9709 AS & A Level Mathematics: past papers
719 papers from 2002 to 2025, with 386 questions sorted by syllabus topic.
Representation of data Paper 5 · 10 questions
Stem-and-leaf diagrams and box plots5
Back-to-back stem-and-leaf, median and IQR, and combined mean and standard deviation.
Median and IQR from a stem-and-leaf diagram, box plots, and mean or median.
Back-to-back stem-and-leaf, median and IQR, and comparing spread.
Back-to-back stem-and-leaf: median, IQR, box plots and choosing an average.
Back-to-back stem-and-leaf: median, IQR, box plots and a comparison.
Histograms and cumulative frequency4
Draw a histogram and estimate the mean of grouped data.
Read a cumulative frequency graph, then estimate the mean and standard deviation of grouped data.
Draw a cumulative frequency graph, estimate from it and estimate a grouped mean.
Draw a histogram and estimate a standard deviation from grouped data.
Mean and standard deviation4
Draw a histogram and estimate the mean of grouped data.
Read a cumulative frequency graph, then estimate the mean and standard deviation of grouped data.
Draw a cumulative frequency graph, estimate from it and estimate a grouped mean.
Draw a histogram and estimate a standard deviation from grouped data.
Coded and combined data2
Back-to-back stem-and-leaf, median and IQR, and combined mean and standard deviation.
Use summary statistics with coding to find the number of values.
Permutations and combinations Paper 5 · 10 questions
Arrangements and factorials8
Arrangements of letters with restrictions, and choosing two different letters.
Arrangements and selections of letters from a word with repeated letters and restrictions.
Arrangements and selections of books with restrictions.
Arrangements of letters with a restriction on a gap.
Arrangements with repeated letters and restrictions, and a probability.
Selections with restrictions and arrangements with grouping or separation.
Arrangements of letters with grouping and spacing, a probability, and selections.
Arrangements with restrictions, selections and splitting into groups.
Arrangements with restrictions9
Arrangements of letters with restrictions, and choosing two different letters.
Arrangements and selections of letters from a word with repeated letters and restrictions.
Arrangements and selections of books with restrictions.
Arrangements of letters with a restriction on a gap.
Arrangements with repeated letters and restrictions, and a probability.
Arrangements with restrictions and a probability of a selection.
Selections with restrictions and arrangements with grouping or separation.
Arrangements of letters with grouping and spacing, a probability, and selections.
Arrangements with restrictions, selections and splitting into groups.
Selections (combinations)8
Arrangements of letters with restrictions, and choosing two different letters.
Arrangements and selections of letters from a word with repeated letters and restrictions.
Arrangements and selections of books with restrictions.
Selecting groups of students with restrictions.
Arrangements with restrictions and a probability of a selection.
Selections with restrictions and arrangements with grouping or separation.
Arrangements of letters with grouping and spacing, a probability, and selections.
Arrangements with restrictions, selections and splitting into groups.
Probability Paper 5 · 12 questions
Combined events and Venn diagrams1
Two-way table: conditional probability, independence and a binomial probability.
Tree diagrams and conditional probability10
Two groups: find an unknown from a ratio, then the probability two cards match.
Conditional probability when drawing marbles with and without replacement.
Choosing toy cars without replacement: same-colour and mixed-colour probabilities.
A biased coin and a choice of marbles, with a conditional probability.
Tree diagram, matching colours and a conditional probability.
Rain on successive days with dependence: several probabilities.
Geometric probabilities, a conditional probability and a binomial “at least”.
Probabilities by type of journey, and a conditional probability.
Fair and biased coins: a conditional probability and a probability distribution.
Choosing without replacement, and a conditional probability.
Independent and mutually exclusive events2
Probability that the first success comes on or before a given trial.
Two-way table: conditional probability, independence and a binomial probability.
Discrete random variables Paper 5 · 24 questions
Probability distributions8
Probability distribution from selections without replacement, and its variance.
Probability distribution for the number of tails from three biased coins.
Distribution of heads from three biased coins, then the variance.
Probability distribution of a coin-and-dice variable and its variance.
Probability distribution, expectation and variance of the total of two coins.
Probability distribution from a formula with an unknown constant, then mean and variance.
Fair and biased coins: a conditional probability and a probability distribution.
Distribution of the sum of two rolls of a non-standard die, mean and variance.
Expectation and variance7
Probability distribution from selections without replacement, and its variance.
Distribution of heads from three biased coins, then the variance.
Probability distribution of a coin-and-dice variable and its variance.
Probability distribution, expectation and variance of the total of two coins.
Unknown probabilities from the expectation, then the variance.
Probability distribution from a formula with an unknown constant, then mean and variance.
Distribution of the sum of two rolls of a non-standard die, mean and variance.
The binomial distribution9
Binomial probabilities and a normal approximation for birthdays.
Normal probabilities, finding the mean and standard deviation from percentages, and a binomial probability.
Binomial probabilities and a normal approximation.
Two-way table: conditional probability, independence and a binomial probability.
Binomial probabilities and the normal approximation to the binomial.
Geometric probability, then a binomial probability over a range.
Geometric probabilities, a conditional probability and a binomial “at least”.
Binomial and normal approximation, with a justification.
Binomial probability for a small sample, normal approximation for a large one.
The geometric distribution8
Geometric distribution: first head on, or after, a given throw.
Probability that the first success comes on or before a given trial.
Normal probabilities, a standard deviation from a percentage, and the first day an event happens.
Geometric distribution and the normal approximation to a binomial.
Geometric probabilities for repeated attempts.
Geometric probability, then a binomial probability over a range.
Geometric probabilities, a conditional probability and a binomial “at least”.
Geometric probabilities for repeated throws.
The normal distribution Paper 5 · 17 questions
Standardising and normal probabilities9
Normal distribution: expected numbers in a range and a standard deviation from a percentage.
Normal probabilities, finding the mean and standard deviation from percentages, and a binomial probability.
Normal probabilities, a standard deviation from a percentage, and the first day an event happens.
Normal distribution: expected count below a value and a standard deviation from a tail.
Normal distribution: a percentage above a value and a boundary value.
Normal probabilities and a value from a tail probability.
Normal probabilities, an unknown standard deviation and the normal approximation.
Normal distribution: expected count and probability within half a standard deviation.
Normal probabilities and an unknown standard deviation.
Inverse normal and finding μ and σ8
Normal distribution: expected numbers in a range and a standard deviation from a percentage.
Normal probabilities, finding the mean and standard deviation from percentages, and a binomial probability.
Normal probabilities, a standard deviation from a percentage, and the first day an event happens.
Normal distribution: expected count below a value and a standard deviation from a tail.
Normal distribution: a percentage above a value and a boundary value.
Normal probabilities and a value from a tail probability.
Normal probabilities, an unknown standard deviation and the normal approximation.
Normal probabilities and an unknown standard deviation.
Normal approximation to the binomial9
Binomial probabilities and a normal approximation for birthdays.
Normal approximation to a binomial probability.
Binomial probabilities and a normal approximation.
Geometric distribution and the normal approximation to a binomial.
Binomial probabilities and the normal approximation to the binomial.
Normal approximation to a binomial.
Normal probabilities, an unknown standard deviation and the normal approximation.
Binomial and normal approximation, with a justification.
Binomial probability for a small sample, normal approximation for a large one.