plumiCumulative distribution functions: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on SD.2 Cumulative distribution functions, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 13 questions on Cumulative distribution functions, as a list
- June 2025, Paper 3 Statistics, Q4 (6 marks): The continuous random variable X has cumulative distribution function F(x) = { 0 x < 0 sin 3x 0 ≤ x ≤ π 6 1 x > π 6 4 (a) Find P(0.1 < X < 0.3) Give your answer
- June 2025, AS Paper 2 Statistics, Q6 (6 marks): The continuous random variable A represents the score achieved by a player in a particular game. The probability density function of A is f (a) The probability
- June 2024, Paper 3 Statistics, Q3 (1 mark): The continuous random variable Y has cumulative distribution function F(y) = 0 y < 2 – 1 9 y2 + 10 9 y – 16 9 2 ≤ y < 5 1 y ≥ 5 { Find the median of Y Circle yo
- June 2024, AS Paper 2 Statistics, Q6 (11 marks): The continuous random variable X has probability density function f(x) = 3x 44 + 1 22 1 ≤ x ≤ 5 0 otherwise { 6 (a) Find P(X > 2) [2 marks] 6 (b) Find the upper
- June 2023, Paper 3 Statistics, Q8 (14 marks): The continuous random variable X has probability density function f (x) = k sin 2x 0 − x − p 6 0 otherwise 8 < : where k is a constant. 8 (a) Show that k = 4 [4
- June 2022, Paper 3 Statistics, Q3 (5 marks): The random variable X has an exponential distribution with probability density function f (x) = le×lx where x × 0 3 (a) Show that the cumulative distribution fu
- June 2022, Paper 3 Statistics, Q8 (11 marks): The continuous random variable X has cumulative distribution function F(x) where F(x) = 0 x = 0 ekx × 1 0 − x − 5 1 x > 5 8 > > < > > : 8 (a) Show that k = 1 5
- June 2022, AS Paper 2 Statistics, Q5 (11 marks): The continuous random variable X has probability density function f (x) = x3 0 < x × 1 9 1696x3(x2 + 1) 1 < x × 3 0 otherwise 8 > > > < > > > : 5 (a) Find P(X <
- November 2021, Paper 3 Statistics, Q5 (6 marks): The continuous random variable X has cumulative distribution function F(x) = 0 x × 1 1 10x × 1 10 1 < x × 6 1 90x2 + 1 10 6 < x × 9 1 x > 9 8 > > > > > > > < >
- November 2021, AS Paper 2 Statistics, Q6 (11 marks): The continuous random variable X has probability density function f (x) = 1 114 (4x + 7) 0 × x × 6 0 otherwise 8 < : 6 (a) Show that the median of X is 3.87, co
- November 2020, Paper 3 Statistics, Q9 (6 marks): The continuous random variable X has the cumulative distribution function shown below. F(x) = 0 x < 0 1 62 (4x3 + 6x2 + 3x) 0 − x − 2 1 x > 2 8 > > > > < > > >
- November 2020, AS Paper 2 Statistics, Q6 (8 marks): The continuous random variable X has probability density function f (x) = 4 45 (x3 × 10x2 + 29x × 20) 1 × x × 4 0 otherwise 8 < : 6 (a) Find P(X < 2) [2 marks]
- June 2019, Paper 3 Statistics, Q5 (7 marks): An insurance company models the claims it pays out in pounds (£) with a random variable X which has probability density function f (x) = k x 1 < x < a 0 otherwi
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