FP1 Tutorials

Edexcel IAL (International A-Level).

FP1 Tutorials

FP1 topics

Complex Numbers

Complex Numbers

  1. Real and imaginary numbers
  2. Addition, subtraction and multiplying complex numbers and simplifying powers of i
  3. Complex conjugates
  4. Division of a complex number by a complex number
  5. Argand diagrams
  6. Modulus and argument of a complex number
  7. Solving problems with complex numbers
  8. Square roots of a complex number
  9. Solving quadratic equations with complex roots
  10. Solving cubic equations
  11. Solving quartic equations
  12. Exam Questions - Complex numbers
  13. Exam Questions - Finding roots

Roots of Polynomial Equations

Roots of Polynomial Equations

  1. Relationships between the roots and coefficients of a quadratic equation
  2. Relationships between the roots and coefficients of a cubic equation
  3. Relationships between the roots and coefficients of a quartic equation

Numerical Solution of Equations

Solution of Equations by Numerical methods

  1. Bisection method for locating a root in a given interval
  2. Exam Questions - Bisection Method
  3. Linear interpolation method for locating a root in a given interval
  4. Exam Questions - Linear Interpolation
  5. Newton-Raphson Method NEW!!
  6. Newton-Raphson method for locating a root in a given interval
  7. Exam Questions - Newton-Raphson

Conics

Parabola

  1. Coordinate geometry: Parabola directrix, focus, locus and equation
  2. Parabola parametric form
  3. Tangents and normals: Cartesian types
  4. Tangents and normals: parametric types
  5. Exam Questions - Parabola

Hyperbola (Rectangular)

  1. Cartesian and parametric type
  2. Tangents and normals : Cartesian type
  3. Tangents and normals: parametric type
  4. Exam Questions - Hyperbola (rectangular)

Matrix Algebra

Matrices

  1. Introduction and dimension of a matrix
  2. Addition and subtraction and multiplying a matrix by a scalar
  3. Matrix multiplication
  4. Identity and Inverse of a 2x2 matrix
  5. Exam Questions - Identity and inverse of a 2x2 matrix

Simultaneous Equations by Matrix Methods

  1. Solving simultaneous linear equations in 2 unknowns

Matrix Linear Transformations

  1. Linear transformations - rotations
  2. Linear transformations - reflections
  3. Linear transformations - enlargement
  4. How well do you know your transformations?
  5. Combinations of transformations
  6. Inverse matrices to reverse linear transformations
  7. Determinant as the area scale factor of a transformation
  8. Exam Questions - Matrix transformations

Exam Questions – Matrix Algebra

    Series

    Standard Summations

    1. Sigma notation
    2. Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)
    3. Sum of the squares of the first n natural numbers ∑r2
    4. Sum of the cubes of the first n natural numbers ∑r3
    5. Using known formulae to sum more complex series
    6. Exam Questions - Series

    Proof by mathematical induction

    Sum of Series

    1. Proof of the sum of the series ∑r
    2. Proof of the sum of the series ∑r²
    3. Proof of the sum of the series ∑r³
    4. Proof for other series
    5. Exam Questions - Sum of series

    Various Types of Proofs

    1. Divisibility and multiple test proofs
    2. Exam Questions - Divisibility and multiple tests
    3. Recurrence relationship proofs
    4. Exam Questions - Recurrence relations
    5. Matrix proofs
    6. Exam Questions - Matrix proofs