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Further Pure Mathematics 1 Course (9231)

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What I will learn?

  • Use the relations between the roots and coefficients of polynomial equations e.g. to evaluate symmetric functions of the roots or to solve problems involving unknown coefficients in equations; restricted to equations of degree 2, 3 or 4 only.
  • Use a substitution to obtain an equation whose roots are related in a simple way to those of the original equation
  • Sketch graphs of simple rational functions, including the determination of oblique asymptotes, in cases where the degree of the numerator and the denominator are at most 2.
  • Use the standard results for to find related sums and use the method of differences to obtain the sum of a finite series.
  • Carry out operations of matrix addition, subtraction and multiplication, and recognise the terms zero matrix and identity (or unit) matrix.
  • Understand the use of 2 X 2 matrices to represent certain geometric transformations in the x-y plane.
  • Understand the meaning of ‘invariant’ as applied to points and lines in the context of transformations represented by matrices, and solve simple problems involving invariant points and invariant lines.
  • Understand the relations between Cartesian and polar coordinates, and convert equations of curves from Cartesian to polar form and vice versa.
  • Use equations of lines and planes, together with scalar and vector products where appropriate, to solve problems concerning distances, angles and intersections.
  • Use the method of mathematical induction to establish a given result.
  • Recognise situations where conjecture based on a limited trial followed by inductive proof is a useful strategy, and carry this out in simple cases.

Course Curriculum

Roots of polynomial equations

  • Introduction
  • Introduction to Quadratic Polynomials
  • Forming new equations by algebraic manipulation
  • Forming new equations by substitution
  • Symmetric function of the roots of a quadratic equation
  • Revision Exercise 1
  • Roots of Cubic polynomial equations
  • 08:30
  • Algebraic Manipulation (Worked Examples)
  • Forming new Cubic polynomial equations by substitution
  • Obtaining sum of squares formula from equation
  • Revision Exercise 2
  • Roots of Quartic polynomial equations
  • Forming new Quartic polynomial equations by substitution
  • Recurrence relations of the roots
  • Revision Exercise 3

Summation of Series

Rational functions and graphs

Matrices & Transformations

Polar Coordinates


Proof by Induction

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A course by

Walter Chatyoka
Walter Chatyoka
Maths Tutor

Material Includes

  • Videos
  • Quizzes
  • Notes
  • Worksheets


  • A desktop or laptop computer is recommended for optimum user experience. However, a phone or tablet can also be used as an alternative.
  • A reliable internet connection for the duration of the course
  • Have good foundational knowledge of Mathematics (IGCSE level).
  • Ideally the student must have studied the majority of the Cambridge International AS & A Level Mathematics (9709).

Target Audience

  • Cambridge AS/A Level students

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