C4 Tutorials – OCR A Level Maths

Contents for C4 OCR

Rational Expressions
Rational Expressions – Simplifying
Partial Fractions
Sequences and Series
Binomial Expansion
Coordinate Geometry
Parametric Equations
Differentiation
Exponential Functions
Trigonometric Functions
Parametric Functions
Implicit Functions
Integration
Common Functions
Trigonometric Functions
Integrals involving Partial Fractions
By Substitution
By Inspection
By Parts
Mixed Examples and Exam Questions
Numerical Integration
Differential Equations
Separating the Variables
Forming Differential Equations
Vectors
Vectors
Scalar Product
Vector Equations of Lines
Exam Questions

Rational Expressions

Rational Expressions – Simplifying

  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

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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

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Sequences and Series

Binomial Expansion

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

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Coordinate Geometry

Parametric Equations

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

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Differentiation

Exponential Functions

  1. Differentiation: Exponential functions of the form y=ax

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Trigonometric Functions

  1. The trig functions sin(x), cos(x) and tan(x)
  2. Chain rule: Trigonometric types

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Parametric Functions

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

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Implicit Functions

  1. Implicit functions
  2. Tangents and normals
  3. Stationary points
  4. Exam Questions - Implicit functions

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Integration

Integration – Common Functions

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

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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

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Integrals involving Partial fractions

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

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Integration by Substitution

  1. Integration by substitution
  2. Square root types
  3. Integration of trigonometric functions by substitution
  4. Integration of exponential types by substitution
  5. Integration by substitution using limits
  6. Integration of trigonometric functions by substitution with limits
  7. Exam Questions - Integration by substitution

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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

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Integration by Parts

  1. Integration by parts
  2. Integration by parts (ln types)
  3. Integration by parts using limits
  4. Proof of the formula - Integration by parts
  5. Exam Questions - Integration by parts

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Mixed Examples & Exam Question – Integration

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

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Numerical Integration

  1. Trapezium rule
  2. Exam Questions - Trapezium rule

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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

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Differential equations – Forming differential equations

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

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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

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Scalar Product (Dot Product)

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

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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

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Exam Questions – Vectors

  1. Exam Questions - Vectors

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