Pearson Edexcel Level 1 / Level 2 GCSE (9-1) In .

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Pearson Edexcel Level 1 /Level 2 GCSE (9-1) inMathematics (1MA1)MOCK (AUTUMN 2016) MODEL ANSWERSFirst certification 2017 Pearson Education Ltd 2016

ContentsContents . 2About this booklet. 3Paper 1F . 41F/1H Common Questions . 8Paper 1H . 12Paper 2F . 192F/2H Common Questions . 26Paper 2H . 28Paper 3F . 35Paper 3F/3H Common Questions . 39Paper 3H . 45 Pearson Education Ltd 2016

About this bookletThis booklet has been produced to support mathematics teachers delivering the newGCSE (9–1) in Mathematics specification (first assessment summer 2017).This booklet provides model answers for problem-solving questions, exemplifying someof the problem-solving strategies.The questions in this booklet have been drawn from the Autumn 2016 Mock Papers. Thequestions selected are those where most of the marks assess AO3 Solve problems withinmathematics and in other contexts.In each pair of Foundation and Higher tier papers, there are common questions thatappear at each tier; in this booklet we have provided the model answers for commonquestions at Higher tier only, but the following selected questions also appear on theFoundation tier papers:1F Q19 1H Q31F Q20 1H Q41F Q21 1H Q52F Q26 2H Q43F Q18 3H Q13F Q20 3H Q33F Q23 3H Q63F Q24 3H Q7 Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1FPaper 1F6penpencilruler32p8p17pRosie has 15 to spend on pens and pencils.She has to buy the same number of pens as pencils.What is the greatest number of pens she can buy?Cost of 1 pen 1 pencil 32p 8p 40p 0.40Finding the amount of sets she can buy for 1515 0.4 150 4 37.5Rosie does not have enough money to buy the 38th pen and pencil sothe answer is rounded down.Alternative Method5 210 430 1235 1436 14.4037 14.40 – not enough money for 38.(Total for Question 6 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1F9The formulae below can be used to work out the cost, C, of a taxi journey of x mileswith three different taxi companies.Which is the cheapest company to use for a taxi journey of 30 miles?You must show how you get your answer.Using a tableCompanyFormula, using x 30Total costReliable TaxisC 1.5 30 45.00Speedy TaxisC (1.1 30) 11.5 44.50City TaxisC (1.25 30) 8 45.50CompareSpeedy Taxis is the cheapest company to use at 44.50 for the totalcost of the journey.(Total for Question 9 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1F13This shape is made from two rectangles.2 cm5 cm2 cm7 cm(a) Work out an estimate for the total area of the shape.Using simpler numbers,estimates for all given sides written on the diagramUsing a flow diagram,Calculate the area of the smaller rectangleCalculate the area of the larger rectangleAdd these two areas together to give thearea of the combined shapeArea of smaller rectangle 2 2 4 cm2Area of larger rectangle 7 5 35 cm2Total area of combined shape 4 35 39cm2. cm2(3)(b) Is your answer to (a) an overestimate or an underestimate?Give a reason for your answer.The answer to (a) is an underestimate because all numbers have beenrounded down. 2cm is less than 2.05cm, 2cm is less than 2.15cm, 7cmis less than 7.37cm and 5cm is less than 5.02cm, therefore theanswer of 39 cm2 will be less than the actual answer.(1)(Total for Question 13 is 4 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1F15ABCD is a kite with AD AB98 98 360 - (116 98 98 )Find the size of the smallest angle of the kite.Using x for the unknown and adding to the diagram,Angles B and D are the same, soRearranging givesSolving for x5x – 147 2x3x 147x 147 3Angle B 2xSubstituting x 49 into the equation,Angle B 2 49 98 which is also equal to angle DAll angles in a quadrilateral sum to 360 , so missing angle C isequal to360 – (116 98 98) 48 . (Total for Question 15 is 4 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1),Paper 1F/1H Common Questions1F/1H Common Questions3ABCDE is a pentagon.3cm4cmWork out the area of ABCDE.Using flow diagrams and adding to the diagram,Divide pentagon into simpler shapes (rectangles and triangles)Calculate perpendicular height of the triangleCalculate area of the triangleCalculate area of the rectangleCalculate area of ABCDE by adding these two areas togetherUsing Pythagoras’ theorem to find height of