PAPER E NAME: Date to be handed in: MARK (out of 60): Qu TOTAL

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1 NAME: PAPER E Date to be handed in: MARK (out of 60): Qu TOTAL Paper 2: Statistics and Mechanics Time 1 hour 15 minutes Practice Paper E Questions to revise: 1

2 SECTION A: Statistics 1. (a) Explain what is meant by a census. (b) Write down two disadvantages of using a census rather than a sample. Each circuit board produced at GC Electronics is given a unique serial number. GC Electronics produces circuit boards in batches of Before selling each batch, the company tests a random sample of 20 circuit boards from the batch to check that they will fit into a standard computer slot. (c) Suggest a suitable sampling frame from which to obtain this sample. (d) Identify the sampling units. (Total 4 marks) 2. On a randomly chosen day the probability that Bill travels to school by car, by bicycle or on foot is 2, 6 and 3 respectively. The probability of being late when using these methods of travel is 5, 5 and 10 respectively. (a) Draw a tree diagram to represent this situation. (b) Find the probability that on a randomly chosen day (i) Bill travels by foot and is late, (ii) Bill is not late. (Total 7 marks) 2

3 3. A random sample of distances travelled to work for 120 commuters from a train station in Devon is recorded. The distances travelled, to the nearest mile, are summarised below. Distance (to the nearest mile) Number of commuters For this distribution: (a) estimate the median. The mid-point of each class was represented by x and its corresponding frequency by f. The mid-point of the lowest class was taken to be 4.75 giving: Σfx = and Σfx 2 = (b) Estimate the mean and the standard deviation of this distribution. (c) Explain why the median is less than the mean for these data. (d) For a second random sample of 120 commuters travelling to work from a train station in Greater London, the mean distance travelled to work is 15.6 miles with standard deviation 21.2 miles. Compare the measures of location and spread for the distance travelled to work for the two samples, giving possible reasons for any differences. (Total 10 marks) 3

4 4. A manufacturer supplies MP3 players to retailers in batches of 20, which are randomly selected. Long-term analysis shows that 5% of the players are faulty. (a) Write down a suitable model for the distribution of the number of faulty MP3 players in a batch giving the value(s) of any parameter(s). (b) Find the probability that a batch contains no faulty MP3 players. (c) Show that the probability of there being more than 4 faulty MP3 players in a batch is equal to to 2 significant figures. (Total 6 marks) 4

5 SECTION B: Mechanics 5. A person runs across a field from point A to point B with a speed of 5.3 m s 1 and then runs back from point B to point A with a speed of 4.8 m s 1. Figure 1 Taking the positive direction as shown in the diagram, state the person s (a) velocity when travelling from A to B, (b) velocity when travelling from B to A. Another person runs 30 m from A in the exact opposite direction of B to a point C. (c) State this person s displacement from A at the point C. (Total 3 marks) 6. A car is initially travelling with a constant velocity of 15 m s 1 for T s. It then decelerates at a constant rate for s, reaching a velocity of 10 m s 1. It then immediately accelerates at a constant rate for s reaching a velocity of 20 m s 1. (a) Sketch a velocity time graph to illustrate the motion. (b) Given that the car travels a total distance of m over the journey described, find the value of T. (Total 7 marks) 5

6 7. A car of mass 1200 kg pulls a trailer of mass 400 kg along a straight horizontal road. The car and trailer are connected by a tow-rope modelled as a light inextensible rod. The engine of the car provides a constant driving force of 3200 N. The horizontal resistances of the car and the trailer are proportional to their respective masses. Given that the acceleration of the car and the trailer is 0.4 m s 2, (a) find the resistance to motion on the trailer, (b) find the tension in the tow-rope. When the car and trailer are travelling at 25 m s 1 the tow-rope breaks. Assuming that the resistances to motion remain unchanged, (c) find the distance the trailer travels before coming to a stop. (d) State how you have used the modelling assumption that the tow-rope is inextensible. (Total 12 marks) 8. A particle P travels in a straight line. At time t s, the displacement of P from a point O on the line is s m. At time t s, the acceleration of P is (12t 4) m s 2. When t = 1, s = 2 and when t = 3, s = 30. Find the displacement when t = 2. (Total 8 marks) TOTAL FOR THIS PAPER IS 60 MARKS 6