Edexcel A-Level Maths 2027 Predicted Practice Paper — Paper 3

Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working.

Section A: Statistics

Statistics, probability and data interpretation questions. Answer ALL questions.

• 1

  Question SECTION-A-STATISTICS1 (8 marks)

  A horticulturist studies the germination time, in hours, of seeds of a new tomato variety. The germination time X is modelled as X ~ N(148, 12^2). (a) Find P(X > 160). (2) (b) Find P(X < 130). (2) (c) A seed is described as 'slow' if it germinates in the slowest 10% of times. Find, to the nearest hour, the minimum germination time for a seed to be classed as 'slow'. (2) (d) State one reason why the normal distribution may not be a fully suitable model for germination time. (2)

  (Total for Question SECTION-A-STATISTICS1 is 8 marks)
• 2

  Question SECTION-A-STATISTICS2 (9 marks)

  A seed supplier claims that at most 35% of a particular batch of seeds will produce plants with red flowers. A gardener plants a random sample of 20 seeds from the batch and finds that 12 produce red flowers. The gardener suspects the true proportion producing red flowers exceeds 35%. (a) Write down suitable null and alternative hypotheses for a test of the gardener's suspicion. (2) (b) Using a 5% significance level, carry out the hypothesis test and state your conclusion in context. (5) (c) Find the critical region for this test at the 5% level. (2)

  (Total for Question SECTION-A-STATISTICS2 is 9 marks)
• 3

  Question SECTION-A-STATISTICS3 (8 marks)

  The number of faulty components Y in a randomly selected box of 15 mass-produced components is modelled as Y ~ B(15, 0.2). (a) Find P(Y = 3). (2) (b) Find P(Y <= 2). (2) (c) Find P(Y >= 4). (2) (d) State the mean and variance of Y. (2)

  (Total for Question SECTION-A-STATISTICS3 is 8 marks)
• 4

  Question SECTION-A-STATISTICS4 (9 marks)

  A climate researcher records, for 8 UK weather stations, the mean daily maximum temperature t (in degrees C) during June and the mean daily sunshine hours h. The product moment correlation coefficient between t and h for the sample is r = 0.86, and the equation of the regression line of h on t is h = -2.4 + 0.55t. (a) Describe the correlation between mean daily maximum temperature and mean daily sunshine hours. (2) (b) Interpret the value 0.55 in the context of this model. (2) (c) Use the regression equation to estimate the mean daily sunshine hours at a station with a mean daily maximum temperature of 21 degrees C. (2) (d) The researcher wishes to estimate the mean daily sunshine hours at a station where t = 34 degrees C. Give one reason why this estimate may be unreliable. (2) (e) Explain why it would not be sensible to use this regression line to estimate t from a known value of h. (1)

  (Total for Question SECTION-A-STATISTICS4 is 9 marks)
• 5

  Question SECTION-A-STATISTICS5 (8 marks)

  A discrete random variable X has probability distribution given by P(X = x) = kx for x = 1, 2, 3, 4, and P(X = x) = 0 otherwise, where k is a constant. (a) Show that k = 0.1. (2) (b) Find E(X). (2) (c) Find Var(X). (3) (d) Find E(2X - 5). (1)

  (Total for Question SECTION-A-STATISTICS5 is 8 marks)
• 6

  Question SECTION-A-STATISTICS6 (8 marks)

  A quality analyst at a bakery weighs a random sample of loaves. The masses, in grams, of the sampled loaves are summarised by n = 40, sum of x = 32160, sum of x^2 = 25 862 800. (a) Calculate the mean mass of the loaves in the sample. (1) (b) Show that the standard deviation of the masses is 12 g (to 2 significant figures). (3) (c) The bakery claims its loaves have a mean mass of 800 g. Using your answers, comment briefly on this claim. (2) (d) One loaf in the sample has a mass of 705 g. Determine whether this loaf is an outlier, using the rule that an outlier is any value more than 2 standard deviations from the mean. (2)

  (Total for Question SECTION-A-STATISTICS6 is 8 marks)

Section B: Mechanics

Mechanics modelling and problem-solving questions. Answer ALL questions.

