Cambridge Mathematics International AS and A Level Further Pure Mathematics 1
Course

Cambridge Mathematics International AS and A Level – Further Pure Mathematics 1

1.1 Matrices
1.2 Transformations using Matrices
1.3 Sequences and Series
1.4 Mathematical Induction
1.5 Quadratic Equations
1.6 Roots and Coefficients of Polynomials
1.7 Graphs
1.8 Vectors

42 Lessons

Course Materials

MATRICES

Matrix Structure

Matrix Operations and Definitions

Matrix Algebra

Matrix Multiplication

Properties of Matrix Multiplication

Determinants

Inverse of a Matrix

SEQUENCES AND SERIES

Sigma Notation for Sums of Arithmetic Sequences

Sigma Notation for Sums of Geometric Sequences

Sum of an Infinite Geometric Series

PRINCIPLE OF MATHEMATICAL INDUCTION

Basic Mathematical Induction

Consideration of Initial Values

Mathematical Induction with Factorials

Mathematical Induction: Two Initial Values

Inequality Proofs by Comparisons

Inequality Proofs using Differences

Inequality Proofs by Finding Initial Values

Inequality Proofs using Assumptions

QUADRATIC EQUATIONS

What are Quadratic Equations?

Finding Solutions by Inspecting Graphs

Forming Quadratic Equations

Sum and Product of Roots

Substitutions into Quadratics

Reducible to Quadratics: Polynomials

ROOTS AND COEFFICIENTS OF POLYNOMIALS

Roots and Coefficients of Cubic Polynomials

GRAPHS

Rational Functions

Graphs of Rational Functions

Curves of Rational Functions in Quadratics by Linear Form

Further Rational Functions

Absolute Value (Modulus) Graphs

Further Graphs of Absolute Value (Modulus) Functions

Further Graphs of Square Root Functions

Reciprocal Functions

Graphs of Reciprocal Trigonometric Functions

VECTORS

Applications of a Line in a Plane