Ten-Year Series
A-Level H2 Mathematics, worked in full
Step-by-step solutions to every H2 Mathematics past paper since 2015. Each one explains the reasoning and points out the common mistakes, and every paper can be downloaded as a PDF.
2024 · Paper 1
Download PDFQ14 marks
Graphs and functions · asymptotes · turning points
Slide a until the turning point landsQ23 marks
Vectors · cross product · scalar product
Open the angle and watch the areaQ34 marks
Complex numbers · conjugate roots
Break the pair and watch the coefficientsQ46 marks
Inequalities · sign diagram · modulus
Test values along the axisQ57 marks
Sequences and series · sum to infinity
Split the sum into head and tailQ68 marks
Differentiation · tangent · area between curves
Aim the tangent, then fill the regionQ78 marks
Trigonometry · method of differences
Lengthen the chain and watch it collapseQ89 marks
Maclaurin series · standard series
Add the terms one at a timeQ910 marks
Parametric equations · tangent · area
Walk a point along the curveQ1014 marks
Integration · area · volume of revolution
Turn the region into a solidQ1112 marks
Differential equations · terminal velocity
Play the whole 2000 m fallQ1215 marks
Vectors · closest approach · skew lines
Turn the scene in 3D2024 · Paper 2
Download PDFQ16 marks
Complex numbers · conjugates · roots
Q26 marks
Differentiation · maximum area
Q38 marks
Functions · range · inverse
Q49 marks
Sequences and series · nth term · sums
Q511 marks
Graphs and transformations · sketches of related graphs
Q66 marks
Sampling · sampling methods
Q78 marks
Probability · combined events
Q88 marks
Hypothesis testing · test of a mean
Q911 marks
Binomial distribution · probabilities in context
Q1012 marks
Normal distribution · sums of normal variables
Q1115 marks
Correlation and regression · transformed models
2023 · Paper 1
Download PDFQ15 marks
Differentiation · Applications of Differentiation
Q25 marks
Sequences and Series · Concepts of Series and Sequences
Q36 marks
Vectors · Scalar and Vector Products
Q410 marks
Integration · Techniques of Integration
Q57 marks
Sequences and Series · Sigma Notation
Q68 marks
Integration · Volume of revolution
Q710 marks
Functions · Inverse Functions
Q810 marks
Complex Numbers · Polar and exponential form
Q913 marks
Vectors · Lines
Q1013 marks
Differential Equations · Application Problems involving DEs
Q1113 marks
Sequences and Series · Arithmetic/Geometric Progression
2023 · Paper 2
Download PDFQ16 marks
Equations and Inequalities · Inequalities
Q29 marks
Maclaurin Series · Deriving Maclaurin Series
Q312 marks
Vectors · 3D Vector Geometry
Q413 marks
Integration · Area under curve
Q55 marks
Probability · Basic Probability Concepts
Q68 marks
Probability · Basic Probability Concepts
Q77 marks
Correlation and Regression · Regression Lines
Q811 marks
Hypothesis Testing · Conducting a hypothesis test
Q914 marks
Normal Distribution · Scenarios involving normal distribution
Q1015 marks
Binomial Distribution · Scenarios involving binomial distribution
2022 · Paper 1
Download PDFQ14 marks
Complex Numbers · Properties of Complex Numbers
Q26 marks
Maclaurin Series · Deriving Maclaurin Series
Q36 marks
Differentiation · Techniques of Differentiation
Q47 marks
Integration · Techniques of Integration
Q58 marks
Graphs and Transformations · Properties of graphs
Q69 marks
Functions · Inverse Functions
Q79 marks
Integration · Area under curve
Q87 marks
Integration · Definite integrals
Q98 marks
Sequences and Series · Arithmetic/Geometric Progression
Q1010 marks
Graphs and Transformations · Properties of graphs
Q1113 marks
Vectors · Planes
Q1213 marks
Differential Equations · Application Problems involving DEs
2022 · Paper 2
Download PDFQ14 marks
Integration · Techniques of Integration
Q27 marks
Integration · Definite integrals
Q39 marks
Complex Numbers · Polar and exponential form
Q49 marks
Sequences and Series · Sigma Notation
Q511 marks
Integration · Volume of revolution
Q66 marks
Probability · Conditional Probability
Q78 marks
Permutations and Combinations · Basic counting
Q89 marks
Normal Distribution · Properties of a Normal Distribution
Q910 marks
Probability · Conditional Probability
Q1014 marks
Correlation and Regression · Regression Lines
Q1113 marks
Hypothesis Testing · Conducting a hypothesis test
2021 · Paper 1
Download PDFQ15 marks
