Pearson Edexcel Centre Number Candidate Number Level 3

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Write your name hereSurnamePearson EdexcelLevel 3 GCEOther namesCentre NumberCandidate NumberMathematicsAdvanced SubsidiaryPaper 3: Statistics and MechanicsSample Assessment Material for first teaching September 2017Time: 2 hoursPaper Reference9MA0/03You must have:Mathematical Formulae and Statistical Tables, calculatorTotal MarksCandidates may use any calculator permitted by Pearson regulations.Calculators must not have the facility for algebraic manipulation,differentiation and integration, or have retrievable mathematicalformulae stored in them.Instructionsblack ink or ball-point pen. UseIf pencil is used for diagrams/sketches/graphs it must be dark (HB or B).Fill in the boxes at the top of this page with your name, centrenumber and candidate number.There are two sections in this question paper. Answer all the questions in SectionA and all the questions in Section B.Answerthein the spaces provided – there may bequestionsmore space than you need.should show sufficient working to make your methods clear. YouAnswers without working may not gain full credit. Answers should be given to three significant figures unless otherwise stated.Information ATherebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.are 10 questions in this question paper. The total mark for this paper is 100. Themarks for each question are shown in brackets– use this as a guide as to how much time to spend on each question.Adviceeach question carefully before you start to answer it. ReadTry to answer every question.your answers if you have time at the end. CheckIf you change your mind about an answer, cross it out and put yournew answer and any working underneath.S60738A 2018 Pearson Education Ltd.1/1/Turn over

SECTION A: STATISTICS1. Kaff coffee is sold in packets. A seller measures the masses of the contents of a random sample of 90packets of Kaff coffee from her stock. The results are shown in the table below.DO NOT WRITE IN THIS AREAAnswer ALL questions. Write your answers in the spaces provided.A histogram is drawn and the class 245 w 248 is represented by a rectangle ofwidth 1.2 cm and height 10 cm.(3)(b) Use linear interpolation to estimate the median mass of the contents of apacket of Kaff coffee to 1 decimal place.(2)(c) Estimate the mean and the standard deviation of the mass of the contents ofa packet of Kaff coffee to 1 decimal place.(3)DO NOT WRITE IN THIS AREA(a) Calculate the width and the height of the rectangle representing theclass 255 w 260The seller claims that the mean mass of the contents of the packets is more than thestated mass.Given that the stated mass of the contents of a packet of Kaff coffee is 250 g and theactual standard deviation of the contents of a packet of Kaff coffee is 4 g,(e) Using your answers to parts (b) and (c), comment on the assumption that the massof the contents of a packet is normally distributed.(5)(1)*S54258A0221*DO NOT WRITE IN THIS AREA(d) test, using a 5% level of significance, whether or not the seller's claim is justified.State your hypotheses clearly.(You may assume that the mass of the contents of a packet is normally distributed.)

DO NOT WRITE IN THIS AREAQuestion 1 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 1 is 14 marks)53

(1)The researcher calculated the product moment correlation coefficient for the 7 placesand obtained r 0.658(b) Stating your hypotheses clearly, test at the 10% level of significance, whether ornot the product moment correlation coefficient for the population is greater thanzero.(c) Using your knowledge of the large data set, suggest the names of the 2 placeslabelled G and H.(e) Suggest how you could make better use of the large data set to investigate therelationship between daily mean temperature and daily total rainfall.(1)(1)(1)54DO NOT WRITE IN THIS AREA(d) Using your knowledge from the large data set, and with reference to thelocations of the 2 places labelled G and H, give a reason why these places havethe highest temperatures in July.(3)DO NOT WRITE IN THIS AREA(a) With reference to the scatter diagram, explain why a linear regression model maynot be suitable for the relationship between t and s.DO NOT WRITE IN THIS AREA2. A researcher believes that there is a linear relationship between dailymean temperature and daily total rainfall. The 7 places in the northernhemisphere from the large data set are used. The mean of the daily meantemperatures, t C, and the mean of the daily total rainfall, s mm, for themonth of July in 2015 are shown on the scatter diagram below.

