Mathematics: Cambridge 2027 syllabus mapping

Cambridge International AS & A Level 9709 · Examination year 2027

AI-assisted conceptual placements, not official Cambridge endorsement or independent teacher approval. A linked practice question does not establish complete teaching, practical competence or exam readiness.

Current question placements: 83 / 83
Direct conceptual matches: 79
Partial matches: 1
Enrichment: 3
Placements needing review: 0
Inventory entries without linked practice: 37

Inventory scope: individual learning outcomes. Source inventory: recorded in full at this scope. Independent teacher approval: pending.

Official references

Cambridge International AS & A Level Mathematics 9709: syllabus for 2026 and 2027 · Version 4, December 2025 · checked 2026-10-24
Cambridge International AS & A Level Mathematics 9709: 2026-2027 syllabus update · December 2025 update, version 4 table (intro retains stale version 3 wording) · checked 2026-10-24

Practice by syllabus reference

both · Paper 1: Pure Mathematics 1; compulsory AS/A (35 entries)

Mathematics 9709: both · Paper 1: Pure Mathematics 1; compulsory AS/A
Reference	Concept	Linked practice
1.1 Quadratics; candidate bullet 1 (bullet ordinal, not an official subcode)	Complete the square and use vertex form	Algebra Graphs And Numerics, question 1 (direct)
1.1 Quadratics; candidate bullet 2 (bullet ordinal, not an official subcode)	Use discriminants and identify repeated roots	Algebra Graphs And Numerics, question 1 (direct)
1.1 Quadratics; candidate bullet 3 (bullet ordinal, not an official subcode)	Solve quadratic equations and inequalities	Algebra Graphs And Numerics, question 1 (direct)
1.1 Quadratics; candidate bullet 4 (bullet ordinal, not an official subcode)	Solve a linear/quadratic simultaneous pair	Algebra Graphs And Numerics, question 1 (direct)
1.1 Quadratics; candidate bullet 5 (bullet ordinal, not an official subcode)	Recognise quadratic substitutions	Algebra and functions, question 6 (direct)
1.2 Functions; candidate bullet 1 (bullet ordinal, not an official subcode)	Function, domain, range, inverse and composition terminology	Algebra and functions, question 2 (direct)
1.2 Functions; candidate bullet 2 (bullet ordinal, not an official subcode)	Find simple ranges and admissible compositions	Algebra and functions, question 2 (direct) Algebra and functions, question 4 (direct)
1.2 Functions; candidate bullet 3 (bullet ordinal, not an official subcode)	Test injectivity and invert simple one-one functions	Algebra and functions, question 4 (direct) Algebra Graphs And Numerics, question 5 (direct)
1.2 Functions; candidate bullet 4 (bullet ordinal, not an official subcode)	Reflect inverse graphs across y=x	Algebra Graphs And Numerics, question 5 (direct)
1.2 Functions; candidate bullet 5 (bullet ordinal, not an official subcode)	Translate, reflect and scale function graphs	Algebra and functions, question 5 (direct)
1.3 Coordinate geometry; candidate bullet 1 (bullet ordinal, not an official subcode)	Determine a straight-line equation	No linked practice
1.3 Coordinate geometry; candidate bullet 2 (bullet ordinal, not an official subcode)	Use line forms, distances, slopes and intersections	No linked practice
1.3 Coordinate geometry; candidate bullet 3 (bullet ordinal, not an official subcode)	Identify circles in centre-radius or expanded form	Vectors and coordinate geometry, question 1 (direct) Vectors and coordinate geometry, question 5 (direct)
1.3 Coordinate geometry; candidate bullet 4 (bullet ordinal, not an official subcode)	Solve line/circle geometry algebraically; no implicit calculus	Vectors and coordinate geometry, question 1 (direct) Vectors and coordinate geometry, question 5 (direct)
1.3 Coordinate geometry; candidate bullet 5 (bullet ordinal, not an official subcode)	Relate graph intersections to equation solutions	Vectors and coordinate geometry, question 5 (direct) Algebra Graphs And Numerics, question 1 (direct)
1.4 Circular measure; candidate bullet 1 (bullet ordinal, not an official subcode)	Convert radians and degrees	No linked practice
1.4 Circular measure; candidate bullet 2 (bullet ordinal, not an official subcode)	Use radian arc length and sector area	Trigonometry, question 5 (direct)
1.5 Trigonometry; candidate bullet 1 (bullet ordinal, not an official subcode)	Sketch sine, cosine and tangent transformations	Algebra Graphs And Numerics, question 5 (direct)
1.5 Trigonometry; candidate bullet 2 (bullet ordinal, not an official subcode)	Use standard exact-angle trigonometric values	Trigonometry, question 1 (direct)
1.5 Trigonometry; candidate bullet 3 (bullet ordinal, not an official subcode)	Use principal inverse-trigonometric notation	No linked practice
1.5 Trigonometry; candidate bullet 4 (bullet ordinal, not an official subcode)	Use tangent-ratio and Pythagorean identities	Trigonometry, question 4 (direct)
1.5 Trigonometry; candidate bullet 5 (bullet ordinal, not an official subcode)	Solve trigonometric equations in specified intervals	Trigonometry, question 1 (direct) Trigonometry, question 4 (direct)
1.6 Series; candidate bullet 1 (bullet ordinal, not an official subcode)	Expand positive integer binomials	Algebra Graphs And Numerics, question 2 (direct)
1.6 Series; candidate bullet 2 (bullet ordinal, not an official subcode)	Identify arithmetic and geometric progressions	Sequences, series and the binomial expansion, question 1 (direct)
1.6 Series; candidate bullet 3 (bullet ordinal, not an official subcode)	Use progression nth-term and finite-sum formulae	Sequences, series and the binomial expansion, question 1 (direct) Sequences, series and the binomial expansion, question 2 (direct) Sequences, series and the binomial expansion, question 3 (direct) Sequences, series and the binomial expansion, question 5 (direct)
1.6 Series; candidate bullet 4 (bullet ordinal, not an official subcode)	Check geometric convergence and sum to infinity	Sequences, series and the binomial expansion, question 3 (direct)
1.7 Differentiation; candidate bullet 1 (bullet ordinal, not an official subcode)	Interpret derivative as limiting chord gradient	No linked practice
1.7 Differentiation; candidate bullet 2 (bullet ordinal, not an official subcode)	Differentiate rational powers and chain-rule composites	Calculus, logarithms and probability, question 1 (direct) Differentiation and its applications, question 2 (direct) Differentiation and its applications, question 5 (direct) Differentiation and its applications, question 6 (direct) Statistics and modelling: decisions and limits, question 6 (direct)
1.7 Differentiation; candidate bullet 3 (bullet ordinal, not an official subcode)	Apply gradients, normals and connected rates	Differentiation and its applications, question 2 (direct) Differentiation and its applications, question 6 (direct)
1.7 Differentiation; candidate bullet 4 (bullet ordinal, not an official subcode)	Find and classify stationary points; no inflexion requirement	Calculus, logarithms and probability, question 1 (direct) Differentiation and its applications, question 3 (direct) Differentiation and its applications, question 5 (direct) Trigonometry, question 5 (direct) Statistics and modelling: decisions and limits, question 5 (direct) Statistics and modelling: decisions and limits, question 6 (direct)
1.8 Integration; candidate bullet 1 (bullet ordinal, not an official subcode)	Reverse differentiation of rational powers and linear composites	No linked practice
1.8 Integration; candidate bullet 2 (bullet ordinal, not an official subcode)	Determine integration constants	No linked practice
1.8 Integration; candidate bullet 3 (bullet ordinal, not an official subcode)	Evaluate definite integrals, including simple improper cases	Integration and mathematical modelling, question 1 (direct) Integration techniques, question 2 (direct)
1.8 Integration; candidate bullet 4, area subitem (bullet ordinal, not an official subcode)	Find bounded planar areas	Integration and mathematical modelling, question 1 (direct) Integration techniques, question 6 (direct)
1.8 Integration; candidate bullet 4, volume subitem (bullet ordinal, not an official subcode)	Find volumes of revolution about coordinate axes	Integration techniques, question 6 (direct)