Equations · simultaneous equations · cubic coefficients
Q26 marks
Graphs · modulus equations
Q36 marks
Differentiation · implicit differentiation
Q47 marks
Complex numbers · polar form · powers
Q57 marks
Sequences and series · method of differences
Q68 marks
Graphs and transformations · asymptotes · translation
Q79 marks
Maclaurin series · repeated differentiation
Q814 marks
Vectors · skew lines · shortest distance
Q913 marks
Integration · stationary points · volume of revolution
Q1012 marks
Differential equations · bacteria growth model
Q1113 marks
Parametric equations · area · greatest and least values
2021 · Paper 2
Download PDFQ15 marks
Complex numbers · conjugate roots
Q26 marks
Integration · rectangle estimates of area
Q39 marks
Functions · composite · inverse functions
Q49 marks
Sequences and series · AP and GP in context
Q511 marks
Integration · techniques of integration
Q67 marks
Discrete random variables · expectation and variance
Q78 marks
Permutations and combinations · repeated letters
Q89 marks
Hypothesis testing · test of a mean
Q97 marks
Correlation and regression · transformed models
Q1015 marks
Normal distribution · sums of normal variables
Q1114 marks
Binomial distribution · probabilities in context
2020 · Paper 1
Download PDFQ14 marks
Vectors · planes · normals
Q26 marks
Differentiation · implicit · tangents
Q37 marks
Maclaurin series · repeated differentiation
Q47 marks
Complex numbers · polar form · arguments
Q59 marks
Vectors · vector product · area
Q68 marks
Complex numbers · roots of quadratics
Q79 marks
Integration · by parts · double angles
Q812 marks
Sequences and series · AP and GP
Q912 marks
Integration · intersecting curves · area
Q1014 marks
Differential equations · population model
Q1112 marks
Differentiation · maximising an angle
2020 · Paper 2
Download PDFQ15 marks
Differentiation · quadratic curves
Q212 marks
Sequences and series · recurrence relations · sums
Q312 marks
Parametric equations · normals · area
Q411 marks
Differentiation · maximum volume
Q510 marks
Discrete random variables · expectation and variance
Q610 marks
Normal distribution · sums of normal variables
Q78 marks
Correlation and regression · transformed models
Q87 marks
Probability · selections · discrete random variables
Q912 marks
Binomial distribution · probabilities in context
Q1013 marks
Hypothesis testing · test of a mean
2019 · Paper 1
Download PDFQ14 marks
Complex numbers · conjugate roots
Q25 marks
Integration · area under a curve
Q35 marks
Graphs and transformations · completing the cube
Q46 marks
Inequalities · modulus · exponential graphs
Q56 marks
Functions · inverse · composite functions
Q66 marks
Sequences and series · method of differences
Q78 marks
Differentiation · tangents · angle between lines
Q811 marks
Sequences and series · AP and GP
Q911 marks
Complex numbers · polar form · roots of unity
Q1012 marks
Parametric equations · area · volume
Q1113 marks
Differential equations · Newton's law of cooling
Q1213 marks
Vectors · lines · planes · reflection
2019 · Paper 2
Download PDFQ16 marks
Integration · by parts · substitution
Q26 marks
Graphs · rational functions · asymptotes
Q37 marks
Differentiation · maximum volume
Q411 marks
Maclaurin series · repeated differentiation
Q510 marks
Vectors · ratio theorem · areas
Q66 marks
Sampling · sampling methods
Q711 marks
Binomial distribution · probabilities in context
Q89 marks
Probability · selections from a table
Q99 marks
Hypothesis testing · test of a mean
Q1013 marks
Correlation and regression · transformed models
Q1112 marks
Normal distribution · sums of normal variables
2018 · Paper 1
Download PDFQ16 marks
Differentiation · integration · definite integrals
Q26 marks
Integration · area between a curve and a line
Q37 marks
Differential equations · substitution
Q48 marks
Inequalities · modulus equations and inequalities
Q55 marks
Functions · composite functions
Q67 marks
Vectors · vector product
Q79 marks
Differentiation · implicit · tangents
Q810 marks
Sequences and series · recurrence relations
Q913 marks
Parametric equations · normals · area
Q1013 marks
Differential equations · electrical circuit
Q1116 marks
Sequences and series · savings plans
2018 · Paper 2
Download PDFQ16 marks
Differential equations · separable equations
Q212 marks
Complex numbers · roots of polynomials · loci