DO NOT WRITE IN THIS AREAQuestion 2 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA*S54258A0521*557Turn over

DO NOT WRITE IN THIS AREAQuestion 2 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA*S54258A01921*1971Turn over

DO NOT WRITE IN THIS AREAQuestion 2 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 2 is 7 marks)*S54258A02121*2173

3. For a particular type of bulb, 36% grow into plants with blue flowers and the remaindergrow into plants with white flowers. Bulbs are sold in mixed bags of 40.(a) Find the probability that fewer than 2 of these bags will contain more bulbs thatgrow into plants with blue flowers than grow into plants with white flowers(4)Maggie takes a random sample of n bulbs.Using a normal approximation, the probability that more than 244 of these n bulbs willgrow into blue flowers is 0.0521 to 4 decimal places.(b) Find the value of n.DO NOT WRITE IN THIS AREARussell selects a random sample of 5 bags of bulbs.(6)DO NOT WRITE IN THIS AREA658*S54258A0621*DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREAQuestion 3 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 3 is 10 marks)*S54258A0721*759Turn over

DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA4. The Venn diagram shows the probabilities of students’ lunch boxes containing a drink,sandwiches and a chocolate bar.D is the event that a lunch box contains a drink,S is the event that a lunch box contains sandwiches,C is the event that a lunch box contains a chocolate bar,u, v and w are probabilities.(a) Write down(1)One day, 80 students each bring in a lunch box.Given that all 80 lunch boxes contain sandwiches and a drink,(b) estimate how many of these 80 lunch boxes will contain a chocolate bar.(3)DO NOT WRITE IN THIS AREA(7)

DO NOT WRITE IN THIS AREAQuestion 4 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 4 is 11 marks)

5. The lifetimes of batteries sold by company X are normally distributed, with mean 150 hoursand standard deviation 25 hours.(a) Find the expected number of these batteries that have a lifetime of more than 160 hours.(3)The lifetimes of batteries sold by company Y are normally distributed, with mean 160hours and 80% of these batteries have a lifetime of less than 180 hours.(b) Find the standard deviation of the lifetimes of batteries from company Y.(3)Both companies sell their batteries for the same price.(c) State which company you would recommend. Give reasons for your answer.DO NOT WRITE IN THIS AREAA box contains 12 batteries from company X.(2)DO NOT WRITE IN THIS AREA860*S54258A0821*DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREAQuestion 5 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 5 is 8 marks)TOTAL FOR SECTION A IS 50 MARKS*S54258A01921*1971Turn over

SECTION B: MECHANICSDO NOT WRITE IN THIS AREAAnswer ALL questions. Write your answers in the spaces provided.Unless otherwise indicated, whenever a numerical value of g is required, take g 9.8 m s–2and give your answer to either 2 significant figures or 3 significant figures.[In this question position vectors are given relative to a fixed origin O.]6. A particle, P, moves with constant acceleration (i – 2j) m s-2.At time t 0 seconds, the particle is at the point A with position vector (2i 5j) m and ismoving with velocity u m s-1.At time t 3 seconds, P is at the point B with position vector (–2.5i 8j) m.Find u.(4)DO NOT WRITE IN THIS AREA1264*S54258A01221*DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREAQuestion 6 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 6 is 4 marks)*S54258A01321*1365Turn over

7. A particle, P, moves under the action of a single force in such a way that at time t seconds,where t 0, its velocity v m s-1 is given byFind the time at which the magnitude of the force acting on P is 6.5 N.(7)DO NOT WRITE IN THIS AREAThe mass of P is 0.5 kg.v (t2 – 3t) i –12t jDO NOT WRITE IN THIS AREA1466*S54258A01421*DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREAQuestion 7 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 7 is 7 marks)*S54258A01521*1567Turn over

