Study Guides

Master OCR GCSE Further Maths Algebraic Fractions (2.1) with this comprehensive study guide. Learn to simplify complex expressions, solve equations, and avoid common exam pitfalls through expert-written content, worked examples, and engaging multi-modal resources designed to secure top marks.

Master OCR GCSE Further Maths with this deep dive into Circle Theorems (5.1). This guide breaks down all seven key theorems, provides algebraic proof strategies, and includes examiner-approved worked examples to help you secure top marks.

This guide provides a deep dive into Completing the Square for OCR GCSE Further Mathematics (2.4). It covers everything from the core algebraic method to its powerful application in finding the turning points of parabolas, ensuring you can tackle exam questions with confidence and secure top marks.

Master the equation of a tangent to a circle for your OCR GCSE Further Maths exam. This guide breaks down the essential perpendicular gradient rule, provides step-by-step worked examples, and offers examiner tips to help you secure every mark.

Error Intervals is a critical topic in OCR GCSE Further Mathematics that examines how candidates apply inequality notation to continuous data with precision. This topic underpins high-level 'Bounds' questions and requires rigorous understanding of the distinction between rounding and truncation. Mastering error intervals is essential for earning reliable marks in both Foundation and Higher tier papers.

Master OCR GCSE Further Maths Functions (2.5) with this guide, covering notation, composition, and inverses. We focus on exam technique, showing you how to secure every mark by understanding how functions are combined and reversed, a key skill for higher-level maths.

Master OCR GCSE Further Maths Topic 3.3 on Gradients and Lines. This guide breaks down how to calculate gradients, understand parallel and perpendicular relationships (m1*m2=-1), and tackle complex exam questions like finding perpendicular bisectors to secure top marks.

Master the power of indices for your OCR GCSE Further Maths exam. This guide breaks down integer and fractional indices, showing you how to manipulate complex expressions and solve exponential equations to secure top marks.

Master OCR GCSE Further Maths Inequalities (2.3) by learning to solve quadratic inequalities algebraically and graphically. This guide breaks down the critical steps, from finding roots to sketching parabolas and selecting the correct regions, ensuring you can secure every mark."

Iteration is a powerful numerical method that allows you to find approximate solutions to equations that cannot be solved algebraically. By repeatedly applying an iterative formula of the form x_{n+1} = g(x_n), you systematically converge on roots to a specified degree of accuracy. This topic is essential for OCR GCSE Further Mathematics and typically appears as structured 4-6 mark questions testing both algebraic manipulation and precise calculator technique.

Proof is the art of constructing watertight algebraic arguments that demonstrate mathematical statements are true for ALL cases, not just specific examples. This topic is a cornerstone of OCR GCSE Further Mathematics, demanding rigorous logic, precise algebraic notation, and clear communication. Mastering proof unlocks high-value marks and develops critical thinking skills that extend far beyond mathematics.

Master the art of mathematical proof for your Edexcel A-Level Further Maths exam. This guide breaks down Proof by Induction into four simple steps, showing you how to secure every mark on questions involving series, divisibility, and matrices.

Sequences in OCR GCSE Further Mathematics extend beyond standard GCSE, requiring mastery of quadratic sequences, geometric progressions, limiting values, and recurrence relations. This topic is essential for top grades, testing algebraic rigour, pattern recognition, and the ability to determine long-term behaviour of mathematical series.

Master the art of solving simultaneous equations in OCR GCSE Further Mathematics. This guide breaks down the essential algebraic techniques for tackling linear and non-linear systems, showing you how to secure top marks by finding the precise intersection points of lines and curves.

This guide provides a comprehensive, exam-focused breakdown of Standard Form for OCR GCSE Further Mathematics. It covers everything from the core principles of writing numbers in the form A × 10ⁿ to performing complex calculations, ensuring you can secure every mark available on this crucial topic.

Surds are irrational roots like √2 that cannot be written as fractions. Mastering surds is essential for exact arithmetic in GCSE Further Maths, as examiners demand rigorous working without decimal approximations. This guide covers simplification, operations, rationalising denominators, and applying surds in geometric contexts to secure full marks.

Master OCR GCSE Further Maths Transformations of Functions (3.4). This guide breaks down translations, reflections, and stretches, showing you how to secure top marks with examiner insights, worked examples, and powerful memory hooks.

This topic extends your trigonometry knowledge beyond right-angled triangles into the realm of any angle, trigonometric identities, and complex equation solving. You'll master the CAST diagram, apply the Sine and Cosine Rules to non-right-angled triangles in 2D and 3D contexts, and prove identities using fundamental relationships. This is a high-value topic in Further Maths exams, frequently appearing in multi-step problem-solving questions worth 4-6 marks.

Vectors in OCR GCSE Further Mathematics goes far beyond basic GCSE column vector arithmetic. You'll master constructing complex vector paths through geometric figures, proving collinearity using scalar multiples, and finding positions of points that divide lines in given ratios. This topic demands algebraic precision, rigorous notation, and explicit geometric reasoning—skills that examiners reward generously when demonstrated correctly.