Maths M1 CCEA GCSE Past Paper and Mark Scheme

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usually illustrated in the published mark scheme. GCSE MATHEMATICS The marks awarded for each question are shown in the right hand column and they are prefixed by the letters M, W and MW as appropriate. The key to the mark scheme is given below: M indicates marks for correct method. W indicates marks for working. MW indicates marks for combined method and working. The solution to a question gains marks for correct method and marks for an accurate working based on this method. Where the method is not correct no marks can be given. A later part of a question may require a candidate to use an answer obtained from an earlier part of the same question. A candidate who gets the wrong answer to the earlier part and goes on to the later part is naturally unaware that the wrong data is being used and is actually undertaking the solution of a parallel problem from the point at which the error occurred. If such a candidate continues to apply correct method, then the candidate's individual working must be followed through from the error. If no further errors are made, then the candidate is penalised only for the initial error. Solutions containing two or more working or transcription errors are treated in the same way. This process is usually referred to as "follow-through marking" and allows a candidate to gain credit for that part of a solution which follows a working or transcription error. Positive marking: It is our intention to reward candidates for any demonstration of relevant knowledge, skills or understanding. For this reason we adopt a policy of following through their answers, that is, having penalised a candidate for an error, we mark the succeeding parts of the question using the candidate's value or answers and award marks accordingly. Some common examples of this occur in the following cases: (a) a numerical error in one entry in a table of values might lead to several answers being incorrect, but these might not be essentially separate errors; (b) readings taken from candidates' inaccurate graphs may not agree with the answers expected but might be consistent with the graphs drawn. When the candidate misreads a question in such a way as to make the question easier only a proportion of the marks will be available (based on the professional judgement of the examining team). 12368.01 2 CE ea CE ea CE ea CE ea 1 Class 12P raised £275 for charity. Class 12T raised £312 for charity. (a) How much money was raised in total by the two classes? (b) How much more money was raised by Class 12T? 12368.05 R *32GMC1103* Answer £ Answer £ [1] [1] [Turn over General Marking Advice (i) If the correct answer is seen in the body of the script and the answer given in the answer line is clearly a transcription error, full marks should be awarded. (ii) If the answer is missing, but the correct answer is seen in the body of the script, full marks should be awarded. (iii) If the correct answer is seen in working but a completely different answer is seen in the answer space, then some marks will be awarded depending on the severity of the error. (iv) Work crossed out but not replaced should be marked. (v) In general, if two or more methods are offered, mark only the method that leads to the answer on the answer line, if two (or more) answers are offered (with no solution offered on the answer line), mark the poorest answer. (vi) For methods not provided for in the mark scheme, give as far as possible equivalent marks for equivalent work. (vii) Where a follow through mark is indicated on the mark scheme for a particular part question, the marker must ensure that you refer back to the answer of the previous part of the question. (viii) Unless the question asks for an answer to a specific degree of accuracy, always mark at the greatest number of significant figures seen, e.g. the answer in the mark scheme is 4.65 and the candidate then correctly rounds to 4.7 or 5 on the answer line. Allow full marks for 4.65 seen in the working. (ix) Anything in the mark scheme which is in brackets (...) is not required for the mark to be earned, but if present it must be correct. (x) For any question, the range of answers given in the mark scheme is inclusive. 