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This lesson gives you a complete overview of the AQA GCSE Mathematics specification, including topic weightings, higher-tier-only content, high-frequency topics, the formula sheet, and a comprehensive revision checklist. Use this as your master revision planning tool in the weeks leading up to the exam.
The AQA GCSE Mathematics specification (8300) is divided into six content areas. All six are tested across all three papers — there is no "algebra paper" or "geometry paper".
| Content Area | Topics Covered | Approximate Weighting |
|---|---|---|
| Number | Integers, decimals, fractions, percentages, powers, roots, standard form, bounds | ~15% |
| Algebra | Expressions, equations, inequalities, sequences, graphs, functions, proof | ~30% |
| Ratio, Proportion and Rates of Change | Ratio, direct/inverse proportion, percentages, compound measures, growth/decay | ~20% |
| Geometry and Measures | Properties of shapes, angles, transformations, constructions, Pythagoras, trigonometry, vectors | ~20% |
| Statistics | Data collection, charts, averages, spread, cumulative frequency, box plots | ~15% |
| Probability | Basic probability, combined events, tree diagrams, conditional probability | (Included in Statistics weighting) |
pie title AQA GCSE Maths Specification Weightings
"Number" : 15
"Algebra" : 30
"Ratio, Proportion & Rates of Change" : 20
"Geometry & Measures" : 20
"Statistics & Probability" : 15
Exam Tip: Allocate your revision time roughly in proportion to the weightings. If you have 20 hours of revision, spend approximately 6 hours on algebra, 4 hours on geometry, 4 hours on ratio/proportion, 3 hours on number, and 3 hours on statistics/probability.
The following topics appear ONLY on the Higher tier papers (grades 4–9). If you are sitting Foundation, you do not need to learn these. If you are sitting Higher, these topics often appear in the later, higher-mark questions.
Exam Tip: If you are aiming for grades 7–9, you must be confident with ALL the Higher-only topics above. These topics provide the grade 7+ marks on the papers. If you are aiming for grades 4–6 on the Higher tier, focus on securing the Foundation-level content first, then add Higher topics one by one.
Analysis of AQA GCSE Mathematics past papers reveals that certain topics appear with very high frequency. These topics should be the foundation of your revision.
| Topic | Typical Question Types |
|---|---|
| Percentages | Finding percentages, percentage change, reverse percentages, compound interest |
| Ratio | Sharing in a ratio, simplifying ratios, ratio problems in context |
| Linear equations | Solving equations, forming and solving equations from word problems |
| Area and perimeter | Compound shapes, circles, sectors |
| Angles | Parallel lines, triangles, polygons, circle theorems [H] |
| Probability | Listing outcomes, tree diagrams, two-way tables |
| Averages | Mean from frequency tables, estimated mean from grouped data |
| Straight-line graphs | Plotting, finding gradient, y = mx + c |
| Quadratics | Factorising, solving, sketching [H: completing the square, quadratic formula] |
| Pythagoras' theorem | Finding missing sides, applying in context |
| Topic | Why Students Struggle |
|---|---|
| Standard form | Students forget the rules for multiplication and division |
| Bounds | Students forget that measured values have upper and lower limits |
| Sequences | Students confuse the nth term with the term itself |
| Constructions and loci | Students do not practise with a compass and ruler |
| Transformations | Students mix up the descriptions — especially rotations and reflections |
| Density, speed, pressure | Students forget the triangle formulas or use wrong units |
The highest-tariff questions (4–6 marks) on AQA papers tend to come from a subset of topics. These questions require multi-step reasoning and often combine two or more topics.
| Topic | Typical 5-Mark Question |
|---|---|
| Algebraic proof | "Prove that the sum of three consecutive even numbers is always divisible by 6" |
| Circle theorems [H] | "Find the angle, giving reasons for each step" (3–4 angle facts chained together) |
| Simultaneous equations (one linear, one quadratic) [H] | "Solve algebraically: y = 2x + 1 and x² + y² = 13" |
| Trigonometry with sine/cosine rule [H] | "Find the area of this triangle" or "Find a missing angle in a non-right-angled triangle" |
| Compound shape area/volume problems | "Find the volume of this prism" (with a cross-section that must be calculated first) |
| Probability with tree diagrams | "Work out the probability that..." (with replacement or without replacement) |
| Reverse percentages / compound interest | "After a 20% decrease the price is £340. What was the original price?" |
| Vectors [H] | "Use vectors to prove that PQ is parallel to RS" |
| Iteration [H] | "Show that x = ... has a solution between 3 and 4, then use the iteration formula..." |
| Ratio and proportion in context | "Jenna and Kyle share money in the ratio 3:5. Jenna gives £20 to Kyle. They now have equal amounts. How much did they have originally?" |
Exam Tip: These high-tariff topics should be prioritised in your revision. Practise at least three past paper questions on each one. If you can consistently score 4 or 5 out of 5 on these question types, you are in a strong position.
