Papers · Edexcel 9MA0/03

A-level Maths Paper 3: statistics and mechanics

2 hours, 100 marks: Section A Statistics 50, Section B Mechanics 50. Try two questions from each, then plan the repair.

1. Question 1 of 4 · Section A: Statistics

   The random variable $X \sim N(50, 4^2)$. Find $P(X > 56)$, giving your answer to 4 decimal places.

   A 0.9332B 0.4332C 0.0668D 0.0013

2. Question 2 of 4 · Section A: Statistics

   In the past, 30% of a shop's customers bought a newspaper. After a price rise, 2 of a random sample of 20 customers bought one. Using $X \sim B(20, 0.3)$, test at the 5% level whether the proportion has decreased. Which conclusion is correct?

   A P(X = 2) = 0.0278 < 0.05, so reject H₀.B P(X ≤ 2) = 0.0355 < 0.05, so the proportion has decreased.C P(X ≤ 2) = 0.0355 > 0.025, so do not reject H₀.D P(X ≤ 2) = 0.0355 < 0.05, so reject H₀: there is evidence the proportion has decreased.

3. Question 3 of 4 · Section B: Mechanics

   A box of mass 2 kg is pulled along a rough horizontal floor by a horizontal force of 10 N. The coefficient of friction between the box and the floor is 0.3. Take $g = 9.8\ \text{m s}^{-2}$. Find the acceleration of the box.

   A 5 m s⁻²B 2.06 m s⁻²C 4.7 m s⁻²D 3.53 m s⁻²

4. Question 4 of 4 · Section B: Mechanics

   A ball is projected horizontally at 14 m s⁻¹ from the top of a cliff 19.6 m high. Take $g = 9.8\ \text{m s}^{-2}$ and ignore air resistance. How far from the base of the cliff does the ball land?

   A 28 mB 19.8 mC 56 mD 14 m