12368.01 3 2 (a) Which shape below is a regular polygon? Circle your answer. (b) Which angle below is obtuse? Circle your answer. s (c) How many vertices has a cube? Circle your answer. 12368.05 R 8 6 *32GMC1104* 12 L 4 [1] [1] [1] ea ea lowing ea Lawning 180 18 180 180 ea ea Leaning lewning ea ning lowing ea Hing CE ning Ce ea Leaming 1 (a) 587 2 3 4 5 (b) 37 (a) Pentagon indicated (five-sided figure) (b) Obtuse angle indicated (last on right) (c) 8 (a) Math Ado About Nothing (b) 10 (c) Sum Like It Hot, Charlie's Angles Allow 1 for 195 minutes used. (a) Chihuahua (b) Kerry Blue Terrier (c) Chihuahua, Westie (a) Chris (b) Alf (c) Dave (d) 1.4 12368.01 4 A1 2 Al A1 Al Al Al A1 M1 Al Al A1 Al Al Al Al A1 A1 AVAILABLE MARKS 2 3 4 4 4 6 7 8 9 (a) 80 (b) 255-80 = 175 175 + 25 = 7 7+5=12 (a) 19 (b) June (c) February 2017 (a) (i) White (b) (i) 4 (ii) No numbers to put in order 12368.01 follow through for numerical error above provided 25 divides into value (a) 200+ 7.5 26.666... 26 (ii) (14+10+10.5 +13 +12.5) ÷ 5 M1 includes addition and division, Al for accurate values 12 correct answer gains 3 marks even without work shown (evidence of knowing to do this) (this value gains first 2 marks even if in answer space) (b) 26 x 7.5 195 (follow through for integer answer in (a)) 5 (c) £10-£4.70= £5.30 (mark gained for sight of 5.30) Pastie, Chips, Soft Drink 5 Al MA1 MA1 MA1 Al Al Al Al A1 A1 M1 Al MA1 MAI MA1 A1 MA1 Al MA1 Al AVAILABLE MARKS 4 3 6 7 CE CE ea CE Ba Ce CE ea 3 Barry downloads five films. The films and their lengths are shown. Sum Like It Hot 90 minutes (a) Which film is closest in length to two hours? Answer 12368.05 R Math Ado About Nothing 125 minutes The Times Tables Machine 85 minutes (b) Barry starts watching Sum Like It Hot at 8.30 pm. What time will the film end? Answer (c) Which two films have a total length of 3 hours and 15 minutes? and Charlie's Angles 105 minutes *32GMC1105* Answer 10² and 1 Dalmations 140 minutes [1] pm [1] [Turn over 4 The table shows information about ten dogs at an Animal Rescue Centre. Breed Basenji Basset Hound Boxer 12368.05 R Chihuahua Doberman Pinscher Fox Terrier Great Dane Kerry Blue Terrier Westie Whippet Size Medium Large Large Small Large Small Large Medium Small Medium Weight (kg) 11 23 33 2.3 40 8 72 17 8 15 (a) What breed has the longest average life expectancy? Answer (b) What breed is the heaviest of the medium size dogs? Recommended amount of food per day (grams) Answer *32GMC1106* 205 370 475 50 550 165 935 290 160 265 Average life expectancy (years) 13 12.5 9 16 11 11.5 8.5 13.5 13 13.5 [1] [1] ea ea lowing Lening 18₁0 181 ea ea Lawning ea glowning Lowning Ce ea flowing CE ea ning Ce ea Leaming 10 (a) 24 (b) 2 correct lines drawn (vertical and horizontal lines through middle of shape) 11 (a) Correct face drawn (rectangle 4 across and 5 down, attached to right-hand edge) (b) Evidence of 5, 2 and 4 5x2x4 40 12 (a) Correct points plotted (b) Point plotted at (x, -2) where -5<x<5 13 4x520 3+20= 23 with indication of Zach 14 (a) 16 (b) 32 (c) 12 (d) 9n = 54 6 12368.01 6 Al Al Al MA1 MA1 Al Al Al A1 Al Al Al Al A1 MA1 Al AVAILABLE MARKS 2 4 3 2 5 15 (a) 0, 1, 2, 6, 11 (award [1] for any 3 correct) (b) 7 16 8e-9w 18 (a) (i) 45 (ii) 38 (b) (i) Stay the same (ii) Stay the same (iii) Increase 17 1400 100 x 