FP1 Tutorials – AQA A Level Maths

Contents

Rational Expressions
Graphs of Rational Functions
Roots of Polynomial Equations
Roots of Polynomial Equations
Inequalities
Fractional Inequalities
Conics
Parabola
Hyperbola(Rectangular)
The ellipse
Complex Numbers
Complex Numbers
Series
Standard Summations
Differentiation
Introduction
Integration
Definite Integration
Numerical Solution of Equations
Solution of Equations by Numerical Methods
Numerical Solution of Linear Differential Equations
Solving Differential Equations
Trigonometry
Exam Questions Mixed Trigonometry
Matrix Algebra
Matrices
Matrix Linear Transformations
Exam Questions

Rational Expressions

Graphs of Rational Functions

  1. Graphs of rational functions

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Roots of Polynomial Equations

Roots of Polynomial Equations

  1. Relationships between the roots and coefficients of a quadratic equation

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Inequalities

Fractional Inequalities

  1. Fractional inequalities

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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

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Hyperbola (Rectangular)

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

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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

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Complex Numbers

Complex Numbers

  1. Real and imaginary numbers
  2. Addition, subtraction and multiplying complex numbers and simplifying powers of i
  3. Solving problems with complex numbers
  4. Square roots of a complex number

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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

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Differentiation

Differentiation – Introduction

  1. The gradient function dy/dx

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Integration

Definite Integration

  1. Convergent and Divergent Integrals

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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

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Numerical Solution of Linear Differential Equations

Solving differential equations of the form dy/dx = f(x)

  1. Step by step methods

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Trigonometry

Exam Questions – Mixed trigonometry

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    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

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    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

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    Exam Questions – Matrix Algebra

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