AQA A-level Mathematics Study Guide 2026 - Practice-Ready Answer Guide

AQA A-level Mathematics Study Guide 2026 - Practice-Ready Answer Guide What are the parameters for a binomial distribution? - answer - X~B(n,p) (n = number, p = probability) What are the parameters for a normal distribution? - answer - X~N(µ, σ²) (µ = population mean, σ² = variance) What is the binomial equation? - answer - What is the mean of a binomial distribution? - answer - µ = np What's the variance of a binomial distribution? - answer - σ² = np(1-p) What values are given in the binomial tables? - answer - P(X x) - if you want x then you need to do 1 - P(X x) Sigma notation for sample mean? - answer - -x- = ∑x ÷ n Sigma notation for sample mean of grouped data? - answer - -x- = ∑ƒx ÷ ∑ƒ Formula for frequency density? (= height on a histrogram) - answer - Class frequency ÷ class width (More complex) formula for sample standard deviation? - answer - Simpler formula for sample standard deviation? - answer - s = √(1/n-1) (∑x² - (∑x)²/n) (More complex) formula for population standard deviation? - answer - Simpler formula for population standard deviation? - answer - σ = √(1/n)(∑x² - µ²) About what proportion of values lie within 1 standard deviation of the mean? - answer - About ²/₃ About what proportion of values lie within 2 standard deviations of the mean? - answer - About 95% About what proportion of values lie within 3 standard deviations of the mean? - answer - Almost all values Formula for sample standard deviation of grouped data? - answer - 1/n-1 × (∑fx² - (∑ƒx)²/n) Formula for population standard deviation of grouped data? - answer - 1/n × (∑fx² - (∑ƒx)²/n) What happens to the mean when adding or subtracting a constant, c from every value? - answer - The mean changes by c What happens to the standard deviation when adding or subtracting a constant, c from every value? - answer - No change to the standard deviation What happens to the mean when multiplying every value by a constant, k? - answer - Multiplies the mean by k What happens to the standard deviation when multiplying every value by a constant, k? - answer - Multiplies the standard deviation by k What happens to the variance when multiplying every value by a constant, k? - answer - Multiplies every value by k² Advantages of the mode? - answer - Certain to have a value that was actually observed Advantages of the median? - answer - Can be calculated where the median or mean can't - think pigeons. Advantages of the mean? - answer - Equally influenced by every value in the data. Statistical modelling (distributions) usually requires the mean Disadvantages of the mode? - answer - May not be unique Often doesn't give useful info - e.g. mean no. eggs broken in any supermarket is probably 0 Disadvantages of the mean? - answer - Can be greatly affected by a mistaken or unusual observation - e.g. a can 'being' 4000g instead of 400g, or a boss' salary being included with the workers' Disadvantages of the median? - answer - Can be difficult to calculate when there's a lot of data Advantages of the range? - answer - Easy to calculate Advantages of IQR? - answer - Doesn't involve squares or roots Not affected by extreme values Advantages of standard deviation? - answer - Equally influenced by each value Important in statistical modelling (sometimes as the variance) Disadvantages of the range? - answer - Too dependant on extreme values Disadvantages of IQR and standard deviation? - answer - Difficuly to calculate without a spreadsheet and/or calculator when there are many values Addition rule for non- mutually exclusive events? - answer - P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Addition rule for mutually exclusive events? - answer - P(A ∪ B) = P(A) + P(B) What are exhaustive events? - answer - When it is certain that at least one of them will occur Multiplication rule for independent events? - answer - P(A ∩ B) = P(A) × P(B) What are independent events? - answer - When knowledge that one event does or doesn't occur doesn't affect th