4 (oe) (or equivalent) 56 56 x 3 = 168 ans 168 gains 3 marks, ans 56 gains 2 marks, with or without work shown 19 Evidence of 160 cm and 80 cm as dimensions 160 + 160 + 80 + 80 (= 480 cm) 4.8 480 as answer gains 2 marks 20 38 x 9.80 = 372.40 2 11 473.90-372.40 = 101.50 101.50 14.50 = 7 follow through for numerical errors 12368.01 0 7 6 A2 A1 Al Al M1 MA1 Al A1 A1 A1 Al A1 MA1 MAI A1 MA1 MA1 A AVAILABLE MARKS 3 2 3 5 3 3 CE ea CE CE ea Ce CE ea (c) Victoria is looking for a dog that weighs no more than 15kg has a life expectancy of at least 12 years and eats less than 200 g of food per day 12368.05 R Which two breeds should she consider? Answer and *32GMC1107* [Turn over 5 The heights of five brothers are shown below. Alf 1.26m Bob They line up for a family photograph in order of height. (a) Who is the tallest? 1.07m (b) Who is in the middle of the photograph? Their times are shown below. Alf 12368.05 R 8.5 seconds The boys timed themselves running to the bottom of the garden. Chris 1.41 m Bob 9 seconds (c) Who has the fastest time? Chris 7.6 seconds Dave 1.30m Answer Answer *32GMC1108* Answer Dave (d) What is the difference between the times for Bob and Chris? 7.45 seconds Answer Eddie 1.18m Eddie [1] 3 8.07 seconds [1] seconds [1] ea ea Lawning 18 18 18 1 ea ea Leaning Lawning ea ning Ce ea flowing CE ning Ce ea Leaming 21 17:42 to 18:00 18 mins 18:00 to 20:00 = 2 hours 18 mins + 2 hours + 11 mins = 2 hours 29 mins correct ans of 2 hours and 29 mins or 149 mins gains 3 marks 22 12.8 100 x 5 (oe) 0.64 or 64p 13.44 23 (a) 6 points plotted correctly (4,43),(1,41),(9,48),(6,45),(5,46),(5,42) (award [1] for 3, 4 or 5 correct) (b) 5 (c) more, higher 24 (a) 4t (b) (i) 4t+21=49 (or similar, accept 4t = 28 but not t = 7) (ii) 4t=28 7 25 Garden Store: 480 ÷ 32 = 15 15 x 27 = 405 Perfect Patio: 480 ÷ 80 = 6 6 x 70=420 10% discount so final price 378 Quinn's Paving: 480+ 16 = 30 Needs to buy 25 boxes to get 30 25 x 17 = 425 Perfect Patio is the cheapest follow through for numerical errors, but not for use of incorrect methods in any of the three calculations 12368.01 8 MA1 MA1 Al MA1 MA1 Al A2 Al A1 Al Al ΜΑΙ A1 MA1 MA1 MA1 MA1 MA1 Al AVAILABLE MARKS 3 3 4 4 6 CE ea GE CE Ce CE ea 6 Jenny's Driving School 1st Lesson FREE Lessons 2-5: From Lesson 6: (a) Melanie books five lessons. 12368.05 R How much does this cost? £20 each £25 each lesson (b) Naomi books lessons costing a total of £255 How many lessons does she book? *32GMC1109* Answer £ Answer [1] [3] [Turn over 26 620 100 × 30 = 186 (or equivalent) 434 correct ans gains 3 marks 27 (a) QPR QRS = 65° (mark gained for angle QRS as 65 in diagram) TSR77° (may be marked in diagram) x = 180-(77 +65)= 38° (3 marks for correct ans) 12368.01 M1 A1 9 Al (b) No because 50+ 142 # 180° or because 65 + 103 # 180° or because the angles between the two lines do not add up to 180 so not parallel or because 38 # 50, corresponding. Allow Al for numerical error but correct argument MA1 MA1 MA1 A2 Total AVAILABLE MARKS 3 5 100 12368.01/2 7 The chart shows the number of rainy days each month over two years at Giant's Causeway. Number of rainy days 20 18 16 14 12 Number of rainy days each month at Giant's Causeway 12368.05 R 2016 2017 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month (a) How many rainy days were there in November 2016? (b) Based on the information shown which is the driest month? Answer There is only one month that had rain on exactly half of its days. (c) Which month and year is this? Answer Answer Month *32GMC1110* Year [1] 3 3 ea ea Low Lening ea ea ea lowning Ce ea ea flowing CE lening Ce ea Leaming CE ea GE ea CE Ce ea 8 (a) The colours of 10 cars were recorded as: red white black green white white blue grey blue yellow 12368.05 R (i) What is the modal colour of the cars? (ii) Explain why it is not possible to find the median colour of the cars. Answer (b) Five basketball players have the shoe sizes shown below. 