Resources
Mathematics study guides
63 published, listed by title. Topic explanations written to be read once and understood.
All 63, by title
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Study Guides
A Level Mathematics: Pure Mathematics 1 - Coordinate Geometry (Cambridge 9709)
Equations of straight lines, the circle equation and its expanded form, and algebraic methods for lines and circles – a deep dive into subtopic 1.3 Coordinate geometry for Cambridge International AS & A Level Mathematics 9709, Pure Mathematics 1.
Mathematics · Cambridge · A LEVELS
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Study Guides
A Level Mathematics: Pure Mathematics 1 - Functions (Cambridge 9709)
Domain, range, one-one functions, inverse functions, composition, and the four standard graph transformations – a deep dive into subtopic 1.2 Functions for Cambridge International AS & A Level Mathematics 9709, Pure Mathematics 1.
Mathematics · Cambridge · A LEVELS
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Study Guides
A Level Mathematics: Pure Mathematics 1 (Cambridge 9709)
Quadratics, functions, coordinate geometry, circular measure, trigonometry, series, differentiation and integration – the full content of Pure Mathematics 1 for Cambridge International AS & A Level Mathematics 9709, 2026-2027 series.
Mathematics · Cambridge · A LEVELS
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Study Guides
A Level Mathematics: Pure Mathematics 2 (Cambridge 9709)
Algebra, logarithmic and exponential functions, trigonometry, differentiation, integration and numerical solution of equations – the full content of Pure Mathematics 2 for Cambridge International AS & A Level Mathematics 9709, 2026-2027 series.
Mathematics · Cambridge · A LEVELS
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Study Guides
Algebraic Manipulation
Simplifying, expanding, factorising and completing the square, plus algebraic fractions, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS
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Study Guides
AQA A-Level Mathematics: Differentiation (7357)
First principles, standard derivatives, stationary points, the product/quotient/chain rules, implicit and parametric differentiation, and forming differential equations – Section G of AQA A-Level Mathematics (7357).
Mathematics · AQA · A LEVELS
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Study Guides
AQA A-Level Mathematics: Overarching Themes (7357)
Mathematical argument, language and proof; mathematical problem solving; and mathematical modelling – the three overarching themes that apply across all content in AQA A-Level Mathematics (7357).
Mathematics · AQA · A LEVELS
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Study Guides
AQA A-Level Mathematics: Quadratics, Simultaneous Equations and Inequalities (7357)
Quadratic functions and the discriminant, solving simultaneous linear-quadratic equations, and linear and quadratic inequalities – B3, B4 and B5 of AQA A-Level Mathematics (7357)'s DfE-prescribed Algebra and Functions content.
Mathematics · AQA · A LEVELS
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Study Guides
AQA GCSE Mathematics 8300: Geometry and measures – Study Guide
AQA GCSE Maths 8300 geometry and measures study guide (G1-G25): angles, constructions, circles, mensuration, trig and vectors, with worked examples.
Mathematics · AQA · GCSE
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Study Guides
AQA GCSE Mathematics 8300: Probability – Study Guide
Study guide for AQA GCSE Maths 8300 Probability (P1-P9): relative frequency, sample spaces, Venn and tree diagrams, and conditional probability.
Mathematics · AQA · GCSE
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Study Guides
AQA GCSE Mathematics 8300: Statistics – Study Guide
Study guide for AQA GCSE Maths 8300 Statistics (S1-S6): sampling, charts, averages and spread, histograms, box plots and scatter graphs.
Mathematics · AQA · GCSE
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Study Guides
AQA GCSE Mathematics: Algebra (8300)
Notation and manipulation, graphs, solving equations and inequalities, and sequences – the full content of Topic 2 Algebra for AQA GCSE Mathematics (8300).
Mathematics · AQA · GCSE
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Study Guides
AQA GCSE Mathematics: Number (8300)
Structure and calculation, fractions/decimals/percentages, and measures and accuracy – the full content of Topic 1 Number for AQA GCSE Mathematics (8300).
Mathematics · AQA · GCSE
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Study Guides
AQA GCSE Mathematics: Ratio, Proportion and Rates of Change (8300)
Percentages, direct and inverse proportion, and compound units – Topic 3 of AQA GCSE Mathematics (8300), the third of six content strands and a common source of exam marks across both Foundation and Higher tiers.
