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.

About the Course

With this course, you will build up a strong grasp of A Level Further Pure Mathematics concepts. You child will learn all the key concepts through prerecorded tutorial videos. Through this course you will also receive ample practice through worksheets to master all the concepts. The difficulty level for this course is moderate since I use simple explanations to explain tough concepts. This course is only suitable for serious learners who want to see serious results!

  • Key concepts of each topic explained

  • How to handle common exam questions

  • High-quality questions to ensure sufficient practice

Course curriculum

    1. Introduction to Roots of Polynomial Equations

    2. Quadratic: Roots of Quadratic Polynomial Equations

    3. Quadratic: Forming new equations 1

    4. Quadratic - Forming new equations 2

    5. Quadratic: Symmetric functions of the roots

    6. Worksheet 1

    7. Roots of Cubic polynomial equations

    8. Algebraic Manipulation with Cubic polynomial equations

    9. Cubic Algebraic Manipulation (Worked Examples)

    10. Forming new Cubic polynomial equations by substitution

    11. Obtaining sum of cubes formula from equation

    12. Solving Problems Involving Matrices

    13. Roots of Quartic polynomial equations

    14. Forming new Quartic polynomial equations by substitution

    15. Recurrence relations of the roots

    16. Worksheet 2

    17. Worksheet 3

    1. Introduction

    2. How to find the asymptotes of a rational graph

    3. Determining the behaviour of a rational graph about the asymptotes

    4. Sketching modulus graphs

    5. Sketching modulus graphs (Worked example)

    6. Oblique asymptotes 1

    7. Oblique asymptotes 1 (worked example)

    8. Oblique asymptotes 2

    9. Oblique asymptotes 2 (worked example)

    10. Oblique asymptotes and Modulus graphs (worked example)

    11. The graph y = f (|x|)

    12. Worksheet 1

    13. Worksheet 2

    1. Introduction

    2. Sum and General Term of a series (Worked Example 1)

    3. Sum and General Term of a series (Worked Example 2)

    4. Standard Results

    5. Standard Results Worked Example

    6. Limits at Infinity

    7. Limits at Infinity Worked Example

    8. Method of differences

    9. Differences Worked example 2

    10. Differences Worked example 1

    11. Differences Worked example 3

    12. Differences Worked example 4

    13. Worksheet 1

    14. Worksheet 2

    1. Introduction

    2. Addition, Subtraction and Scalar Multiplication

    3. Multiplication of Matrices

    4. Multiplication of Matrices (worked examples)

    5. Determinant and Inverse of a 2 x 2 Matrix

    6. Determinant of a 3 x 3 Matrix

    7. Inverse of a 3 x 3 Matrix

    8. Singular Matrices

    9. The product of a matrix and it’s inverse

    10. Inverse of the product of two matrices

    11. Transformations (Introduction)

    12. Reflection

    13. Rotation

    14. Enlargement

    15. Shear

    16. Stretch

    17. Successive transformations

    18. Area Scale Factor

    19. Invariant Points

    20. Invariant Points (worked example)

    21. Invariant lines

    22. Worked Example 1

    23. Worked Example 2

    24. Worked Example 3

    25. Worksheet 1

    26. Worksheet 2

    1. Introduction

    2. Plotting points on a Polar graph

    3. Converting between Polar and Cartesian coordinates

    4. Converting equations from Cartesian to Polar form

    5. Converting equations Polar to Cartesian form

    6. Sketching Polar Graphs

    7. Sketching Circles

    8. Cardioid Graphs

    9. Area enclosed by a Polar graph

    10. Cardioid Graphs (worked example)

    11. Finding the area enclosed by two Polar Graphs

    12. Sketching Polar graphs for any given equation

    13. Greatest distance of a point from the pole

    14. Greatest distance of a point from the pole (worked example)

    15. The point furthest from the initial line

    16. The point furthest from the vertical line

    17. Worksheet 1

    18. Worksheet 2

    1. Equation of plane 1

    2. Vector Product

    3. Equation of plane 2

    4. Equation of plane (worked examples)

    5. A line parallel to a plane

    6. Distance of a plane from the origin

    7. Distance from a point to a plane 1

    8. Distance from a point to a plane 2

    9. Perpendicular distance from a point to a line

    10. Worked Example 1...

    11. Shortest distance between two skew lines

    12. Angle between a line and a plane

    13. Worked Example 2...

    14. Angle between two planes

    15. Worked Example 3....

    16. Worked Example 4

    17. Worked Example 5

    18. Worksheet 1

    19. Worksheet 2

About this course

  • $64.00
  • 126 lessons
  • 15.5 hours of video content


Walter Chatyoka

Maths Teacher

With over a decade of experience teaching High School Maths and Science , I have grown to become a very effective and versatile teacher. I'm very passionate about teaching Maths and I have managed to produce excellent results for my students.

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