AS · Paper 2: Pure Mathematics 2; AS pure-only route 1+2, no carry-forward to A (21 entries)

Mathematics 9709: AS · Paper 2: Pure Mathematics 2; AS pure-only route 1+2, no carry-forward to A
Reference	Concept	Linked practice
2.1 Algebra; candidate bullet 1 (bullet ordinal, not an official subcode)	Use linear modulus graphs, equations and inequalities	Algebra and functions, question 1 (direct)
2.1 Algebra; candidate bullet 2 (bullet ordinal, not an official subcode)	Divide polynomials of degree at most four	Algebra Graphs And Numerics, question 2 (direct)
2.1 Algebra; candidate bullet 3 (bullet ordinal, not an official subcode)	Use factor and remainder theorems	Algebra Graphs And Numerics, question 2 (direct)
2.2 Logarithmic and exponential functions; candidate bullet 1 (bullet ordinal, not an official subcode)	Use index and logarithm laws; no change-of-base requirement	Calculus, logarithms and probability, question 2 (direct) Algebra Graphs And Numerics, question 3 (direct)
2.2 Logarithmic and exponential functions; candidate bullet 2 (bullet ordinal, not an official subcode)	Use exponential/logarithm inverses and graphs	No linked practice
2.2 Logarithmic and exponential functions; candidate bullet 3 (bullet ordinal, not an official subcode)	Solve exponential equations and inequalities using logarithms	No linked practice
2.2 Logarithmic and exponential functions; candidate bullet 4 (bullet ordinal, not an official subcode)	Linearise power/exponential relationships and infer constants	Algebra Graphs And Numerics, question 3 (direct)
2.3 Trigonometry; candidate bullet 1 (bullet ordinal, not an official subcode)	Use all six trigonometric functions and graphs	Trigonometry, question 2 (direct)
2.3 Trigonometry; candidate bullet 2, reciprocal subitem (bullet ordinal, not an official subcode)	Use squared reciprocal-function identities	No linked practice
2.3 Trigonometry; candidate bullet 2, compound subitem (bullet ordinal, not an official subcode)	Use compound-angle expansions	No linked practice
2.3 Trigonometry; candidate bullet 2, double subitem (bullet ordinal, not an official subcode)	Use double-angle formulae	Trigonometry, question 2 (direct) Trigonometry, question 6 (direct)
2.3 Trigonometry; candidate bullet 2, harmonic subitem (bullet ordinal, not an official subcode)	Rewrite a sin(theta)+b cos(theta) in harmonic form	Trigonometry, question 3 (direct)
2.4 Differentiation; candidate bullet 1 (bullet ordinal, not an official subcode)	Differentiate exponential, logarithmic and trigonometric composites	Differentiation and its applications, question 1 (direct)
2.4 Differentiation; candidate bullet 2 (bullet ordinal, not an official subcode)	Apply product and quotient differentiation	Differentiation and its applications, question 1 (direct) Differentiation and its applications, question 3 (direct) Parametric calculus and differential models, question 2 (direct)
2.4 Differentiation; candidate bullet 3 (bullet ordinal, not an official subcode)	Differentiate implicit/parametric curves and find tangents	Differentiation and its applications, question 4 (direct) Vectors and coordinate geometry, question 6 (direct) Parametric calculus and differential models, question 1 (direct)
2.5 Integration; candidate bullet 1 (bullet ordinal, not an official subcode)	Integrate linear exponential, reciprocal and trigonometric composites	Integration techniques, question 1 (direct) Integration techniques, question 2 (direct) Parametric calculus and differential models, question 6 (direct)
2.5 Integration; candidate bullet 2 (bullet ordinal, not an official subcode)	Use trigonometric identities when integrating	No linked practice
2.5 Integration; candidate bullet 3 (bullet ordinal, not an official subcode)	Apply trapezium estimates and determine error direction	Parametric calculus and differential models, question 6 (direct)
2.6 Numerical solution of equations; candidate bullet 1 (bullet ordinal, not an official subcode)	Bracket roots graphically or with sign changes	Algebra Graphs And Numerics, question 4 (direct)
2.6 Numerical solution of equations; candidate bullet 2 (bullet ordinal, not an official subcode)	Interpret convergent approximation sequences	Algebra Graphs And Numerics, question 4 (direct)
2.6 Numerical solution of equations; candidate bullet 3 (bullet ordinal, not an official subcode)	Use given fixed-point iterations to prescribed accuracy	Algebra Graphs And Numerics, question 4 (direct)

A · Paper 3: Pure Mathematics 3; compulsory A (44 entries)

