C4 Tutorials – MEI A Level Maths

Rational Expressions

Rational Expressions

  1. Simplifying algebraic fractions
  2. Exam Questions - Simplifying a rational expression
  3. Addition and subtraction of algebraic fractions
  4. Exam Questions - Addition & subtraction
  5. Multiplication of algebraic fractions
  6. Further simplifying of 'stacked fractions'
  7. Exam Questions - Algebraic long division

Partial Fractions

  1. Partial fractions
  2. Denominator contains 2 or 3 linear factors
  3. Denominator contains repeated factors
  4. Exam Questions - Partial fractions
  5. Improper types

Sequences and Series

Binomial Expansion

  1. Exam Questions - Binomial expansion for rational and negative powers
  2. Exam Questions - Partial fractions with the binomial expansion

Trigonometry

Trigonometric Equations

  1. Quadrant rule to solve trig equations
  2. Trig equations with different ranges
  3. Trig equations with multiple angles
  4. Trig equations that factorise

Trigonometric Identities

  1. Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
  2. Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
  3. Solving equations using identities
  4. Exam Questions - Trigonometric identities

Sec θ, Cosec θ and Cot θ

  1. Trig functions sec θ, cosec θ and cot θ
  2. Graphs of sec θ, cosec θ and cot θ

Inverse trigonometric functions

  1. Inverse trigonometric functions - arcsin x, arccos x, arctan x
  2. Examples using Inverse trigonometric functions

Identities & Equations – Pythagorean Type

  1. sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x
  2. Solving equations using Pythagorean identities

Identities – Addition type

  1. sin(A±B), cos(A±B) and tan(A±B)
  2. Using the Addition formulae to get exact values
  3. Proving identities using the addition formulae
  4. Identities - Addition type - Equations

Identities & Equations – Double angle type

  1. Identities for sin2A, cos2A and tan2A
  2. Examples using double angle identities
  3. Solving equations using double angle identities
  4. Exam Questions - Double Angles

Identities – Half angle type

  1. Examples using half angle identities

Identities – Triple angle type

  1. Identity for cos 3θ and sin 3θ

Identities – Factor Formulae

  1. Proving identities using the factor formulae

Identities & Equations – Harmonic Formulae

  1. Harmonic Identities Rsin(x ± α), Rcos(x ± α)
  2. Equations using harmonic identities
  3. Harmonic identities - Max and Min
  4. Exam Questions - Harmonic identities and equations

Small-angle Approximations

  1. Small-angle approximations
  2. Exam Questions - Small Angle Approximations

Exam Questions – Mixed trigonometry

  1. Exam Questions - Mixed trigonometry

Coordinate Geometry

Parametric Equations

  1. Parametric equations
  2. Converting to Cartesian form
  3. Exam Questions - Parametric to Cartesian equations
  4. Sketching parametric graphs
  5. Parametric equations of circle, ellipse, parabola and hyperbola
  6. Finding Points of Intersection between a Parametric and Cartesian Equation
  7. Exam Questions - Parametric equations

Differentiation

Parametric Functions

  1. Differentiation: Parametric functions
  2. Tangents and normals
  3. Stationary points
  4. Exam Questions - Parametric functions

Integration

Integration – Common Functions

  1. Integrals of the form : f '(x)/f(x)
  2. Integrals of the form : f'(x)ef(x)

Integrals of Trigonometric Functions

  1. Integrals of sin x, cos x, sec² x
  2. Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types
  3. Integrals Using Trigonometric Identities
  4. sin2x and cos2x types
  5. Exam Questions - Trigonometric types

Integrals involving Partial fractions

  1. Integrals involving partial fractions
  2. Exam Questions - Integrals involving partial fractions

Integrating Products of the form f[g(x)]g'(x) by inspection

  1. Integrating products of the form f[g(x)]g'(x) by inspection

Mixed Examples & Exam Question – Integration

  1. Integration - General Methods
  2. Mixed Examples - Integration
  3. Exam Questions - Integration

Applications of Integration – Area bound by a curve

  1. Area under a graph : parametric type

Applications of Integration – Volumes of revolution

  1. Volume of revolution about the x-axis
  2. Exam Questions - Volume of revolution about the x-axis
  3. Volume of revolution about the x-axis generated between curves
  4. Volume of Revolution about the y-axis
  5. Exam Questions - Volume of Revolution about the y-axis
  6. Volume of Revolution about the y-axis generated between curves

Vectors

Vectors

  1. What is a vector and a scalar quantity?
  2. Vector notation
  3. Position vectors
  4. Equal and negative vectors
  5. Multiplying a vector by a scalar
  6. Addition and subtraction of vectors
  7. Magnitude of a 2 dimensional vector
  8. Magnitude of a 3 dimensional vector
  9. Unit vectors

Scalar Product (Dot Product)

  1. Scalar product
  2. Perpendicular vectors
  3. Exam Questions - Scalar product

Vector Equations of Lines

  1. Vector equation of a line
  2. Angle between two lines
  3. Parallel lines
  4. Intersecting and skew lines
  5. Exam Questions - Parallel intersecting and skew lines
  6. Closest point to a line and shortest distance from the origin
  7. Shortest distance of a point to a line

Lines

  1. Cartesian form of a line

Exam Questions – Vectors

  1. Exam Questions - Vectors

Planes

  1. Parametric vector form of a plane
  2. Scalar product forms of a plane
  3. Cartesian form of a plane
  4. Finding the point of intersection between a line and a plane
  5. The equation of the line of intersection between two non parallel planes
  6. Shortest distance from a point to a plane
  7. The angle between two planes

First Order Linear Differential Equations

Separating the variables

  1. Differential Equations - Finding a general and a particular solution
  2. Working with constants in log types
  3. Differential Equations - Exponential and trig type

Forming differential equations

  1. Direct proportion type
  2. Inverse proportion type
  3. Newton's law of cooling
  4. Exam Questions – Forming differential equations