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FP1 Tutorials

FP1 Tutorials – MEI A Level Maths

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

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

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. Using complex numbers to represent regions on an Argand diagram
  5. Exam Questions - Loci in the complex plane

Rational Expressions

Graphs of Rational Functions

  1. Graphs of rational functions

Inequalities

Fractional Inequalities

  1. Fractional inequalities
  2. Range of values taken by a function

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

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

Series

Method of Differences

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