Mathematics · AQA · GCSE
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Circular measure – Study Guide
Radians, arc length, sector area, segments and tangent problems taught step by step with worked examples, for Cambridge 9709 Pure Mathematics 1.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Integration (Pure Mathematics 1) – Study Guide
Study guide to Cambridge 9709 Pure Mathematics 1 section 1.8 Integration: reverse differentiation, definite integrals, areas and volumes, fully worked.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Mechanics – Study Guide
Study guide to Cambridge 9709 Mechanics (Paper 4): forces, kinematics, momentum, Newton's laws, and energy, work and power, with worked examples.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Probability & Statistics 1 – Study Guide
Study guide for Cambridge 9709 Probability & Statistics 1 (Paper 5): data, arrangements, probability, binomial, geometric and normal, with worked examples.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Probability & Statistics 2 – Study Guide
Study guide for Cambridge 9709 Probability & Statistics 2 (Paper 6): Poisson, linear combinations, PDFs, estimation and hypothesis tests, fully worked.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 1 Differentiation – Study Guide
Study guide to Cambridge 9709 Paper 1 differentiation (section 1.7): chords and limits, the chain rule, tangents, rates of change and stationary points.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 1 Trigonometry – Study Guide
Study guide to Cambridge 9709 Pure Mathematics 1 section 1.5 Trigonometry: graphs, exact values, sin⁻¹x, two identities and equations, fully worked.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 Algebra – Study Guide
Study guide to Cambridge 9709 Paper 2 section 2.1 Algebra: the modulus function, polynomial division, and the factor and remainder theorems, fully worked.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 Differentiation – Study Guide
Study guide for Cambridge 9709 Pure Mathematics 2 section 2.4: derivatives of eˣ, ln x and trig, product and quotient rules, parametric and implicit.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 Integration – Study Guide
Study guide for Cambridge 9709 Pure Mathematics 2 section 2.5: integrating eˣ, 1/(ax + b) and trig functions, using identities, and the trapezium rule.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 Logarithms and Exponentials – Study Guide
Study guide for Cambridge 9709 Pure Mathematics 2 section 2.2: log laws, eˣ and ln x, equations in indices, and linear form, with worked examples.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 Numerical Solution of Equations – Study Guide
Study guide for Cambridge 9709 Pure Mathematics 2 section 2.6: locating roots by sign change and using iterative formulae, with worked examples.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 Trigonometry – Study Guide
Study guide for Cambridge 9709 Pure Mathematics 2 section 2.3: sec, cosec, cot, compound and double angles, and R-form, with worked examples.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 3 – Study Guide
Study guide to Cambridge 9709 Pure Mathematics 3 (Paper 3): sections 3.1 to 3.9 taught step by step with a fully worked example for each topic.
Mathematics · Cambridge · A LEVELS
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Study Guides
Cambridge International AS & A Level Mathematics 9709: Series – Study Guide
Study guide to Cambridge 9709 Pure Mathematics 1 section 1.6 Series: binomial expansion, arithmetic and geometric progressions, sum to infinity.
Mathematics · Cambridge · A LEVELS
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Study Guides
Edexcel A Level Mathematics: Pure Mathematics 1 (YMA01)
Algebra and functions, coordinate geometry, trigonometry, differentiation and integration – the full content of Unit P1 for Pearson Edexcel International A Level Mathematics (YMA01).
Mathematics · Pearson Edexcel · A LEVELS
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Study Guides
Edexcel A Level Mathematics: Pure Mathematics 2 (YMA01)
Proof, algebra and functions, coordinate geometry, sequences and series, exponentials and logarithms, trigonometry, differentiation and integration – the full content of Unit P2 for Pearson Edexcel International A Level Mathematics (YMA01).
Mathematics · Pearson Edexcel · A LEVELS
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Study Guides
Edexcel IGCSE Mathematics: Numbers and the Number System (4MA1)
Integers, fractions, decimals, powers and roots, set language, percentages, ratio and proportion, degree of accuracy, standard form and calculator use – the full content of Topic 1 for Pearson Edexcel International GCSE Mathematics A (4MA1).