101/2 14 Answer 10 (i) What is the range of the shoe sizes? (ii) Calculate the mean shoe size. *32GMC1111* 13 12/ Answer Answer [1] _ [¹] [1] [3] [Turn over 9 A supporters' club can buy match tickets for £7.50 each. They have £200 to spend. (a) What is the greatest number of tickets they can buy? (b) How much money will be left? (c) At the match there is food and drink for sale. 12368.05 R Burger Hot Dog Pastie Chips Soft Drink £3.50 £2.20 £1.60 £2.40 £1.30 Graeme has a £10 note. He buys three items and gets £4.70 change. What three items did he buy? Answer *32GMC1112* Answer Answer £ [3] ea ea clowning Ling ea ea ea Lening lewning ea Hening Ce ea Hing CE ea lening Ce ea Leaming CE ea CE ea CE Ce CE ea 10 A shape is drawn on a centimetre squared grid as shown below. (a) Work out the area of the shape. (b) Draw all the lines of symmetry on the shape. 12368.05 R *32GMC1113* Answer cm² [1] [1] [Turn over 11 Part of the net of a cuboid is drawn on centimetre squared paper. One face is missing. A (a) Complete the net by drawing the missing face. (b) The net is folded up to make a cuboid. Work out the volume of the cuboid. | 12368.05 R *32GMC1114* Answer [1] cm³ [3] ea ea Low ning ea ea Leaning ea ea Ce ea fing CE ea ning Ce ea Leaming CE ea CE ea CE ea CE GE ea 12 T YA 4- 12368.05 R 2- Look at the coordinate grid above. The point A (-2, 2) has been plotted for you. (a) Plot and label the points B (3, 2) and C (5,-2) on the grid. (b) Plot and label a point D on the grid so that ABCD is a trapezium. *32GMC1115* [2] [1] [Turn over 13 James and Zach are trying to find the value of James says it is 35 Zach thinks it is 23 Who is correct? Give a reason for your answer. Answer 12368.05 R because *32GMC1116* 3+4x5 ea ea ning ea pa Leaning Lawning Leaning ea Hing Lawning ea Hing CE ning Ce ea Leaming CE ea GE ea CE CE CE ea 14 Solve the equations (a) 5w=80 = 4 (c) 30= c + 18 (d) 9n-2=52 12368.05 R *32GMC1117* Answer w= Answer t = Answer C = Answer n = _ [1] [1] [1] [2] [Turn over 15 A sports team recorded information about whether players were able to play on Saturday only, Sunday only, or both. (a) Complete the two-way table below. Defenders Midfielders 12368.05 R Attackers Saturday only 16 Simplify the expression 5 4 (b) The team decides to play on Saturday. How many midfielders are able to play? Sunday only 2 *32GMC1118* 3 6 6e-5w+2e- 4w Both Saturday and Sunday Answer Answer 3 1 4 7 8 21 2 3 ea ea lowing Pa ning ea ea pa Leaning Lawning ea ning ea Ce ea Hing CE ning Ce ea Coming CE ea GE CE Ce ea CE ea 17 Jake earns £1400 each month. Every month he pays 4% of his earnings into a savings scheme. How much money will he have paid into this scheme after three months? 12368.05 R *32GMC1119* Answer £ [3] [Turn over 18 Martin asks 20 workers how many hours they normally work in a week. The results are shown in the stem and leaf diagram below. 0 1 2 3 4 5 8 3 2 2 0 1 (a) For the data above, work out (i) the range, (ii) the median. 12368.05 R 7 5 2 0 3 (ii) The range will (iii) The median will 8 4 2 Key 6 4 4 42 4 *32GMC1120* Answer means 42 hours Answer (b) Another worker normally works 39 hours in a week. This value is added to the stem and leaf diagram. Circle the correct word or words to make each of the following statements correct. (i) The mode will increase/decrease/stay the same [1] increase/decrease/stay the same 7 increase/decrease/stay the same 8 hours [1] hours [1] [1] [1] ea ea lowing Lowing ea ea Leaning Lawning ea wing lowing Ce ea ing CE ning Ce ea Coming CE ea CE ea CE Ce GE ea 19 A garden table is tiled using square tiles and rectangular tiles, as shown below. 