Mathematics 9709: A · Paper 3: Pure Mathematics 3; compulsory A
Reference	Concept	Linked practice
3.1 Algebra; candidate bullet 1 (bullet ordinal, not an official subcode)	Use linear modulus graphs, equations and inequalities	Algebra and functions, question 1 (direct)
3.1 Algebra; candidate bullet 2 (bullet ordinal, not an official subcode)	Divide polynomials of degree at most four	Algebra Graphs And Numerics, question 2 (direct)
3.1 Algebra; candidate bullet 3 (bullet ordinal, not an official subcode)	Use factor and remainder theorems	Algebra Graphs And Numerics, question 2 (direct)
3.1 Algebra; candidate bullet 4 (bullet ordinal, not an official subcode)	Decompose permitted linear/repeated/irreducible-quadratic fractions	Integration and mathematical modelling, question 3 (direct) Algebra and functions, question 3 (direct) Integration techniques, question 5 (direct)
3.1 Algebra; candidate bullet 5 (bullet ordinal, not an official subcode)	Expand rational-power binomials within their validity range	Sequences, series and the binomial expansion, question 4 (direct) Sequences, series and the binomial expansion, question 6 (direct)
3.2 Logarithmic and exponential functions; candidate bullet 1 (bullet ordinal, not an official subcode)	Use index and logarithm laws; no change-of-base requirement	Calculus, logarithms and probability, question 2 (direct) Algebra Graphs And Numerics, question 3 (direct)
3.2 Logarithmic and exponential functions; candidate bullet 2 (bullet ordinal, not an official subcode)	Use exponential/logarithm inverses and graphs	No linked practice
3.2 Logarithmic and exponential functions; candidate bullet 3 (bullet ordinal, not an official subcode)	Solve exponential equations and inequalities using logarithms	No linked practice
3.2 Logarithmic and exponential functions; candidate bullet 4 (bullet ordinal, not an official subcode)	Linearise power/exponential relationships and infer constants	Algebra Graphs And Numerics, question 3 (direct)
3.3 Trigonometry; candidate bullet 1 (bullet ordinal, not an official subcode)	Use all six trigonometric functions and graphs	Trigonometry, question 2 (direct)
3.3 Trigonometry; candidate bullet 2, reciprocal subitem (bullet ordinal, not an official subcode)	Use squared reciprocal-function identities	No linked practice
3.3 Trigonometry; candidate bullet 2, compound subitem (bullet ordinal, not an official subcode)	Use compound-angle expansions	No linked practice
3.3 Trigonometry; candidate bullet 2, double subitem (bullet ordinal, not an official subcode)	Use double-angle formulae	Trigonometry, question 2 (direct) Trigonometry, question 6 (direct)
3.3 Trigonometry; candidate bullet 2, harmonic subitem (bullet ordinal, not an official subcode)	Rewrite a sin(theta)+b cos(theta) in harmonic form	Trigonometry, question 3 (direct)
3.4 Differentiation; candidate bullet 1 (bullet ordinal, not an official subcode)	Differentiate elementary composites including arctan; not arcsin/arccos	Differentiation and its applications, question 1 (direct)
3.4 Differentiation; candidate bullet 2 (bullet ordinal, not an official subcode)	Apply product and quotient differentiation	Differentiation and its applications, question 1 (direct) Differentiation and its applications, question 3 (direct) Parametric calculus and differential models, question 2 (direct)
3.4 Differentiation; candidate bullet 3 (bullet ordinal, not an official subcode)	Differentiate implicit/parametric curves and find tangents	Differentiation and its applications, question 4 (direct) Vectors and coordinate geometry, question 6 (direct) Parametric calculus and differential models, question 1 (direct) Parametric calculus and differential models, question 3 (partial)
3.5 Integration; candidate bullet 1 (bullet ordinal, not an official subcode)	Integrate elementary linear composites and reciprocal quadratics	Integration techniques, question 1 (direct) Integration techniques, question 2 (direct)
3.5 Integration; candidate bullet 2 (bullet ordinal, not an official subcode)	Use trigonometric identities when integrating	No linked practice
3.5 Integration; candidate bullet 3 (bullet ordinal, not an official subcode)	Integrate permitted partial-fraction decompositions	Integration techniques, question 5 (direct)