Mathematics · Pearson Edexcel · IGCSE
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Study Guides
Edexcel International GCSE Mathematics A 4MA1: Geometry and trigonometry – Study Guide
Study guide for Edexcel IGCSE Maths A 4MA1 sections 4.1-4.8: angles, polygons, measures, constructions, circle theorems and trigonometry.
Mathematics · Pearson Edexcel · IGCSE
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Study Guides
Edexcel International GCSE Mathematics A 4MA1: Sequences, functions and graphs – Study Guide
Study guide for Edexcel IGCSE Maths A 4MA1 Topic 3: sequences, functions, straight-line and curved graphs, and calculus, with full worked examples.
Mathematics · Pearson Edexcel · IGCSE
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Study Guides
Functions
Function notation, domain and range, inverse functions and composite functions, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS
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Study Guides
Graphs in Practical Situations
Travel graphs, conversion graphs, and applying rate of change to distance-time and speed-time graphs, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS
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Study Guides
Graphs of Functions and Sketching Curves
Plotting graphs from tables of values, solving equations graphically, exponential growth and decay, and sketching linear, quadratic, cubic, reciprocal and exponential curves, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS
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Study Guides
IB Middle Years Programme Mathematics: Syllabus Guide
The four branches of the IB Middle Years Programme Mathematics framework – numerical and abstract reasoning, thinking with models, spatial reasoning, reasoning with data – and its four assessment criteria, for first assessment 2022.
Mathematics · International Baccalaureate · IB
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Study Guides
IB MYP Mathematics: Reasoning with Data
Statistics, probability and drawing conclusions from data – one of four branches of the IB Middle Years Programme Mathematics framework, tied to the four MYP assessment criteria.
Mathematics · International Baccalaureate · IB
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Study Guides
IB MYP Mathematics: The Four Assessment Criteria in Practice
Worked, criterion-by-criterion guidance on what top-band evidence actually looks like for MYP Mathematics's four assessment criteria – Knowing and understanding, Investigating patterns, Communicating, and Applying mathematics.
Mathematics · International Baccalaureate · IB
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Study Guides
IGCSE Mathematics: Algebra and Graphs (Cambridge 0580)
Algebraic manipulation, equations, inequalities, sequences and graphs – the Core and Extended content of Topic 2 Algebra and graphs for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Coordinate Geometry (Cambridge 0580)
Coordinates, straight-line graphs, gradient, length, midpoint, and parallel and perpendicular lines – the Core and Extended content of Topic 3 Coordinate geometry for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Geometry (Cambridge 0580)
Geometrical vocabulary, constructions, scale drawings, similarity, symmetry, angle properties and circle theorems – the Core and Extended content of Topic 4 Geometry for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Mensuration (Cambridge 0580)
Units of measure, area and perimeter, circles/arcs/sectors, surface area and volume, and compound shapes – the Core and Extended content of Topic 5 Mensuration for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Number (Cambridge 0580)
Types of number, sets, powers and roots, fractions/decimals/percentages, indices, standard form, estimation, ratio, rates and time – the Core content of Topic 1 Number for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Probability (Cambridge 0580)
The probability scale, relative and expected frequency, and combined and conditional events using sample space, Venn and tree diagrams – the Core and Extended content of Topic 8 Probability for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Statistics (Cambridge 0580)
Classifying and interpreting data, averages and range, statistical charts, scatter diagrams, cumulative frequency and histograms – the Core and Extended content of Topic 9 Statistics for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Transformations and Vectors (Cambridge 0580)
Reflection, rotation, enlargement and translation, plus vector notation, magnitude and vector geometry – the Core and Extended content of Topic 7 Transformations and Vectors for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
IGCSE Mathematics: Trigonometry (Cambridge 0580)
Pythagoras' theorem, right-angled triangle trigonometry, exact values, trig functions, the sine and cosine rules and 3D problems – the Core and Extended content of Topic 6 Trigonometry for Cambridge IGCSE Mathematics 0580, 2025-2027 series.
