FP3 Tutorials – Edexcel IAL (International A-Level)

It is advisable to check the official FP3 Edexcel IAL (International A-Level) specification in case of any changes.

Hyperbolic Functions

Hyperbolic Functions

  1. Definitions
  2. Graphs of sinh(x), cosh(x) and tanh(x)
  3. Graphs of sech(x), cosech(x) and coth(x)
  4. Solving equations using inverse and exponential functions
  5. Hyperbolic identities
  6. Osborn's rule
  7. Inverse hyperbolic functions and their graphs
  8. Expressing inverse hyperbolic functions as natural logarithms
  9. Solving hyperbolic equations using hyperbolic identities

Conics

Conic Sections

  1. The conic sections of a circle, parabola, ellipse and hyperbola

The Ellipse

  1. The Ellipse - Cartesian and parametric forms
  2. Tangents and normals to an ellipse
  3. Equation of the directrix and coordinates of the focus

The Hyperbola

  1. Cartesian and parametric equations and asymptotes for a hyperbola
  2. Cartesian equation, focus and directrices
  3. Finding equations of tangents and normals to a hyperbola
  4. Finding equations of simple loci

Differentiation

Inverse Trigonometric Functions

  1. Derivatives of sin-1(x), cos-1(x) and tan-1(x)
  2. Mixed examples : Differentiating inverse trig functions

Hyperbolic Functions

  1. Differentiation of hyperbolic functions
  2. Differentiation of inverse hyperbolic functions

Series

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

Integration

Standard Integrals Involving Inverse Trigonometric Functions

  1. Integrals of the form 1/(a2+x2) and 1/√(a2-x2)

Standard Integrals Involving Hyperbolic Functions

  1. Integrating expressions involving hyperbolic functions

Deriving and using reduction formulae

  1. Deriving and using reduction formulae

Applications of Integration – Arcs

  1. Length of an arc

Applications of Integration – Surface area of revolution

  1. Area of surface of revolution about the x-axis

Vectors

Vector Product

  1. Vector product (cross product)
  2. Applications : Area of a triangle and parallelogram

Triple Scalar Product

  1. Triple scalar product
  2. Applications: volume

Lines

  1. Cartesian form of a line
  2. Vector product form of a line
  3. Shortest distance between two skew lines

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

Matrix Algebra

Further matrix algebra

  1. Transposed and symmetric matrices
  2. Finding the determinant of a 3x3 matrix
  3. Linear transformations in 3 dimensions
  4. Using inverse matrices to reverse the effects of a linear transformation
  5. Eigenvalues and eigenvectors
  6. Reducing a symmetrical matrix to diagonal form
  7. Finding the inverse of a 3x3 matrix where it exists