triangle,52 42 c252 42 c2c 52 -42 3Area of triangle (base height) 2 (8 3) 12 cm2Area of rectangle base height 4 8 32 cm2Area of ABCDE 12 cm2 32 cm2 44 cm2(Total for Question 3 is 5 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1),Paper 1F/1H Common Questions4On Monday, Tarek travelled by train from Manchester to London.Tarek’s train left Manchester at 08 35It got to London at 11 05The train travelled at an average speed of 110 miles per hour.On Wednesday, Gill travelled by train from Manchester to London.Gill’s train also left at 08 35 but was diverted.The train had to travel an extra 37 miles.The train got to London at 11 35Work out the difference between the average speed of Tarek’s train and the average speedof Gill’s train.In order to calculate Gill’s average speed, we need to know thedistance from Manchester to London.Tarek’s journey time from 08 35 to 11 05 is 2.5 hours.Using a diagram,distanced speed time 110 2.5 275 milesstGill’s journey time from 08 35 to 11 35 is 3 hours.Gill’s average speed distance time (275 37) 3 104 miles per hourDifference between the average speed of Tarek’s train and theaverage speed of Gill’s train is110 – 104 6 miles per hour. miles per hour(Total for Question 4 is 4 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1),Paper 1F/1H Common Questions5The diagram shows a rectangular wall.Frank is going to cover the wall with rectangular tiles.Each tile is 60 cm by 30 cm.3of the tiles will be white.5Some of the tiles will be green.The rest of the tiles will be blue.The ratio of the number of green tiles to the number of blue tiles will be 1 : 3(a) Assuming there are no gaps between the tiles, how many tiles of each colour will Frank need?30cm60cm1.8m6mArranged to fit the wall with 3 rows of 20, there are 60 tiles intotal.Using bar models,601515151515121212121236so 36 tiles are white.ORWhite tiles 35of 60 60 5 3 36The number of tiles remaining are 60 – 36 24 Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1),Paper 1F/1H Common QuestionsThe remaining 24 tiles will be green and blue in a ratio of 1:324 tiles into 4 parts 24 4 6 tiles per partUsing bar models,246666OR1 part 6 tilesGreen tiles 6 1 6Blue tiles 6 3 18There are 6 green tiles and 18 blue tiles.White tiles 36Green tiles 6Blue tiles 18white tiles .green tiles .blue tiles .(5)Frank is told that he should leave gaps between the tiles.(b) If Frank leaves gaps between the tiles, how could this affect the number of tiles heneeds?Frank may need fewer tiles.(1)(Total for Question 5 is 6 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1HPaper 1H9A company orders a number of bottles from a factory.The 8 machines in the factory could make all the bottles in 5 days.All the machines work at the same rate.For 2 days, only 4 machines are used to make the bottles.From the 3rd day, all 8 machines are used to make the bottles.Work out the total number of days taken to make all the bottles.Using bar models,Machine12345678Days55555555 40machine days40 machine days are required to make all the bottles.4 machines are used for 2 daysMachine1234Days2222 8 machine daysThere are 40 - 8 32 more machine days needed to complete the job.8 machines are used for the remainder of days until completionMachine12345678Days? 32machine days32 8 4 daysTotal time taken to make all the bottles is 2 4 6 days Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1HORMachine days needed 8 5 404 machines working for 2 days 4 2 8 machine daysThere are 40 - 8 32 more machine days needed to complete the job.Using x for the unknown,8 machines working for x days 8x 32 machine daysx 32 8 4 daysTotal time taken to make all the bottles is 2 4 6 daysOR4 machines for 2 days 8 machines for 1 dayTherefore, only one extra day required giving a total of 6 days.OR8 machines for 5 days 100%8 machines for 1 day 20%4 machines for 1 day 10%4 machines for 2 days 20%80% remaining which is 4 days with 8 machines. Giving a total of 6days. days(Total for Question 9 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1H15Here is a sketch of a vertical cross section through the centre of a bowl.The cross section is the shaded region between the curve and the x-axis.The curve has equationy x2 3x where x and y are both measured in centimetres.10Find the depth of the bowl.Using