3.5 Integration; candidate bullet 4 (bullet ordinal, not an official subcode)	Recognise logarithmic derivative integrands	Parametric calculus and differential models, question 4 (direct)
3.5 Integration; candidate bullet 5 (bullet ordinal, not an official subcode)	Integrate products by parts	Integration techniques, question 4 (direct) Parametric calculus and differential models, question 2 (direct)
3.5 Integration; candidate bullet 6 (bullet ordinal, not an official subcode)	Evaluate integrals with a given substitution	Integration techniques, question 3 (direct) Parametric calculus and differential models, question 4 (direct)
3.6 Numerical solution of equations; candidate bullet 1 (bullet ordinal, not an official subcode)	Bracket roots graphically or with sign changes	Algebra Graphs And Numerics, question 4 (direct)
3.6 Numerical solution of equations; candidate bullet 2 (bullet ordinal, not an official subcode)	Interpret convergent approximation sequences	Algebra Graphs And Numerics, question 4 (direct)
3.6 Numerical solution of equations; candidate bullet 3 (bullet ordinal, not an official subcode)	Use given fixed-point iterations to prescribed accuracy	Algebra Graphs And Numerics, question 4 (direct)
3.7 Vectors; candidate bullet 1 (bullet ordinal, not an official subcode)	Use standard two/three-dimensional vector notation	No linked practice
3.7 Vectors; candidate bullet 2 (bullet ordinal, not an official subcode)	Add, subtract and scale vectors geometrically	Vectors and coordinate geometry, question 3 (direct)
3.7 Vectors; candidate bullet 3 (bullet ordinal, not an official subcode)	Find magnitudes and use unit/position/displacement vectors	Vectors and coordinate geometry, question 2 (direct)
3.7 Vectors; candidate bullet 4 (bullet ordinal, not an official subcode)	Construct and interpret vector line equations	Vectors and coordinate geometry, question 3 (direct)
3.7 Vectors; candidate bullet 5 (bullet ordinal, not an official subcode)	Classify pairs of lines and find intersections	Vectors and coordinate geometry, question 4 (direct)
3.7 Vectors; candidate bullet 6 (bullet ordinal, not an official subcode)	Use scalar products for angles and line/point geometry	Vectors and coordinate geometry, question 2 (direct)
3.8 Differential equations; candidate bullet 1 (bullet ordinal, not an official subcode)	Translate a rate model into a differential equation	No linked practice
3.8 Differential equations; candidate bullet 2 (bullet ordinal, not an official subcode)	Solve separable first-order equations	Integration and mathematical modelling, question 3 (direct) Parametric calculus and differential models, question 5 (direct)
3.8 Differential equations; candidate bullet 3 (bullet ordinal, not an official subcode)	Apply initial conditions to choose a solution	Integration and mathematical modelling, question 3 (direct) Parametric calculus and differential models, question 5 (direct)
3.8 Differential equations; candidate bullet 4 (bullet ordinal, not an official subcode)	Interpret a differential-equation model solution	Integration and mathematical modelling, question 3 (direct) Statistics and modelling: decisions and limits, question 5 (direct)
3.9 Complex numbers; candidate bullet 1 (bullet ordinal, not an official subcode)	Use Cartesian components, modulus, argument and conjugation	No linked practice
3.9 Complex numbers; candidate bullet 2 (bullet ordinal, not an official subcode)	Perform Cartesian complex arithmetic	No linked practice
3.9 Complex numbers; candidate bullet 3 (bullet ordinal, not an official subcode)	Use conjugate roots for real-coefficient polynomials	No linked practice
3.9 Complex numbers; candidate bullet 4 (bullet ordinal, not an official subcode)	Represent numbers on Argand diagrams	No linked practice
3.9 Complex numbers; candidate bullet 5 (bullet ordinal, not an official subcode)	Multiply and divide using polar/exponential forms	No linked practice
3.9 Complex numbers; candidate bullet 6 (bullet ordinal, not an official subcode)	Find complex square roots in Cartesian form	No linked practice
3.9 Complex numbers; candidate bullet 7 (bullet ordinal, not an official subcode)	Interpret complex arithmetic geometrically	No linked practice
3.9 Complex numbers; candidate bullet 8 (bullet ordinal, not an official subcode)	Draw simple complex equations and inequalities as loci	No linked practice

both · Paper 4: Mechanics; AS 1+4; A 1+3+4+5, not with Paper 6 (24 entries)