Mathematics · Cambridge · IGCSE
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Study Guides
Indices and Equations
Positive, negative and fractional indices, then linear, fractional, simultaneous and quadratic equations, and changing the subject of a formula, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS
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Study Guides
Inequalities
Representing inequalities on a number line and graphically, solving linear inequalities, and listing the inequalities that define a region, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS
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Study Guides
OCR A Level Mathematics: Statistics (H240)
Statistical sampling, data presentation and interpretation (including bivariate data and correlation), probability, statistical distributions, and statistical hypothesis testing (binomial, normal mean and correlation tests) – the full content of the Statistics strand for OCR A Level Mathematics A (H240).
Mathematics · OCR · A LEVELS
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Study Guides
OCR A-Level Mathematics: Pure Mathematics (H240)
Proof, algebra and functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, integration, numerical methods, and vectors – the full content of Pure Mathematics for OCR A-Level Mathematics A (H240).
Mathematics · OCR · A LEVELS
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Study Guides
OCR GCSE Mathematics: Fractions, Decimals and Percentages (J560)
Fractions, decimal fractions, percentages, and ordering fractions/decimals/percentages – the full content of Topic 2 for OCR GCSE (9-1) Mathematics (J560).
Mathematics · OCR · GCSE
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Study Guides
OCR GCSE Mathematics: Number Operations and Integers (J560)
Calculations with integers, whole number theory, combining arithmetic operations, and inverse operations – the full content of Topic 1 for OCR GCSE Mathematics (J560) – with supporting notes on indices, standard form, rounding and error intervals from Topics 3 and 4.
Mathematics · OCR · GCSE
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Study Guides
OxfordAQA A-Level Mathematics: Bernoulli and Binomial Distributions (9660)
Conditions for a Bernoulli distribution, deriving its mean and variance, and building the binomial distribution as a sum of independent Bernoulli trials – S1.3 of OxfordAQA International AS and A-Level Mathematics (9660).
Mathematics · OxfordAQA · A LEVELS
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Study Guides
OxfordAQA IGCSE Mathematics: Algebra – Notation and Manipulation (9260)
Generalised expressions, formulae, expanding and factorising, index laws and algebraic fractions – sub-topic 3.2.1 Notation and Manipulation, the opening sub-topic of Algebra in OxfordAQA International GCSE Mathematics (9260).
Mathematics · OxfordAQA · IGCSE
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Study Guides
OxfordAQA International A-Level Mathematics: Unit P1 Pure Maths (9660)
Algebra, coordinate geometry, differentiation, integration, and sequences and series – the full content of Unit P1 for OxfordAQA International AS and A-Level Mathematics (9660).
Mathematics · OxfordAQA · A LEVELS
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Study Guides
OxfordAQA International GCSE Mathematics: Number (9260)
Structure and calculation, fractions/decimals and percentages, and ratio and proportion – the full content of Topic 1 Number for OxfordAQA International GCSE Mathematics (9260).
Mathematics · OxfordAQA · IGCSE
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Study Guides
Pearson Edexcel IGCSE Mathematics: Use of Symbols and Algebraic Manipulation (4MA1)
Fractional and negative indices, expanding and factorising, algebraic fractions and completing the square – sub-topics 2.1-2.2 of Topic 2 Equations, Formulae and Identities, Pearson Edexcel International GCSE Mathematics (Specification A, 4MA1), Higher Tier.
Mathematics · Pearson Edexcel · IGCSE
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Study Guides
Pearson Edexcel International GCSE Mathematics A 4MA1: Statistics and probability – Study Guide
Study guide for Edexcel IGCSE Maths 4MA1 topic 6: charts, histograms, cumulative frequency, averages, quartiles, Venn diagrams and tree diagrams.
Mathematics · Pearson Edexcel · IGCSE
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Study Guides
Pearson Edexcel International GCSE Mathematics A 4MA1: Vectors and transformation geometry – Study Guide
Study guide for Edexcel IGCSE Maths 4MA1 topic 5: vectors, column vectors, vector proof, rotations, reflections, translations and enlargements.
Mathematics · Pearson Edexcel · IGCSE
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Study Guides
Sequences and Proportion
Finding the nth term of linear, quadratic, cubic and exponential sequences, and direct and inverse proportion, for Cambridge O Level Mathematics (Syllabus D) 4024.
Mathematics · Cambridge · O LEVELS