Study guides

Additional Pure Mathematics

OCR·GCSE

OCR-GCSE-Further-Mathematics

Master the geometry of 3D surfaces and the calculus used to analyse them. This topic connects your understanding of differentiation to multi-variable functions, allowing you to classify complex stationary points using the Hessian matrix.

Algebraic Fractions

OCR·GCSE

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.

Box Plots

OCR·GCSE

Master the art of constructing and interpreting box plots for your OCR GCSE Further Mathematics exam. This guide breaks down how to earn full marks on questions about quartiles, skewness, and comparing distributions, turning a tricky topic into guaranteed marks.

Circle Theorems

OCR·GCSE

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.

Completing the Square

OCR·GCSE

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.

Cumulative Frequency

OCR·GCSE

Master Cumulative Frequency for your OCR GCSE Further Maths exam. This guide breaks down how to construct and interpret cumulative frequency graphs, calculate key statistics like the median and IQR, and compare datasets to secure top marks.

Discrete Mathematics

OCR·GCSE

OCR-GCSE-Further-Mathematics

Master the Simplex Algorithm for GCSE Further Mathematics with this comprehensive guide. Learn how to systematically solve complex linear programming problems using algebraic tableaus, identify optimal solutions, and secure maximum marks with examiner-approved techniques.

Discrete Random Variables

OCR·A-Level

Master Discrete Random Variables for your OCR A-Level Further Maths exam. This guide breaks down the core concepts of expectation and variance, reveals common examiner traps, and provides worked examples to help you secure every mark. Learn the crucial difference between Var(2X) and Var(X₁+X₂) and why stating independence is a mark-winner.

Equation of a Circle

OCR·GCSE

Master the Equation of a Circle for your OCR GCSE Further Maths exam. This guide breaks down everything from the standard form and completing the square to finding tangents and solving complex intersection problems, ensuring you can secure top marks.

Equation of a Tangent to a Circle

OCR·GCSE

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

OCR·GCSE

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.

Functions (notation and composition)

OCR·GCSE

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.

Further Algebra and Functions

WJEC·A-Level

Master the core of WJEC A-Level Further Maths with this guide to Further Algebra and Functions. We break down polynomial roots, series summation, and advanced partial fractions to show you how to secure top marks in your exams.

Gradients and Parallel/Perpendicular Lines

OCR·GCSE

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.

Histograms

OCR·GCSE

Master OCR GCSE Further Maths Histograms by understanding the crucial link between area and frequency. This guide breaks down how to calculate frequency density, construct accurate diagrams, and tackle tricky reverse problems to secure top marks."

Indices (integer and fractional)

OCR·GCSE

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.

Inequalities

OCR·GCSE

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

OCR·GCSE

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.

Mechanics

OCR·GCSE

OCR-GCSE-Further-Mathematics

Master the dynamics of moving objects with Impulse, Momentum, and Collisions. This topic is crucial for solving complex physical problems and frequently appears as high-mark, multi-step calculations in the exam.

Probability Generating Functions

OCR·A-Level

Master one of the most powerful tools in A-Level Further Maths. This guide breaks down Probability Generating Functions (PGFs), showing you how to encode entire distributions into a single function, then differentiate to find the mean and variance. It’s your key to unlocking top marks in OCR exam questions on discrete distributions.

Proof

Pearson Edexcel·A-Level

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.

Proof

OCR·GCSE

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.

Pure Core

OCR·GCSE

OCR-GCSE-Further-Mathematics

This topic connects the algebraic structure of polynomials directly to their roots, allowing you to manipulate equations without solving them. It also equips you with the partial fractions technique, an essential tool for breaking down complex rational functions into simpler components for integration and binomial expansion.

Pythagoras' Theorem in 3D

OCR·GCSE

Master Pythagoras in 3D for your OCR GCSE Further Maths exam. This guide breaks down how to find space diagonals and pyramid heights, showing you how to secure top marks by applying 2D concepts to 3D shapes and avoiding common examiner traps.

Sequences

OCR·GCSE

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.

Set Notation

OCR·GCSE

Master OCR GCSE Further Maths Set Notation (5.5) with this comprehensive guide. Learn to fluently use symbols, interpret Venn diagrams, and tackle exam questions on intersection, union, and complements to secure top marks."

Similar Shapes

OCR·GCSE

Master the crucial relationship between linear, area, and volume scale factors for similar shapes. This guide provides everything you need to tackle complex OCR Further Maths questions involving frustums, composite solids, and mass/density problems, securing top marks.

Simultaneous Equations (linear and non-linear)

OCR·GCSE

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.

Standard Form

OCR·GCSE

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

OCR·GCSE

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.