Mathematics 9709: both · Paper 4: Mechanics; AS 1+4; A 1+3+4+5, not with Paper 6
Reference	Concept	Linked practice
4.1 Forces and equilibrium; candidate bullet 1 (bullet ordinal, not an official subcode)	Identify forces and draw force diagrams	Forces Momentum And Energy, question 1 (direct)
4.1 Forces and equilibrium; candidate bullet 2 (bullet ordinal, not an official subcode)	Resolve forces and compute resultants	Forces Momentum And Energy, question 1 (direct)
4.1 Forces and equilibrium; candidate bullet 3 (bullet ordinal, not an official subcode)	Use zero resultant for particle equilibrium	Forces Momentum And Energy, question 1 (direct)
4.1 Forces and equilibrium; candidate bullet 4 (bullet ordinal, not an official subcode)	Separate normal contact and friction components	Forces Momentum And Energy, question 1 (direct)
4.1 Forces and equilibrium; candidate bullet 5 (bullet ordinal, not an official subcode)	Use smooth-contact assumptions and limitations	No linked practice
4.1 Forces and equilibrium; candidate bullet 6 (bullet ordinal, not an official subcode)	Use limiting friction and F<=mu*R	Forces Momentum And Energy, question 1 (direct)
4.1 Forces and equilibrium; candidate bullet 7 (bullet ordinal, not an official subcode)	Apply Newton's third law	No linked practice
4.2 Kinematics of motion in a straight line; candidate bullet 1 (bullet ordinal, not an official subcode)	Distinguish signed motion from distance and speed	Integration and mathematical modelling, question 2 (direct) Mechanics: motion, forces and moments, question 6 (direct)
4.2 Kinematics of motion in a straight line; candidate bullet 2, area subitem (bullet ordinal, not an official subcode)	Interpret velocity-time area as displacement	No linked practice
4.2 Kinematics of motion in a straight line; candidate bullet 2, position subitem (bullet ordinal, not an official subcode)	Interpret displacement-time slope as velocity	No linked practice
4.2 Kinematics of motion in a straight line; candidate bullet 2, velocity subitem (bullet ordinal, not an official subcode)	Interpret velocity-time slope as acceleration	No linked practice
4.2 Kinematics of motion in a straight line; candidate bullet 3 (bullet ordinal, not an official subcode)	Differentiate/integrate time-polynomial motion	Integration and mathematical modelling, question 2 (direct) Mechanics: motion, forces and moments, question 6 (direct) Statistics and modelling: decisions and limits, question 2 (direct)
4.2 Kinematics of motion in a straight line; candidate bullet 4 (bullet ordinal, not an official subcode)	Use constant-acceleration straight-line equations	Mechanics: motion, forces and moments, question 1 (direct) Mechanics: motion, forces and moments, question 2 (direct)
4.3 Momentum; candidate bullet 1 (bullet ordinal, not an official subcode)	Use signed one-dimensional linear momentum	Forces Momentum And Energy, question 2 (direct)
4.3 Momentum; candidate bullet 2 (bullet ordinal, not an official subcode)	Conserve momentum in direct impacts, including coalescence	Forces Momentum And Energy, question 2 (direct)
4.4 Newton's laws of motion; candidate bullet 1 (bullet ordinal, not an official subcode)	Apply Newton's laws to constant-force particle motion	Mechanics: motion, forces and moments, question 2 (direct)
4.4 Newton's laws of motion; candidate bullet 2 (bullet ordinal, not an official subcode)	Relate mass and weight; component convention g about 10	Mechanics: motion, forces and moments, question 4 (direct)
4.4 Newton's laws of motion; candidate bullet 3 (bullet ordinal, not an official subcode)	Solve vertical/inclined-plane constant-acceleration motion	No linked practice
4.4 Newton's laws of motion; candidate bullet 4 (bullet ordinal, not an official subcode)	Solve light-string or tow-bar connected-particle problems	Mechanics: motion, forces and moments, question 4 (direct)
4.5 Energy, work and power; candidate bullet 1 (bullet ordinal, not an official subcode)	Compute work for a constant force and displacement angle	Forces Momentum And Energy, question 2 (direct)
4.5 Energy, work and power; candidate bullet 2 (bullet ordinal, not an official subcode)	Calculate gravitational potential and kinetic energies	Forces Momentum And Energy, question 2 (direct)
4.5 Energy, work and power; candidate bullet 3 (bullet ordinal, not an official subcode)	Use external work and energy conservation	Forces Momentum And Energy, question 2 (direct)
4.5 Energy, work and power; candidate bullet 4 (bullet ordinal, not an official subcode)	Use average power and instantaneous P=Fv	Forces Momentum And Energy, question 2 (direct)
4.5 Energy, work and power; candidate bullet 5 (bullet ordinal, not an official subcode)	Model vehicle acceleration under power and resistance	No linked practice

both · Paper 5: Probability & Statistics 1; AS 1+5; compulsory A (19 entries)

