Edexcel 2020 Paper 3 Statistics and Mechanics

Edexcel 2020 Statistics Paper 31 (Question Paper)
Edexcel 2020 Statistics Paper 31 (Mark Scheme)

Edexcel 2020 Mechanics Paper 32 (Question Paper)
Edexcel 2020 Mechanics Paper 32 (Mark Scheme)

1. The Venn diagram shows the probabilities associated with four events, A, B, C and D
   (a) Write down any pair of mutually exclusive events from A, B, C and D
   Given that P(B) = 0.4
   (b) find the value of p
   Given also that A and B are independent
   (c) find the value of q
   Given further that P(Bʹ |C) = 0.64
   (d) find
   (i) the value of r
   (ii) the value of s
2. A random sample of 15 days is taken from the large data set for Perth in June and July 1987.
   The scatter diagram in Figure 1 displays the values of two of the variables for these 15 days.
   (a) Describe the correlation.
   The variable on the x-axis is Daily Mean Temperature measured in °C.
   (b) Using your knowledge of the large data set,
   (i) suggest which variable is on the y-axis,
   (ii) state the units that are used in the large data set for this variable.
3. Each member of a group of 27 people was timed when completing a puzzle.
   The time taken, x minutes, for each member of the group was recorded
   . These times are summarised in the following box and whisker plot.
   (a) Find the range of the times.
   (b) Find the interquartile range of the times.
4. The discrete random variable D has the following probability distribution
5. A health centre claims that the time a doctor spends with a patient can be modelled by a normal distribution with a mean of 10 minutes and a standard deviation of 4 minutes.
   (a) Using this model, find the probability that the time spent with a randomly selected patient is more than 15 minutes.
   Some patients complain that the mean time the doctor spends with a patient is more than 10 minutes.
   The receptionist takes a random sample of 20 patients and finds that the mean time the doctor spends with a patient is 11.5 minutes.
   (b) Stating your hypotheses clearly and using a 5% significance level, test whether or not there is evidence to support the patients’ complaint.

1. A rough plane is inclined to the horizontal at an angle α, where tan α = 3/4
   A brick P of mass m is placed on the plane.
   The coefficient of friction between P and the plane is μ
   Brick P is in equilibrium and on the point of sliding down the plane.
   Brick P is modelled as a particle.
   Using the model,
   (a) find, in terms of m and g, the magnitude of the normal reaction of the plane on brick P
2. A particle P moves with acceleration (4i − 5j)ms⁻²
   At time t = 0, P is moving with velocity (−2i + 2j)ms⁻¹
   (a) Find the velocity of P at time t = 2 seconds.
   At time t = 0, P passes through the origin O.
   At time t = T seconds, where T > 0, the particle P passes through the point A.
   The position vector of A is (λi − 4.5j)m relative to O, where λ is a constant.
   (b) Find the value of T
3. (i) At time t seconds, where t ≥ 0 , a particle P moves so that its acceleration ams⁻² is given by
4. A ladder AB has mass M and length 6a.
   The end A of the ladder is on rough horizontal ground.
   The ladder rests against a fixed smooth horizontal rail at the point C.
   The point C is at a vertical height 4a above the ground.
   The vertical plane containing AB is perpendicular to the rail.
5. A small ball is projected with speed Ums−1 from a point O at the top of a vertical cliff.
   The point O is 25m vertically above the point N which is on horizontal ground.
   The ball is projected at an angle of 45° above the horizontal.
   The ball hits the ground at a point A, where AN = 100m, as shown in Figure 2.
   The motion of the ball is modelled as that of a particle moving freely under gravity.
   Using this initial model,
   (a) show that U = 28

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