graphs,The curve hits the x-axis where y 0, sox2 3x 0101𝑥 (10 𝑥 3) 0, so1𝑥10 3 01𝑥10 3, so𝑥 0 and𝑥 30The depth of the bowl is therefore the y value at x 30 2 15Substituting x into the equation of the curve,𝑦 15210̶ (3 15) 22.5 45 -22.5The depth of the bowl is 22.5cm. cm(Total for Question 15 is 4 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1H18The diagram shows the first 10 sides of a spiral pattern.It also gives the lengths, in cm, of the first 5 sides.The lengths, in cm, of the sides of the spiral form a sequence.Find an expression in terms of n for the length, in cm, of the nth side.Looking for patterns,1.535.51.52.5193.5113.54.5First differences1Second differencesCommon second differences, therefore sides of the spiral form aquadratic sequence. If the second difference is 2, we start with n2,but the second difference is 1 so we start with ½ n2Using a table,nLengthn2½ n2½ n2 n expression for the length of the nth side is therefore ½ n2 1(Total for Question 18 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1H23The histogram shows information about the ages of the members of a footballsupporters club.There are 20 members aged between 25 and 30One member of the club is chosen at random.What is the probability that this member is more than 30 years old?Using flow diagrams,Find frequency density of 25-30 barFind frequency of all other barsFind probability25-30 yearsFrequency density frequency class width 20 5 4Marking the scale on the y-axis on the graph, we can now calculatefrequencies of the other bars. Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1HUsing a table,Age (years)Frequency density Frequencyclass width0-100.7 10710-252 153025-302030-502.6 205250-800.3 309Total118Members over 3052 9 61Probability of member being over 30 Members over 30 Total members 61118.(Total for Question 23 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 1H24There are6 black counters and 4 white counters in bag A7 black counters and 3 white counters in bag B5 black counters and 5 white counters in bag CBernie takes at random a counter from bag A and puts the counter in bag B.He then takes at random a counter from bag B and puts the counter in bag C.Find the probability that there are now more black counters than white counters in bag C.There are more black counters than white counters in bag C if thecounter Bernie takes from bag B is black.There are two scenarios:A black counter is taken from bag A and thena black counter is taken from bag BORA white counter is taken from bag A and thena black counter is taken from bag B.Using bar models,AIf a black counter is chosen, bag B will have 8 black and 3 white:BIf a white counter is chosen, bag B will have 7 black and 4 white:BThe probability of the first scenario is thereforeprobability of the second scenario is410 610 811and the711The probability of either of these scenarios is therefore6(10 8)114 (10 7)11 4828 110110 76110(Total for Question 24 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2HPaper 2F7Here is a regular hexagon.There are six identical hexagons.Three of the hexagons are joined to make shape A.The other three hexagons are joined to make shape B.6527134438291101251161114127101389Which shape has the greater perimeter, shape A or shape B?You must show how you get your answer.Using diagrams,Counting the sides (labelled on diagram), Shape A has 14 sides andShape B has 12 sides.Shape A therefore has the greatest perimeter.(Total for Question 7 is 2 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2H13Drinks and snacks can be bought in a cinema.Laura is going to buy one drink and two different snacks.Work out the most money that Laura can save by using the Special Offer.Laura saves the most money by purchasing the most expensive items,so we add these items together to get the total price without usingthe Special Offer. 1.50 1.75 1.60 4.85Using bar models to find the money saved using the Special Offer, 4.85 3.99?Amount saved 4.85 - 3.99 0.86 86p.(Total for Question 13 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2H15Jake is going to make a path from small paving stones and large paving stones.The diagram shows Jake’s design for the path.The rest of the path is made using the same pattern of paving stones.121673452389 10A small paving stone costs 2.30A large paving stone costs 3.65Jake needs to buy enough paving stones to make a path that is 6 metres long.