Mathematics 9709: both · Paper 5: Probability & Statistics 1; AS 1+5; compulsory A
Reference	Concept	Linked practice
5.1 Representation of data; candidate bullet 1 (bullet ordinal, not an official subcode)	Choose data displays and discuss their limitations	No linked practice
5.1 Representation of data; candidate bullet 2 (bullet ordinal, not an official subcode)	Construct/interpret stem plots, boxes, histograms and cumulative graphs	Data Counting And Distributions, question 1 (direct)
5.1 Representation of data; candidate bullet 3 (bullet ordinal, not an official subcode)	Compare central tendency and spread	Data Counting And Distributions, question 1 (direct)
5.1 Representation of data; candidate bullet 4 (bullet ordinal, not an official subcode)	Estimate quartiles, percentiles and proportions from cumulative graphs	Data Counting And Distributions, question 1 (direct)
5.1 Representation of data; candidate bullet 5 (bullet ordinal, not an official subcode)	Calculate mean/SD from raw, grouped or coded totals	Data Counting And Distributions, question 1 (direct)
5.2 Permutations and combinations; candidate bullet 1 (bullet ordinal, not an official subcode)	Count selections with permutations and combinations	Data Counting And Distributions, question 2 (direct)
5.2 Permutations and combinations; candidate bullet 2, repetition subitem (bullet ordinal, not an official subcode)	Count linear arrangements with repeated objects	Data Counting And Distributions, question 2 (direct)
5.2 Permutations and combinations; candidate bullet 2, restriction subitem (bullet ordinal, not an official subcode)	Count linear arrangements under adjacency restrictions	Data Counting And Distributions, question 2 (direct)
5.3 Probability; candidate bullet 1 (bullet ordinal, not an official subcode)	Enumerate equiprobable outcomes or count selections	No linked practice
5.3 Probability; candidate bullet 2 (bullet ordinal, not an official subcode)	Use addition and multiplication of probabilities	Statistics: probability, distributions and hypothesis tests, question 3 (direct)
5.3 Probability; candidate bullet 3 (bullet ordinal, not an official subcode)	Distinguish exclusivity and independence	Statistics: probability, distributions and hypothesis tests, question 3 (direct)
5.3 Probability; candidate bullet 4 (bullet ordinal, not an official subcode)	Calculate conditional probabilities	Statistics: probability, distributions and hypothesis tests, question 3 (direct)
5.4 Discrete random variables; candidate bullet 1 (bullet ordinal, not an official subcode)	Build discrete probability tables and compute moments	Data Counting And Distributions, question 3 (direct)
5.4 Discrete random variables; candidate bullet 2 (bullet ordinal, not an official subcode)	Calculate binomial/geometric probabilities and justify models	Calculus, logarithms and probability, question 3 (direct) Statistics: probability, distributions and hypothesis tests, question 1 (direct) Data Counting And Distributions, question 3 (direct)
5.4 Discrete random variables; candidate bullet 3 (bullet ordinal, not an official subcode)	Use binomial moments and geometric expectation	Data Counting And Distributions, question 3 (direct)
5.5 The normal distribution; candidate bullet 1 (bullet ordinal, not an official subcode)	Model continuous data with a normal distribution	Statistics: probability, distributions and hypothesis tests, question 2 (direct)
5.5 The normal distribution; candidate bullet 2, probability subitem (bullet ordinal, not an official subcode)	Standardise and evaluate normal probabilities	Statistics: probability, distributions and hypothesis tests, question 2 (direct) Statistics and modelling: decisions and limits, question 4 (direct)
5.5 The normal distribution; candidate bullet 2, inverse subitem (bullet ordinal, not an official subcode)	Infer parameters or cutoffs from normal probabilities	Statistics and modelling: decisions and limits, question 4 (direct)
5.5 The normal distribution; candidate bullet 3 (bullet ordinal, not an official subcode)	Approximate binomial probabilities with continuity correction	Data Counting And Distributions, question 4 (direct)

A · Paper 6: Probability & Statistics 2; A route 1+3+5+6 only (27 entries)

