9709 AS & A Level Mathematics: past papers
719 papers from 2002 to 2025, with 386 questions sorted by syllabus topic.
The Poisson distribution Paper 6 · 9 questions
Poisson probabilities5
Conditions for a Poisson model, and probabilities over 4 and 20 weeks with an approximation.
Poisson probability in terms of e, and the value of n making two probabilities equal.
Poisson probabilities, sums and a normal approximation.
Poisson mean and variance, when Poisson approximates binomial, and a tail probability.
Poisson conditions, probabilities over different periods, and a Poisson total.
Scaling rates and sums4
Conditions for a Poisson model, and probabilities over 4 and 20 weeks with an approximation.
Poisson probabilities, sums and a normal approximation.
Sums of independent Poisson variables and a conditional probability.
Poisson conditions, probabilities over different periods, and a Poisson total.
Poisson and normal approximations6
Conditions for a Poisson model, and probabilities over 4 and 20 weeks with an approximation.
Approximate binomial and Poisson probabilities with suitable distributions.
Poisson approximation to a binomial probability.
Poisson probabilities, sums and a normal approximation.
Normal approximation to a Poisson probability, with justification.
Poisson mean and variance, when Poisson approximates binomial, and a tail probability.
Linear combinations of random variables Paper 6 · 5 questions
E and Var of aX + b and aX + bY1
Standard deviations of combinations of normal and Poisson variables.
Sums of observations and multiples1
Difference and weighted sum of normal variables.
Combining normal and Poisson variables5
Standard deviations of combinations of normal and Poisson variables.
Use a dice to choose at random, then the probability that a difference of two normal times exceeds a value.
Probabilities for combinations of two independent normal variables.
Sums of independent Poisson variables and a conditional probability.
Difference and weighted sum of normal variables.
Continuous random variables Paper 6 · 5 questions
Probability density functions5
Find a constant in a probability density function, then use the median for a probability.
Probability density function: find a constant, a parameter from the mean, and the median.
Continuous distribution: constants and the median.
Probability density function: a constant, the median and E(X).
Linear density function: constant, expectation and a limit from the median.
Mean and variance3
Probability density function: find a constant, a parameter from the mean, and the median.
Probability density function: a constant, the median and E(X).
Linear density function: constant, expectation and a limit from the median.
Median and percentiles5
Find a constant in a probability density function, then use the median for a probability.
Probability density function: find a constant, a parameter from the mean, and the median.
Continuous distribution: constants and the median.
Probability density function: a constant, the median and E(X).
Linear density function: constant, expectation and a limit from the median.
Sampling and estimation Paper 6 · 10 questions
Sampling and unbiased estimates4
Use a dice to choose at random, then the probability that a difference of two normal times exceeds a value.
Find a sample mean from data using an unbiased estimate of variance.
Random sampling, unbiased estimates of mean and variance.
Unbiased estimates from summary data, then a test of a mean at 1%.
The sample mean and the Central Limit Theorem3
Standard deviation from a confidence interval, the Central Limit Theorem and repeated intervals.
Read a confidence interval for a mean and estimate the standard deviation.
Distribution of the sample mean: a probability, then a boundary value.
Confidence intervals5
Standard deviation from a confidence interval, the Central Limit Theorem and repeated intervals.
Work back from the width of a confidence interval to possible sample proportions.
Read a confidence interval for a mean and estimate the standard deviation.
Confidence level from a confidence interval for a proportion.
Confidence interval for a proportion.
Hypothesis tests Paper 6 · 9 questions
Binomial and Poisson tests4
Binomial test for a proportion, and why a Poisson approximation does not suit.
Binomial test on the chance of rolling a six, then Type I and Type II error probabilities.
Binomial hypothesis test at 10%, and whether the model suits the context.
Type I error from a binomial test and a Type II error.
Tests for a population mean5
Test for a normal mean, with Type I and Type II error probabilities.
Test a normal mean, state an assumption and find the smallest significant sample mean.
Type I error, a large-sample test of a mean, and a Type II claim.
One-tailed test of a mean, then the probability of a Type II error.
Unbiased estimates from summary data, then a test of a mean at 1%.
Type I and Type II errors5
Test for a normal mean, with Type I and Type II error probabilities.
Binomial test on the chance of rolling a six, then Type I and Type II error probabilities.
Type I error, a large-sample test of a mean, and a Type II claim.
One-tailed test of a mean, then the probability of a Type II error.
Type I error from a binomial test and a Type II error.