• 1

  Question SECTION-B-MECHANICS1 (8 marks)

  [In this question use g = 9.8 m s^-2.] A small ball is projected from a point O on horizontal ground with speed 24.5 m s^-1 at an angle of 30 degrees above the horizontal. The ball is modelled as a particle moving freely under gravity. (a) Show that the initial vertical component of velocity is 12.25 m s^-1. (1) (b) Find the total time for which the ball is in the air before it first returns to the ground. (3) (c) Find the horizontal range of the ball. (2) (d) Find the greatest height reached by the ball above the ground. (2)

  (Total for Question SECTION-B-MECHANICS1 is 8 marks)
• 2

  Question SECTION-B-MECHANICS2 (9 marks)

  [In this question use g = 9.8 m s^-2.] Two particles A and B, of masses 3 kg and 5 kg respectively, are connected by a light inextensible string which passes over a smooth fixed pulley. The particles hang vertically and are released from rest with the string taut. (a) Find the acceleration of the particles. (4) (b) Find the tension in the string. (2) (c) After being released, particle B descends a distance of 1.2 m before it is momentarily brought to rest by hitting the floor. Find the speed of B just before it hits the floor. (3)

  (Total for Question SECTION-B-MECHANICS2 is 9 marks)
• 3

  Question SECTION-B-MECHANICS3 (8 marks)

  [In this question use g = 9.8 m s^-2.] A block of mass 8 kg is released from rest and slides down a rough plane inclined at 25 degrees to the horizontal. The coefficient of friction between the block and the plane is 0.3. The block is modelled as a particle. (a) Show that the normal reaction between the block and the plane is 71.1 N (to 3 significant figures). (2) (b) Find the frictional force acting on the block. (2) (c) Find the acceleration of the block down the plane. (4)

  (Total for Question SECTION-B-MECHANICS3 is 8 marks)
• 4

  Question SECTION-B-MECHANICS4 (9 marks)

  A particle P moves in a straight line. At time t seconds (t >= 0) its velocity v m s^-1 is given by v = 3t^2 - 12t + 9. (a) Find the values of t at which P is instantaneously at rest. (3) (b) Find the acceleration of P at time t = 2 s. (2) (c) Find the displacement of P from its starting point at time t = 3 s. (2) (d) Find the total distance travelled by P in the interval from t = 0 to t = 3 s. (2)

  (Total for Question SECTION-B-MECHANICS4 is 9 marks)
• 5

  Question SECTION-B-MECHANICS5 (8 marks)

  A uniform rod AB has length 3 m and mass 12 kg. The rod rests horizontally in equilibrium on two supports, P and Q, where P is 0.5 m from A and Q is 2.5 m from A. [Use g = 9.8 m s^-2.] (a) By taking moments about P, find the magnitude of the reaction on the rod at Q. (3) (b) Hence find the magnitude of the reaction on the rod at P. (2) (c) A particle of mass m kg is now attached to the rod at the end A. Given that the rod is on the point of tilting about Q, find the value of m. (3)

  (Total for Question SECTION-B-MECHANICS5 is 8 marks)
• 6

  Question SECTION-B-MECHANICS6 (8 marks)

  A particle of mass 0.5 kg moves in a horizontal plane. At time t seconds its position vector, in metres relative to a fixed origin O, is r = (3t^2 - 4t) i + (t^3 - 2t) j, where i and j are perpendicular unit vectors. (a) Find an expression for the velocity of the particle at time t. (2) (b) Find the speed of the particle when t = 2 s. (2) (c) Find the magnitude of the acceleration of the particle when t = 2 s. (2) (d) Find the magnitude of the resultant force acting on the particle when t = 2 s. (2)

  (Total for Question SECTION-B-MECHANICS6 is 8 marks)