8.DO NOT WRITE IN THIS AREAA small box of mass 3 kg moves on a rough plane which is inclined at an angle of 20o tothe horizontal.The box is pulled up a line of greatest slope of the plane using a rope which is attached tothe box.The rope lies in the vertical plane which contains a line of greatest slope of the plane.The coefficient of friction between the box and the plane is 0.3.The tension in the rope is 25 N.The box is modelled as a particle, the rope is modelled as a light inextensible string and airresistance is ignored.(a) Using the model, find the acceleration of the box.(b) Suggest one improvement to the model that would make it more realistic.(7)DO NOT WRITE IN THIS AREAThe rope makes an angle of 30o with the plane, as shown in Figure 1.(1)The rope now breaks and the box slows down and comes to rest.(3)1668*S54258A01621*DO NOT WRITE IN THIS AREA(c) Show that, after the box comes to rest, it immediately starts to move down theplane.

DO NOT WRITE IN THIS AREAQuestion 8 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 8 is 11 marks)*S54258A01721*1769Turn over

A beam %, of mass 20 kg and length 3 m, is smoothly hinged to a vertical wall at one end .The beam is held in equilibrium in a horizontal position by a rope of length 1 m.One end of the rope is fixed to a point & on the wall which is vertically above .The other end of the rope is fixed to the point ' on the beam so that angle &' is 30R , asshown in Figure 2.The beam is modelled as a uniform rod and the rope is modelled as a light inextensible string.DO NOTNOT WRITE IN THIS AREADO NOTNOT WRITE IN THIS AREA9.8sing the model, findE WKH GLUHFWLRQ RI WKH IRUFH H[HUWHG E\ WKH ZDOO RQ WKH EHDP DW F ,I WKH URSH ZHUH QRW PRGHOOHG DV EHLQJ OLJKW VWDWH KRZ WKLV ZRXOG DIIHFW WKH WHQVLRQ LQ WKH URSH H[SODLQLQJ \RXU DQVZHU FDUHIXOO\ 7KH URSH LV QRZ UHPRYHG DQG UHSODFHG E\ D ORQJHU URSH ZKLFK LV VWLOO DWWDFKHG WR WKH ZDOO DW & EXW LV QRZ DWWDFKHG WR WKH EHDP DW * ZKHUH * LV WKH PLGSRLQW RI % 7KH EHDP % UHPDLQV LQ HTXLOLEULXP LQ D KRUL]RQWDO SRVLWLRQ G 6KRZ WKDW WKH IRUFH H[HUWHG E\ WKH ZDOO RQ WKH EHDP DW QRZ acts horizontally DO NOTNOT WRITE IN THIS AREA(a) Whe tension in the rope,

DO NOT WRITE IN THIS AREAQuestion 9 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 9 is 14 marks)*S54258A01721*1769Turn over

10.DO NOT WRITE IN THIS AREAA tennis player serves a ball so as to pass over the net.The ball is given an initial velocity of 45 m s-1 in a direction 10o below the horizontal.The ball is modelled as a particle moving freely under gravity.The ball passes over the net at a point which is vertically above B.Using the model,(a) find, in centimetres to 2 significant figures, the distance between the ball and the top ofthe net, as the ball passes over the net,(8)(b) find, to 2 significant figures, the speed of the ball as it passes over the net.(c) State two limitations of the model that could affect the reliability of youranswers.(4)(2)18*S54258A01821*DO NOT WRITE IN THIS AREA70DO NOT WRITE IN THIS AREAThe ball is struck at a point O which is 3.5 m vertically above the point A which is onhorizontal ground.The bottom of the net is the point B which is on the ground and AB 12 m.The height of the net is 1 m, as shown in Figure 3.

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DO NOT WRITE IN THIS AREAQuestion 10 continuedDO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA(Total for Question 10 is 14 marks)TOTAL FOR SECTION B IS 50 MARKSTOTAL FOR PAPER IS 100 MARKS2173

Pearson Edexcel Level 3 GCE Turn over *S54258A0221* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA SECTION A: STATISTICS Answer

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