Mathematics 9709: A · Paper 6: Probability & Statistics 2; A route 1+3+5+6 only
Reference	Concept	Linked practice
6.1 The Poisson distribution; candidate bullet 1 (bullet ordinal, not an official subcode)	Evaluate Poisson probabilities	Statistics Two Models And Inference, question 1 (direct)
6.1 The Poisson distribution; candidate bullet 2 (bullet ordinal, not an official subcode)	Use Poisson mean and variance	Statistics Two Models And Inference, question 1 (direct)
6.1 The Poisson distribution; candidate bullet 3 (bullet ordinal, not an official subcode)	Justify a Poisson event-count model	Statistics Two Models And Inference, question 1 (direct)
6.1 The Poisson distribution; candidate bullet 4 (bullet ordinal, not an official subcode)	Approximate rare binomial counts by Poisson	Statistics Two Models And Inference, question 1 (direct)
6.1 The Poisson distribution; candidate bullet 5 (bullet ordinal, not an official subcode)	Approximate large Poisson counts by continuity-corrected normal	Statistics Two Models And Inference, question 1 (direct)
6.2 Linear combinations of random variables; candidate bullet 1, affine subitem (bullet ordinal, not an official subcode)	Find affine expectation and variance	Statistics Two Models And Inference, question 2 (direct)
6.2 Linear combinations of random variables; candidate bullet 1, mean subitem (bullet ordinal, not an official subcode)	Use linearity of expectation	Statistics Two Models And Inference, question 2 (direct)
6.2 Linear combinations of random variables; candidate bullet 1, variance subitem (bullet ordinal, not an official subcode)	Combine independent variances with squared coefficients	Statistics Two Models And Inference, question 2 (direct)
6.2 Linear combinations of random variables; candidate bullet 1, normal subitem (bullet ordinal, not an official subcode)	Transform a normal random variable affinely	Statistics Two Models And Inference, question 2 (direct)
6.2 Linear combinations of random variables; candidate bullet 1, normalpair subitem (bullet ordinal, not an official subcode)	Combine independent normal random variables	Statistics Two Models And Inference, question 2 (direct)
6.2 Linear combinations of random variables; candidate bullet 1, poisson subitem (bullet ordinal, not an official subcode)	Sum independent Poisson random variables	Statistics Two Models And Inference, question 2 (direct)
6.3 Continuous random variables; candidate bullet 1 (bullet ordinal, not an official subcode)	Normalise a single-interval probability density	Statistics Two Models And Inference, question 3 (direct)
6.3 Continuous random variables; candidate bullet 2 (bullet ordinal, not an official subcode)	Integrate a density for probabilities, quantiles and moments	Statistics Two Models And Inference, question 3 (direct)
6.4 Sampling and estimation; candidate bullet 1 (bullet ordinal, not an official subcode)	Distinguish populations/samples and random selection	Statistics Two Models And Inference, question 4 (direct)
6.4 Sampling and estimation; candidate bullet 2 (bullet ordinal, not an official subcode)	Critique biased sampling and use random numbers	Statistics Two Models And Inference, question 4 (direct)
6.4 Sampling and estimation; candidate bullet 3 (bullet ordinal, not an official subcode)	Find sampling-mean expectation and variance	Statistics Two Models And Inference, question 4 (direct) Statistics Two Models And Inference, question 6 (direct)
6.4 Sampling and estimation; candidate bullet 4 (bullet ordinal, not an official subcode)	Use exact normality of normal-population sample means	Statistics: probability, distributions and hypothesis tests, question 5 (direct) Statistics and modelling: decisions and limits, question 1 (direct) Statistics Two Models And Inference, question 4 (direct)
6.4 Sampling and estimation; candidate bullet 5 (bullet ordinal, not an official subcode)	Apply the informal central limit theorem	Statistics Two Models And Inference, question 6 (direct)
6.4 Sampling and estimation; candidate bullet 6 (bullet ordinal, not an official subcode)	Estimate population mean/variance without bias	Statistics Two Models And Inference, question 6 (direct)
6.4 Sampling and estimation; candidate bullet 7 (bullet ordinal, not an official subcode)	Construct and interpret population-mean confidence intervals	Statistics Two Models And Inference, question 4 (direct)
6.4 Sampling and estimation; candidate bullet 8 (bullet ordinal, not an official subcode)	Construct large-sample proportion confidence intervals	Statistics Two Models And Inference, question 4 (direct)
6.5 Hypothesis tests; candidate bullet 1 (bullet ordinal, not an official subcode)	Use hypothesis-test terminology and distinguish tails	Statistics: probability, distributions and hypothesis tests, question 4 (direct) Statistics and modelling: decisions and limits, question 3 (direct) Statistics Two Models And Inference, question 5 (direct)
6.5 Hypothesis tests; candidate bullet 2, exact subitem (bullet ordinal, not an official subcode)	Test binomial/Poisson hypotheses with exact tails	Statistics: probability, distributions and hypothesis tests, question 4 (direct) Statistics and modelling: decisions and limits, question 3 (direct) Statistics Two Models And Inference, question 5 (direct)
6.5 Hypothesis tests; candidate bullet 2, normal subitem (bullet ordinal, not an official subcode)	Test discrete hypotheses with suitable normal approximations	No linked practice
6.5 Hypothesis tests; candidate bullet 3 (bullet ordinal, not an official subcode)	Test a normal known-variance or large-sample population mean	Statistics: probability, distributions and hypothesis tests, question 5 (direct) Statistics and modelling: decisions and limits, question 1 (direct)
6.5 Hypothesis tests; candidate bullet 4 (bullet ordinal, not an official subcode)	Distinguish Type I and Type II errors	Statistics Two Models And Inference, question 5 (direct)
6.5 Hypothesis tests; candidate bullet 5 (bullet ordinal, not an official subcode)	Calculate Type I/II error probabilities	Statistics Two Models And Inference, question 5 (direct)

