Study guides

G: Differentiation: Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points, points of inflection. Identify where functions are increasing or decreasing.

AQA·A-Level

7357

G: Differentiation: Construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand).

AQA·A-Level

7357

G: Differentiation: Differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions.

AQA·A-Level

7357

G: Differentiation: Differentiate xⁿ, for rational values of n, and related constant multiples, sums and differences. Differentiate e^(kx) and a^(kx), sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x as 1/x.

AQA·A-Level

7357

G: Differentiation: Understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles for small positive integer powers of x and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection.

AQA·A-Level

7357

Galaxies

OCR·GCSE

Unlock top marks in your OCR GCSE Physics exam by mastering Galaxies (Topic 8.7). This guide breaks down the vastness of space into bite-sized, exam-focused chunks, from the structure of our Milky Way to the mind-bending evidence for the Big Bang.

Gas Pressure

OCR·GCSE

This guide provides a comprehensive, exam-focused breakdown of Gas Pressure (OCR GCSE Physics 6.7). It covers the core particle model, Boyle's Law, and Higher Tier concepts like work done on a gas, all reinforced with multi-modal assets to secure top marks.

Gene Technologies

OCR·A-Level

Master the complex interactions of life from DNA to entire ecosystems in Module 6. This crucial topic connects inheritance patterns with evolutionary pressures and energy flow, testing your ability to apply mathematical models to biological systems.

General vocabulary: Other expressions

AQA·GCSE

8662

This topic covers essential general vocabulary, including quantity words, degree adverbs, and approximation phrases. These 'other expressions' are crucial connective tissue that examiners look for across all four skills (Listening, Speaking, Reading, and Writing) to award higher grades.

General vocabulary: Shape

AQA·GCSE

8662

Mastering shape vocabulary ('Formen') is a secret weapon for GCSE German, helping you pick up crucial marks across all four skills. This guide covers essential nouns and adjectives, vital grammar like adjective endings, and how to use this vocabulary to ace the speaking photo card and extended writing tasks.

Geographical investigations − fieldwork: Investigating human environments (central/inner urban area OR rural settlements)

Pearson Edexcel·GCSE

Pearson-GCSE-Geography

Master the Geographical Enquiry Process for human environments, covering both urban and rural fieldwork. This guide ensures you know exactly how to select, justify, and evaluate your data collection methods to secure top marks.

Geographical investigations − fieldwork: Investigating physical environments (river landscapes OR coastal landscapes)

Pearson Edexcel·GCSE

Pearson-GCSE-Geography

Master the GCSE Geography fieldwork investigation for physical environments. This guide breaks down the geographical enquiry cycle for river and coastal landscapes, showing you exactly how to collect, process, and evaluate data to secure top marks.

Geometry and measures

Eduqas·GCSE

WJEC-GCSE-Mathematics

Geometry and Measures is a fundamental pillar of GCSE Mathematics, testing your ability to understand spatial relationships, apply formulas, and construct logical geometric proofs. Mastering this topic is crucial, as it often features in high-tariff questions that separate the top grades.

Geometry and measures

Pearson Edexcel·GCSE

601/4700/3

Geometry and Measures forms the foundation of spatial reasoning in GCSE Mathematics. Mastering angle rules, polygons, and parallel lines guarantees you can secure highly predictable marks in both Foundation and Higher tier papers.

Geometry and measures - Mensuration and calculation: apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures (Higher tier)

Pearson Edexcel·GCSE

1MA1

Why does doubling a model’s height require four times the paint but eight times the filling material? Master congruence proofs and the k, k², k³ relationships, then use roots to tackle the reverse-scaling questions that distinguish strong Higher-tier answers.

Geometry and measures - Mensuration and calculation: apply the concepts of congruence and similarity, including the relationships between lengths, in similar figures (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: calculate arc lengths, angles and areas of sectors of circles

Pearson Edexcel·GCSE

1MA1

One fraction unlocks the curved edge, shaded area and missing angle of any circle sector. Learn how to turn θ/360 into reliable Edexcel GCSE marks, avoid the perimeter trap and test your recall with worked questions, diagrams and a ten-minute tutor podcast.

Geometry and measures - Mensuration and calculation: know and apply Area = ½ab sin C to calculate the area, sides or angles of any triangle (Higher tier only)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: know and apply the sine rule a/sin A = b/sin B = c/sin C , and cosine rule a² = b² + c² – 2bc cos A, to find unknown lengths and angles (Higher tier only)

Pearson Edexcel·GCSE

1MA1

When a triangle has no right angle, the sine and cosine rules turn unfamiliar diagrams into solvable calculations. Learn to choose the right rule, show mark-worthy working and handle obtuse angles, then test yourself with worked examples, original Edexcel-style questions and a ten-minute tutor podcast.

Geometry and measures - Mensuration and calculation: know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°

Pearson Edexcel·GCSE

1MA1

Two triangles unlock the exact sine, cosine and tangent values that Edexcel GCSE candidates must recall without a calculator. Learn how to rebuild the table, use it in exact calculations, and avoid the swaps and premature rounding that cost marks. Foundation recall is clearly separated from Higher surd algebra and extensions.

Geometry and measures - Mensuration and calculation: know the formulae for: Pythagoras’ theorem a² + b² = c² , and the trigonometric ratios, sin θ = opposite/hypotenuse , cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent ; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures (Higher tier)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: know the formulae for: Pythagoras’ theorem a² + b² = c² , and the trigonometric ratios, sin θ = opposite/hypotenuse , cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent ; apply them to find angles and lengths in right-angled triangles in two-dimensional figures (Foundation tier)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: know the formulae: circumference of a circle = 2πr = πd , area of a circle = πr² ; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Mensuration and calculation: use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Properties and constructions: apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results (Higher tier only)

Pearson Edexcel·GCSE

1MA1

A single radius or chord can unlock a whole circle-theorem question. Learn to calculate angles and lengths, give the precise reasons examiners expect, and build Higher-tier proofs rather than guess from a diagram.

Geometry and measures - Properties and constructions: apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Properties and constructions: apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

Pearson Edexcel·GCSE

1MA1

Geometry and measures - Properties and constructions: construct and interpret plans and elevations of 3D shapes

Pearson Edexcel·GCSE

1MA1

Turn a 3D solid into three accurate flat views, then use those views to recover dimensions, recognise shapes and count cubes. This GCSE guide shows candidates how to secure drawing and calculation marks without confusing perspective, footprints and volume. Download the [complete JSON study guide](/home/ubuntu/plans_elevations_guide/plans_and_elevations_study_guide.json) for all explanations, answers and the full podcast script.