(a) How much will Jake have to pay for the paving stones he needs?Using the diagram to count how many of each type of tile, there are10 small paving stones and 3 large paving stones in each 1.5msection.Using bar models to find the total cost of each 1.5m section, 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 4.60 6.90 9.20 11.50 13.80 16.10 18.40 20.70 23.00 3.65 3.65 3.65 3.65 7.30 10.95Total cost of each 1.5m section 23.00 10.95 33.95ORCost of each 1.5m section (10 2.30) (3 3.65) 23.00 10.95 33.95There are 6 1.5 4 of these sectionsTherefore the total cost is 4 33.95 135.80 .(4) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2HHarry designs a different path that is also 6 metres long using the large paving stones.Harry says that the cost of his path will be less than half of the cost of the path that Jakedesigned.(b) Is Harry correct?You must show how you get your answer.Harry’s pattern uses 6 large paving stones that cost 3.65 each,Therefore the cost of each 1.5 section is6 3.65 21.90From part (a), we know that there are 4 of these 1.5m sections, sothe total cost is21.90 4 87.60Half the cost of Jake’s path is135.80 2 67.90Comparing these costs, 87.60 67.90Therefore Harry’s path costs more than half the cost of Jake’s pathand Harry is wrong.(2)(Total for Question 15 is 6 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2H16In September Sharon paid 565 for some books.She sold all the books for a total of 780In October Sharon bought and sold some more books.The total profit she made in October was 13% greater than the total profit she made in September.In November Sharon wants to pay a bill of 30Sharon thinks that the 13% extra profit she made in October will be enough to pay this bill.Is Sharon correct?You must show all your working.Using flow diagrams,Calculate September’s profitCalculate October’s profitCompare October’s profit with bill of 30Using bar models, 780 565?September profit Price books sold for - price books bought for 780 - 565 215Finding 13% of 215 using bar models, 21.5010% 21.5020% 21.5030% 21.5040% 21.5050% 21.5060% 21.5070% 21.5080% 21.5090% 21.50100% 2.151% 2.152% 2.153% 2.154% 2.155% 2.156% 2.157% 2.158% 2.159% 2.1510%The extra profit made in October is13% of 215 21.50 2.15 2.15 2.15 27.95OR13% of 215 215 100 13 27.95OR13% of 215 0.13 215 27.95 27.95 30, so the extra profit is not enough to pay the bill.(Total for Question 16 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2H20The diagram shows a shape made by overlapping two identical squares.341434The area of the shaded region is 25% of the area of each square.Work out what fraction of the area of the whole shape is shaded.Labelling the diagram,Whole shape 1434 34 74The fraction of the area of the whole shape that is shaded is,Using x for the unknown,x ofx74 14 14 74 17ORWhole shape 25% 75% 75% 175%Fraction Shaded 25175 17.(Total for Question 20 is 3 marks) Pearson Education Ltd 2016

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1), Paper 2H21There are 240 students in Year 7 at a school.The pie chart shows the proportion of boys and the proportion of girls in Year 7.There are 8 more girls in Year 8 than in Year 7.There are 32 fewer boys in Year 8 than in Year 7.Andy draws a pie chart to show the proportion of boys and the proportion of girls in Year 8Work out the angle of the sector in Andy’s pie chart that represents girls.Using flow diagrams,Find number of girls in Year 7Find total number of students in Year 8Find number of girls in Year 8Find angle for girls in Year 8177360Number of girls in Year 7 240 118Year 8 girls 118 8 126Year 8 boys (240 - 118) - 32 90Total number of students in Year 8 Year 8 girls Year 8 boys 126 90 216Angle for girls in Year 8 Girls in Year 8 360 Total students in Year 8

(b) Is your answer to (a) an overestimate or an underestimate? Give a reason for your answer. The answer to (a) is an underestimate because all numbers have been rounded down. 2cm is less than 2.05cm, 2cm is less than 2.15cm, 7cm is less than 7.37cm and 5cm is less than 5.02cm, therefore the answer of 39 cm2 will be less than the actual answer.

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