20 cm 60 cm The tiled table looks like this. Work out the perimeter of the table. Give your answer in metres. 12368.05 R *32GMC1121* Answer 20 cm m [3] [Turn over 20 Louise normally works 38 hours per week and is paid £9.80 per hour. If she works any extra hours, she is paid at the overtime rate of £14.50 for each extra hour. Last week her total earnings were £473.90 How many extra hours did she work last week? 12368.05 R *32GMC1122* Answer [3] ea ea clowning ea ea Leaning lening ea Hening Lening Ce ea Hing CE ning Ce ea Leaming CE ea GE ea CE Ce CE GE ea 21 Wayne wants to travel from Glasgow to Carlisle by train. Glasgow Carlisle How long will this journey take? Depart Arrive Answer 22 Suzie notices this sign in her local takeaway. 12368.05 R 5% charge on card payments for orders under £15 She orders food costing £12.80 and decides to pay by card. How much will she have to pay in total? *32GMC1123* 17:42 20:11 Answer £ [3] [Turn over 23 A group of 10 people sat their driving theory test. Their driving instructor recorded how many practice tests they did and their score in the real test. The information is recorded in the table below. Person 12368.05 R Number of practice tests Real test score Real test score 50 (a) Show this information on the scatter graph below. The first four points have been plotted for you. 49 48 47 46 45 44 43 42 41 40 A B CD E F G H 0 2 5 42 44 41 45 43 1 7 2 1 *32GMC1124* 41 48 3 4 5 6 7 Number of practice tests H 8 45 46 42 9 J 10 ea ea Low ea lening ea ea Leaming ea Ce 18 18 18 1 ea flowing CE ning Ce ea Leaning CE ea CE CE Ce ea (b) The pass mark for the test is 44 How many of the 10 people passed the test? (c) Complete the statement: "In general, the 12368.05 R the practice tests completed, the test score." Answer *32GMC1125* [1] [1] [Turn over 24 A cinema ticket for an adult costs £t A cinema ticket for a child costs £3 James bought four adult tickets and seven child tickets. The total cost was £49 (a) Write down an expression for the cost of the four adult tickets. (b) (i) Form an equation that can be solved to find the cost of an adult ticket. 12368.05 R Answer Answer (ii) Solve your equation to find the cost of an adult ticket. *32GMC1126* Answer t = 3 [1] ea ea lowing leaning ea ea Leaning leng ea lening Ce ea Hing CE ea lening Ce ea Coming CE CE GE CE CE ea 25 Bob is going to pave a patio. He needs 480 paving slabs. He looks in three different stores. Garden Store 12368.05 R 32 slabs in a box Box price = £27 Perfect Patio Store 80 slabs in a box Box price = £70 10% discount on 5 or more boxes Which store will be the cheapest for him to buy the slabs in? Show all your working. Answer *32GMC1127* Quinn's Paving Store 16 slabs in a box Box price = £17 Buy 5 boxes, get one extra box free [6] [Turn over 26 The price of a phone was £620 The price is reduced by 30%. Calculate the new price. 12368.05 R *32GMC1128* Answer £ ea ea clowning ea ea Leaming lening ea Lening Ce ea flowing CE ning Ce ea Looming CE ea CE ea CE ea CE ea 27 P Triangle PQR is isosceles with PQ = QR. (a) Calculate the size of angle x 12368.05 R because 50° 103° S (b) Hence decide if the lines PQ and ST are parallel. T X *32GMC1129* R Answer diagram not drawn accurately THIS IS THE END OF THE QUESTION PAPER _° [3] [2] 12368.05 R BLANK PAGE DO NOT WRITE ON THIS PAGE *32GMC1130* ea ea clowning ea owning ea ea ea Leaming Hewang ea Ce ea Hing CE ning Ce ea Leaming CE ea CE ea CE Ce CE ea 12368.05 R BLANK PAGE DO NOT WRITE ON THIS PAGE *32GMC1131* DO NOT WRITE ON THIS PAGE Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright holders may have been unsuccessful and CCEA will be happy to rectify any omissions of acknowledgement in future if notified.. 12368.05 R *32GMC1132* Examiner Number For Examiner's use only Question Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Total Marks Marks