FP2 Edexcel Maths Tutorials

It is advisable to check the official FP2 Edexcel specification in case of changes: specification

Contents

Inequalities
Fractional Inequalities
Modulus Inequalities
Series 1
Method of Differences
Complex Numbers
Further Complex Numbers
De Moivres Theorem
Loci in the Complex Plane
Transformations in the Complex Plane
First Order Differential Equations
Separating the Variables
Exact Equations (Integrating Factors)
Substitution Type
Second Order Differential Equations
Equations of the form ad²y/dx²+ bdy/dx+cy =f(x)
Using a Substitution
Series 2
Maclaurin’s Series
Taylor’s Series
Polar Coordinates and Curves
Polar Co-ordinates
Equations of Curves
Area Bounded by a Polar Curve
Tangents

Inequalities

Fractional Inequalities

  1. Fractional inequalities

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Modulus Inequalities

  1. Modulus inequalities fractional type
  2. Exam Questions - Modulus inequalities fractional type

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Series 1

Method of Differences

  1. Method of differences
  2. Exam Questions - Method of differences

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Complex Numbers

Further Complex Numbers

  1. Modulus-argument form of a complex number
  2. Exponential Form (Euler's relation)
  3. Multiplication and division rules for mod and argument of two complex numbers
  4. Exam Questions - Further complex numbers

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De Moivre’s Theorem

  1. De Moivre's theorem
  2. Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
  3. Exam Questions - Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
  4. Expressing sinnθ and cosnθ in terms of sin(kθ) and cos(kθ)
  5. nth roots of a complex number
  6. Exam Questions - nth roots of a complex number

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Loci in the Complex Plane

  1. The locus of a point moving in a circle
  2. The locus of a point moving along a perpendicular bisector
  3. The locus of a point moving along a half-line
  4. The locus of a point moving on the arc of a circle
  5. Using complex numbers to represent regions on an Argand diagram
  6. Exam Questions - Loci in the complex plane

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Transformations of the Complex Plane

  1. Transformations of the complex plane
  2. Further transformations
  3. Exam Questions - Transformations of the complex plane

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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
  4. Separating the variables and sketching a family of curves

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Exact Equations (Integrating Factors)

  1. Exact equations where one side is the exact derivative of a product
  2. Solving equations of the form dy/dx + Py = Q using an integrating factor
  3. Exam Questions - Exact equations (integrating factors)

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Substitution Types

  1. Using substitution to reduce a differential equation to a known form
  2. Exam Questions - Substitution types

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Second Order Linear Differential Equations

Equations of the form a d²y/dx² + b dy/dx + cy = 0

  1. How to solve second order linear differential equations that equal zero

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Equations of the form a d²y/dx² + b dy/dx + cy = f(x)

  1. General solutions where f(x) = k (constant types)
  2. General solutions where f(x) = kx (linear types)
  3. General solutions where f(x) = kx2 (quadratic types)
  4. General solutions where f(x) = kepx (exponential types)
  5. General solutions where f(x) = λ cosωx + µ sinωx (trig types)
  6. Special types of particular integrals
  7. Exam Questions - General solutions where f(x) = kx (linear types)
  8. Particular solutions using boundary conditions to solve differential equations
  9. Exam Questions - Exponential Type kepx (exponential types)
  10. Exam Questions - Particular solutions using boundary conditions

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Using a Substitution

  1. Using substitution to reduce a differential equation to a known form

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Series 2

Maclaurin’s Series

  1. Maclaurin's series expansion
  2. Series expansion for ex
  3. Series expansion for sin(x) and cos(x)
  4. Series expansion for ln(1+x)
  5. Further series
  6. Exam Questions - Maclaurin’s series

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Taylor’s Series

  1. Taylor's series
  2. Solution to differential equations using Taylor's series
  3. Exam Questions - Taylor’s series

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Polar Coordinates and Curves

Polar Coordinates

  1. Defining the position of a point
  2. Converting Cartesian coordinates to polar coordinates
  3. Converting polar coordinates to Cartesian coordinates

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Equations of Curves

  1. Converting the equation of a polar curve to Cartesian form
  2. Converting the equation of a Cartesian curve to polar form
  3. Sketching polar curves a spiral
  4. Sketching polar curves a half-line
  5. Sketching curves a circle and arc
  6. Sketching curves the cardioid r = a (1+cosθ)
  7. Sketching curves the curve r = asin 2θ

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Area Bounded by a Polar Curve

  1. Area bounded by a polar curve
  2. Area bounded by a cardioid and a loop
  3. Exam Questions - Area bounded by a polar curve

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Tangents

  1. Finding equations of tangents parallel to and perpendicular to the initial line
  2. Exam Questions - Tangents

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