### Exam-Ready Series: Further Pure Mathematics 1 Course

• #### 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.

### Course curriculum

• 1
##### Roots of Polynomial Equations
• Introduction to Roots of 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