Remaining academic requirements

Conceptual alignment only, not Cambridge certification, teacher approval, exam-entry advice or complete teaching coverage. Every placement has teacherApproved:false. The 120 pre-existing questions retain their IDs and current English editorial revisions.
Inventory enumerates every candidate-content bullet in all numbered subject-content sections and splits independently assessable nested lists. Internal b-number identifiers are editorial locators, never official subcodes. Worked examples and notes constrain the outcomes rather than create separate official codes. pdfPage is one-based actual PDF page.
Read the version-4 syllabus subject content on PDF pages 19-39, prior knowledge on 18, routes on 10-16, assessment on 40-41, and the one-page update. The update's opening version-3 sentence is stale; its December 2025 table and syllabus change log identify version 4. Prior version-3 changes to pages 21,26,28 are included in this PDF.
Route constraints: Paper 1 is compulsory at AS/A; Pure 2 is AS-only (1+2), not an A-level carry-forward route. Other AS routes are 1+4 or 1+5. A-level routes are 1+3+4+5 or 1+3+5+6. Neither taking all six papers nor a Mechanics+Statistics 2 combination is inferred.
Pure 3 assumes Pure 1, not Pure 2; duplicated Pure 2/3 outcome references remain distinct. Mechanics models particles moving in one dimension; supplied g=9.8 in existing examples is a stated model constant, not an asserted Cambridge default. Regression, projectiles and rigid-body moments remain enrichment in this subject.
Some Pure 3 vector, complex-number, differential-equation, trigonometric and Statistics 2 test contexts remain sparse despite short existing examples. Parametric second derivatives only partially align here. Additional normal-approximation testing and independent-Poisson testing need more worked practice.
No current mapped or partial question directly evidences these 37 inventory items: caie27-9709-1.3-b1 (Determine a straight-line equation); caie27-9709-1.3-b2 (Use line forms, distances, slopes and intersections); caie27-9709-1.4-b1 (Convert radians and degrees); caie27-9709-1.5-b3 (Use principal inverse-trigonometric notation); caie27-9709-1.7-b1 (Interpret derivative as limiting chord gradient); caie27-9709-1.8-b1 (Reverse differentiation of rational powers and linear composites); caie27-9709-1.8-b2 (Determine integration constants); caie27-9709-2.2-b2 (Use exponential/logarithm inverses and graphs); caie27-9709-2.2-b3 (Solve exponential equations and inequalities using logarithms); caie27-9709-3.2-b2 (Use exponential/logarithm inverses and graphs); caie27-9709-3.2-b3 (Solve exponential equations and inequalities using logarithms); caie27-9709-2.3-b2-reciprocal (Use squared reciprocal-function identities); caie27-9709-2.3-b2-compound (Use compound-angle expansions); caie27-9709-3.3-b2-reciprocal (Use squared reciprocal-function identities); caie27-9709-3.3-b2-compound (Use compound-angle expansions); caie27-9709-2.5-b2 (Use trigonometric identities when integrating); caie27-9709-3.5-b2 (Use trigonometric identities when integrating); caie27-9709-3.7-b1 (Use standard two/three-dimensional vector notation); caie27-9709-3.8-b1 (Translate a rate model into a differential equation); caie27-9709-3.9-b1 (Use Cartesian components, modulus, argument and conjugation); caie27-9709-3.9-b2 (Perform Cartesian complex arithmetic); caie27-9709-3.9-b3 (Use conjugate roots for real-coefficient polynomials); caie27-9709-3.9-b4 (Represent numbers on Argand diagrams); caie27-9709-3.9-b5 (Multiply and divide using polar/exponential forms); caie27-9709-3.9-b6 (Find complex square roots in Cartesian form); caie27-9709-3.9-b7 (Interpret complex arithmetic geometrically); caie27-9709-3.9-b8 (Draw simple complex equations and inequalities as loci); caie27-9709-4.1-b5 (Use smooth-contact assumptions and limitations); caie27-9709-4.1-b7 (Apply Newton's third law); caie27-9709-4.2-b2-area (Interpret velocity-time area as displacement); caie27-9709-4.2-b2-position (Interpret displacement-time slope as velocity); caie27-9709-4.2-b2-velocity (Interpret velocity-time slope as acceleration); caie27-9709-4.4-b3 (Solve vertical/inclined-plane constant-acceleration motion); caie27-9709-4.5-b5 (Model vehicle acceleration under power and resistance); caie27-9709-5.1-b1 (Choose data displays and discuss their limitations); caie27-9709-5.3-b1 (Enumerate equiprobable outcomes or count selections); caie27-9709-6.5-b2-normal (Test discrete hypotheses with suitable normal approximations).
A represented outcome means at least one limited task, not mastery or complete coverage of all its forms, examples and modelling contexts. Partial placements must not be counted as full-outcome coverage.
Teacher review is still required for indicative mark allocations, diagrams/sketch quality, alternative methods, data/model limitations and complete timed structured papers. Short self-marking answers do not replace teaching, externally assessed work or MF19/non-graphical-calculator exam preparation. No new question is teacher approved.

Return to Mathematics practice