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OCR GCSE (9–1) Mathematics (J560)

Spec code J560 · v2015 · valid from 2015

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6 domains · 97 topics

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N

Number

16 topics
  1. N1Order positive and negative integers, decimals and fractions
  2. N2Apply the four operations to integers, decimals and simple fractions
  3. N3Recognise and use inverse operations and relationships between operations
  4. N4Use vocabulary of primes, factors, multiples; HCF and LCM
  5. N5Apply systematic listing strategies and the product rule for counting
  6. N6Use positive integer powers and associated real roots (square, cube, higher)
  7. N7Calculate with roots and integer indices; fractional indices
  8. N8Calculate exactly with fractions, multiples of π, and surds
  9. N9Calculate with and interpret standard form A × 10ⁿ
  10. N10Convert terminating decimals to fractions; recurring decimals to fractions
  11. N11Identify and work with fractions in ratio problems
  12. N12Interpret fractions and percentages as operators
  13. N13Use standard units of mass, length, time, money and other measures
  14. N14Estimate answers; check using approximation and estimation
  15. N15Round numbers and measures to an appropriate degree of accuracy
  16. N16Apply and interpret limits of accuracy including upper and lower bounds
A

Algebra

25 topics
  1. A1Use and interpret algebraic notation
  2. A2Substitute numerical values into formulae and expressions
  3. A3Vocabulary of expressions, equations, formulae, inequalities, terms, factors
  4. A4Simplify expressions: collect like terms, multiply over brackets, factorise; expand binomials; factor quadratics
  5. A5Use standard mathematical formulae; rearrange to change the subject
  6. A6Distinguish equations, identities, formulae; argue with algebraic equivalence
  7. A7Interpret expressions as functions; inverse and composite functions
  8. A8Work with coordinates in all four quadrants
  9. A9Plot linear graphs; y = mx + c; parallel and perpendicular lines
  10. A10Identify and interpret gradients and intercepts of linear functions
  11. A11Identify roots, intercepts, turning points of quadratics; complete the square
  12. A12Recognise and sketch linear, quadratic, cubic, reciprocal, exponential and trig graphs
  13. A13Sketch translations and reflections of a given function
  14. A14Plot and interpret real-context graphs; kinematic problems
  15. A15Calculate or estimate gradients and areas under graphs; interpret in context
  16. A16Recognise circle equations centred at origin; find tangent equations
  17. A17Solve linear equations algebraically and graphically
  18. A18Solve quadratics by factorising; completing the square; quadratic formula
  19. A19Solve simultaneous equations: linear/linear; linear/quadratic
  20. A20Find approximate solutions to equations using iteration
  21. A21Translate situations into algebraic expressions; derive and solve in context
  22. A22Solve linear inequalities; represent solutions on number lines and graphs
  23. A23Generate sequences from term-to-term and position-to-term rules
  24. A24Recognise sequences: triangular, square, cube, Fibonacci, arithmetic, geometric, quadratic
  25. A25Deduce nth term for linear and quadratic sequences
R

Ratio, proportion and rates of change

16 topics
  1. R1Convert between related standard units and compound units
  2. R2Use scale factors, scale diagrams and maps
  3. R3Express one quantity as a fraction of another
  4. R4Use ratio notation including reduction to simplest form
  5. R5Divide quantities into ratio parts; apply ratio to real contexts
  6. R6Express a multiplicative relationship as ratio or fraction
  7. R7Understand and use proportion as equality of ratios
  8. R8Relate ratios to fractions and to linear functions
  9. R9Percentage change, reverse percentages, problem-solving
  10. R10Solve problems involving direct and inverse proportion
  11. R11Compound units including speed, density, pressure
  12. R12Compare dimensions using ratio; similarity links
  13. R13Inverse proportionality; construct equations describing proportion
  14. R14Interpret gradient as rate of change; proportion graphs
  15. R15Interpret gradient at a point on a curve as instantaneous rate of change
  16. R16Growth and decay; compound interest; iterative processes
G

Geometry and measures

25 topics
  1. G1Conventional terms and notations: points, lines, vertices, planes
  2. G2Standard ruler-and-compass constructions
  3. G3Properties of angles at a point; angles on a straight line; in parallel lines
  4. G4Properties of special quadrilaterals
  5. G5Triangle congruence: SSS, SAS, ASA, RHS
  6. G6Apply angle facts, congruence, similarity and quadrilateral properties
  7. G7Identify and construct congruent and similar shapes; fractional and negative scale factors
  8. G8Changes and invariance under rotation, reflection, translation, enlargement combinations
  9. G9Circle definitions and properties; tangent, arc, sector, segment
  10. G10Apply and prove standard circle theorems
  11. G11Solve geometric problems on coordinate axes
  12. G12Properties of faces, surfaces, edges and vertices of 3D solids
  13. G13Interpret and construct plans and elevations of 3D shapes
  14. G14Standard units of measure: length, area, volume, capacity, mass, time, money
  15. G15Measure line segments and angles; interpret maps and scale drawings
  16. G16Formulae for area of triangles, parallelograms, trapezia
  17. G17Circumference and area of a circle; surface area / volume of spheres, pyramids, cones
  18. G18Arc lengths, angles and areas of sectors of circles
  19. G19Congruence and similarity; areas and volumes in similar figures
  20. G20Pythagoras and trigonometric ratios; extension to general triangles in 3D
  21. G21Exact values of sin θ and cos θ for 0°, 30°, 45°, 60°, 90°
  22. G22Sine rule and cosine rule for unknown lengths and angles
  23. G23Area = ½ab sin C for area, sides or angles of a triangle
  24. G24Describe translations as 2D vectors
  25. G25Vector addition, subtraction, scalar multiplication; geometric arguments and proofs
P

Probability

9 topics
  1. P1Record, describe and analyse outcome frequencies; tables and frequency trees
  2. P2Apply randomness, fairness and equally likely events to expected outcomes
  3. P3Relative expected frequencies vs theoretical probability; 0–1 scale
  4. P4Probabilities of an exhaustive set of outcomes sum to 1
  5. P5Empirical samples tend to theoretical distributions with sample size
  6. P6Enumerate sets and combinations: tables, grids, Venn diagrams
  7. P7Construct possibility spaces for single and combined experiments
  8. P8Probability of independent and dependent combined events; tree diagrams
  9. P9Conditional probabilities via two-way tables, trees, Venn diagrams
S

Statistics

6 topics
  1. S1Infer properties of populations from samples; sampling limitations
  2. S2Tables, charts and diagrams: frequency tables, bar charts, pie charts, pictograms
  3. S3Diagrams for grouped data: histograms (equal/unequal class widths) and cumulative frequency graphs
  4. S4Compare distributions; measures of central tendency and spread
  5. S5Apply statistics to describe a population
  6. S6Interpret scatter graphs; correlation and causation