Exam-Ready Series: Further Pure Mathematics 1 Course

A course designed to help you master important concepts and pass your exams once and for all!

  • Video Tutorials

    For each syllabus topic, you will get a series of videos where the core concepts are well-explained with relevant worked examples to give you a deeper understanding

  • Exam-Style Questions

    Learn how to answer typical exam questions with confidence. In this course, you will be exposed to worked example videos which demonstrate how to answer exam questions.

  • Worksheets

    Each topic has downloadable worksheets (with solutions) to help you test your understanding along the way. All the questions within the worksheets are from past papers.

Course curriculum

  • 1
    Roots of Polynomial Equations
    • Introduction to Roots of Polynomial Equations
    • Quadratic: Roots of Quadratic Polynomial Equations
    • Quadratic: Forming new equations 1
    • Quadratic - Forming new equations 2
    • Quadratic: Symmetric functions of the roots
    • Worksheet 1
    • Roots of Cubic polynomial equations
    • Algebraic Manipulation with Cubic polynomial equations
    • Cubic Algebraic Manipulation (Worked Examples)
    • Forming new Cubic polynomial equations by substitution
    • Obtaining sum of cubes formula from equation
    • Solving Problems Involving Matrices
    • Roots of Quartic polynomial equations
    • Forming new Quartic polynomial equations by substitution
    • Recurrence relations of the roots
    • Worksheet 2
    • Worksheet 3
  • 2
    Rational Functions and Graphs
    • Introduction
    • How to find the asymptotes of a rational graph
    • Determining the behaviour of a rational graph about the asymptotes
    • Sketching modulus graphs
    • Sketching modulus graphs (Worked example)
    • Oblique asymptotes 1
    • Oblique asymptotes 1 (worked example)
    • Oblique asymptotes 2
    • Oblique asymptotes 2 (worked example)
    • Oblique asymptotes and Modulus graphs (worked example)
    • The graph y = f (|x|)
    • Worksheet 1
    • Worksheet 2
  • 3
    Summation of series
    • Introduction
    • Sum and General Term of a series (Worked Example 1)
    • Sum and General Term of a series (Worked Example 2)
    • Standard Results
    • Standard Results Worked Example
    • Limits at Infinity
    • Limits at Infinity Worked Example
    • Method of differences
    • Differences Worked example 2
    • Differences Worked example 1
    • Differences Worked example 3
    • Differences Worked example 4
    • Worksheet 1
    • Worksheet 2
  • 4
    Matrices
    • Introduction
    • Addition, Subtraction and Scalar Multiplication
    • Multiplication of Matrices
    • Multiplication of Matrices (worked examples)
    • Determinant and Inverse of a 2 x 2 Matrix
    • Determinant of a 3 x 3 Matrix
    • Inverse of a 3 x 3 Matrix
    • Singular Matrices
    • The product of a matrix and it’s inverse
    • Inverse of the product of two matrices
    • Transformations (Introduction)
    • Reflection
    • Rotation
    • Enlargement
    • Shear
    • Stretch
    • Successive transformations
    • Area Scale Factor
    • Invariant Points
    • Invariant Points (worked example)
    • Invariant lines
    • Worked Example 1
    • Worked Example 2
    • Worked Example 3
    • Worksheet 1
    • Worksheet 2
  • 5
    Polar Coordinates
    • Introduction
    • Plotting points on a Polar graph
    • Converting between Polar and Cartesian coordinates
    • Converting equations from Cartesian to Polar form
    • Converting equations Polar to Cartesian form
    • Sketching Polar Graphs
    • Sketching Circles
    • Cardioid Graphs
    • Area enclosed by a Polar graph
    • Cardioid Graphs (worked example)
    • Finding the area enclosed by two Polar Graphs
    • Sketching Polar graphs for any given equation
    • Greatest distance of a point from the pole
    • Greatest distance of a point from the pole (worked example)
    • The point furthest from the initial line
    • The point furthest from the vertical line
    • Worksheet 1
    • Worksheet 2
  • 6
    Vectors
    • Equation of plane 1
    • Vector Product
    • Equation of plane 2
    • Equation of plane (worked examples)
    • A line parallel to a plane
    • Distance of a plane from the origin
    • Distance from a point to a plane 1
    • Distance from a point to a plane 2
    • Perpendicular distance from a point to a line
    • Worked Example 1...
    • Shortest distance between two skew lines
    • Angle between a line and a plane
    • Worked Example 2...
    • Angle between two planes
    • Worked Example 3....
    • Worked Example 4
    • Worked Example 5
    • Worksheet 1
    • Worksheet 2
  • 7
    Proof by Induction
    • Introduction
    • Matrices (worked example)
    • Divisibility (worked example 1)
    • Divisibility (worked example 2)
    • Divisibility (worked example 3)
    • Divisibility (worked example 4)
    • Divisibility (worked example 5)
    • Sequences (worked example 1)
    • Sequences (worked example 2)
    • Sequences (worked example 3)
    • Sequences (worked example 4)
    • Differentiation (worked example 1)
    • Differentiation (worked example 2)
    • Differentiation (worked example 3)
    • Series (worked example 1)
    • Series (worked example 2)
    • Series (worked example 3)
    • Worksheet 1
    • Worksheet 2

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