FP2 Tutorials – Edexcel IAL (International A-Level)

It is advisable to check the official FP2 Edexcel IAL (International A-Level) specification in case of any changes.

Inequalities

Fractional Inequalities

  1. Fractional inequalities

Modulus Inequalities

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

Series 1

Method of Differences

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

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

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

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

Transformations of the Complex Plane

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

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

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)

Substitution Types

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

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

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

Using a Substitution

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

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

Taylor’s Series

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

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

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

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

Tangents

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