AQA provides a formula sheet at the front of each exam paper. However, only a limited set of formulas are given. You must memorise the rest.
| Formula | When You Use It |
|---|---|
| Quadratic formula: x = (-b ± sqrt(b² - 4ac)) / 2a | Solving quadratics that do not factorise easily [H] |
| Cosine rule: a² = b² + c² - 2bc cos A | Finding a side in a non-right-angled triangle [H] |
| Sine rule: a/sin A = b/sin B = c/sin C | Finding a side or angle in a non-right-angled triangle [H] |
| Area of a triangle: Area = 1/2 ab sin C | Finding area when you know two sides and the included angle [H] |
| Cone curved surface area: pi r l | Finding the curved surface area of a cone |
| Cone volume: 1/3 pi r² h | Finding the volume of a cone |
| Sphere surface area: 4 pi r² | Finding the surface area of a sphere |
| Sphere volume: 4/3 pi r³ | Finding the volume of a sphere |
| Pyramid volume: 1/3 x base area x h | Finding the volume of a pyramid |
These are NOT on the formula sheet. You must know them by heart.
Number and Algebra:
| Formula | Usage |
|---|---|
| Percentage multiplier: original x (1 + r/100) | Percentage increase |
| Percentage multiplier: original x (1 - r/100) | Percentage decrease |
| Compound interest: P x (1 + r/100)^n | Repeated percentage change [H] |
| Speed = distance / time | Compound measures |
| Density = mass / volume | Compound measures |
| Pressure = force / area | Compound measures |
Geometry:
| Formula | Usage |
|---|---|
| Area of rectangle = length x width | Basic shape |
| Area of triangle = 1/2 x base x height | Basic shape |
| Area of parallelogram = base x height | Basic shape |
| Area of trapezium = 1/2 (a + b) x h | Basic shape |
| Circumference of circle = pi x d = 2 pi r | Circle |
| Area of circle = pi r² | Circle |
| Arc length = (theta/360) x 2 pi r | Sectors [H] |
| Sector area = (theta/360) x pi r² | Sectors [H] |
| Volume of prism = cross-section area x length | Prisms |
| Volume of cylinder = pi r² h | Cylinder |
| Surface area of cylinder = 2 pi r h + 2 pi r² | Cylinder |
| Pythagoras: a² + b² = c² | Right-angled triangles |
| Trigonometry: sin = opp/hyp, cos = adj/hyp, tan = opp/adj | Right-angled triangles |
Statistics and Probability:
| Formula | Usage |
|---|---|
| Mean = sum of values / number of values | Averages |
| P(event) = favourable outcomes / total outcomes | Probability |
| P(A or B) = P(A) + P(B) - P(A and B) | Combined probability [H] |
| P(not A) = 1 - P(A) | Complementary probability |
Exam Tip: Create flashcards for every formula you must memorise. Test yourself daily. In the exam, the formula sheet is provided for the complex formulas — but you still need to know WHICH formula to use and WHEN. Understanding the formula is just as important as remembering it.
Use this checklist to track your revision progress. For each topic, rate your confidence: Green (confident), Amber (need more practice), or Red (need to learn).
| Topic | F/H | Confidence |
|---|---|---|
| Place value and ordering | F + H | |
| Addition, subtraction, multiplication, division | F + H | |
| Factors, multiples, primes | F + H | |
| HCF and LCM | F + H | |
| Powers and roots | F + H | |
| Standard form | F + H | |
| Fractions: four operations | F + H | |
| Decimals: four operations | F + H | |
| Percentages: finding and comparing | F + H | |
| Rounding and estimation | F + H | |
| Surds: simplifying and rationalising | H only | |
| Upper and lower bounds | H only | |
| Fractional and negative indices | H only |
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