Q312 marks
Vectors · planes · pyramid geometry
Q410 marks
Maclaurin series · standard series
Q57 marks
Hypothesis testing · test of a mean
Q67 marks
Probability · tree diagrams · paths
Q78 marks
Probability · independent and exclusive events
Q811 marks
Discrete random variables · expectation and variance
Q912 marks
Correlation and regression · regression lines
Q1015 marks
Normal distribution · sums of normal variables
2017 · Paper 1
Download PDFQ14 marks
Maclaurin series · standard series
Q26 marks
Inequalities · graphical solution · modulus
Q37 marks
Differentiation · implicit · stationary points
Q48 marks
Differentiation · gradient · transformations
Q510 marks
Equations · remainder theorem · curve sketching
Q68 marks
Vectors · geometrical interpretation of equations
Q78 marks
Integration · products of sines
Q810 marks
Complex numbers · roots · polar form
Q913 marks
Sequences and series · sums · AP and GP
Q1013 marks
Vectors · lines and planes in context
Q1113 marks
Differential equations · motion under gravity
2017 · Paper 2
Download PDFQ18 marks
Parametric equations · tangents · area
Q29 marks
Sequences and series · AP and GP
Q312 marks
Graphs and transformations · functions and inverses
Q411 marks
Integration · area · volume of revolution
Q57 marks
Discrete random variables · expectation and variance
Q69 marks
Permutations and combinations · circular arrangements
Q710 marks
Hypothesis testing · central limit theorem
Q810 marks
Correlation and regression · scatter diagrams
Q912 marks
Binomial distribution · assumptions · probabilities
Q1012 marks
Normal distribution · sums of normal variables
2016 · Paper 1
Download PDFQ15 marks
Inequalities · rational inequalities
Q25 marks
Differentiation · tangents
Q36 marks
Graphs and transformations · sequence of transformations
Q47 marks
Sequences and series · AP and GP
Q58 marks
Vectors · scalar and vector products
Q610 marks
Sequences and series · induction · recurrence relations
Q710 marks
Complex numbers · roots of equations
Q811 marks
Maclaurin series · repeated differentiation
Q912 marks
Differential equations · motion in a fluid
Q1013 marks
Functions · inverse · composite functions
Q1113 marks
Vectors · planes · lines
2016 · Paper 2
Download PDFQ17 marks
Differentiation · rates of change
Q210 marks
Integration · by parts · definite integrals
Q311 marks
Parametric equations · sketch · area · normal
Q412 marks
Complex numbers · loci in the Argand diagram
Q55 marks
Discrete random variables · expectation and variance
Q610 marks
Probability · conditional probability from a table
Q710 marks
Permutations and combinations · selections and arrangements
Q811 marks
Correlation and regression · regression lines
Q910 marks
Normal and binomial distributions
Q1014 marks
Poisson distribution · approximations
2015 · Paper 1
Download PDFQ17 marks
Equations · simultaneous equations from a curve
Q26 marks
Graphs · modulus · asymptotes
Q35 marks
Integration · limit of a sum · definite integrals
Q46 marks
Differentiation · maximum and minimum problems
Q57 marks
Graphs and transformations · sequence of transformations
Q68 marks
Maclaurin series · standard series
Q710 marks
Vectors · ratio theorem · area
Q811 marks
Sequences and series · AP and GP in context
Q913 marks
Complex numbers · conjugates · polar form
Q1012 marks
Integration · area · volume of revolution
Q1115 marks
Parametric equations · turning points · area
2015 · Paper 2
Download PDFQ16 marks
Differential equations · modelling growth
Q210 marks
Vectors · lines · angles and distances
Q310 marks
Functions · inverse functions
Q414 marks
Sequences and series · mathematical induction
Q54 marks
Sampling · sampling methods
Q67 marks
Binomial distribution · normal approximation
Q77 marks
Poisson distribution · assumptions · probabilities
Q87 marks
Hypothesis testing · one-tailed test of a mean
Q98 marks
Probability · independent and combined events
Q109 marks
Correlation and regression · transformed models
Q119 marks
Permutations and combinations · repeated letters
Q129 marks
Normal distribution · sums of normal variables
No question text is reproduced anywhere in this section. The A-Level H2 Mathematics papers are © UCLES/SEAB — refer to the official papers for the wording. The worked solutions, diagrams and interactive models are original work by The Learning Cave.