebra & Functions

• Introduction to Modulus Functions

• Sketching Moduluis Functions

Coordinate Geometry

• Introduction to Parametric Equations

• Converting Parametric Equations to Cartesian Equations 

• Calculating the Derivative of Parametric Equations

Exponentials & Logarithms

• What are Logarithms? 

• Laws of Logarithms (With Proofs)

• Solving Logarithmic Equations

Statistics

• Standard Deviation & Variance

• Introduction to Binomial Distribution 

Mechanics

• Constant Acceleration Equations (SUVAT)

• Calculus for Kinematics

• Using Vectors to Describe Motion

• Projectiles

• Resultant Forces