WJEC+Eduqas+GCSE+Maths+SAMs+-+FINAL+%2826.6.15%29

GCSE MATHEMATICS Sample Assessment Materials 101 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS COMPONENT 2 Calculator-Allowed Mathematics Foundation Tier SPECIMEN PAPER 2 hours 15 minutes ADDITIONAL MATERIALS For Examiner’s use only A calculator will be required for this examination. A ruler, protractor and a pair of compasses may be Question Maximum Mark required. Mark Awarded 1. 6 INSTRUCTIONS TO CANDIDATES 2. 2 Write your name, centre number and candidate number in 3. 2 the spaces at the top of this page. 4. 3 5. 2 Answer all the questions in the spaces provided in this 6. 4 booklet. 7. 2 8. 6 Take π as 3∙14 or use the π button on your calculator. 9. 4 10. 3 INFORMATION FOR CANDIDATES 11. 3 12. 2 You should give details of your method of solution when 13. 5 appropriate. 14. 5 15. 5 Unless stated, diagrams are not drawn to scale. 16. 5 17. 4 Scale drawing solutions will not be acceptable where you 18. 5 are asked to calculate. 19. 4 20. 6 The number of marks is given in brackets at the end of 21. 3 each question or part-question. 22. 4 23. 7 You are reminded of the need for good English and orderly, 24. 3 clear presentation in your answers. 25. 5 26. 2 No certificate will be awarded to a candidate detected in 27. 6 any unfair practice during the examination. 28. 4 29. 4 30. 4 TOTAL 120 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 102 Formula list Area and volume formulae Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone: Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a sphere  4 πr3 3 Volume of a cone  1 πr2h 3 Kinematics formulae Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t = 0 and t is time taken: v  u  at s  ut  1 at2 2 v2  u2  2as © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 103 1. (a) Lisa buys the following items from an online music store. [3] Complete her bill. Item Cost 10 badges at 85p each £ 3 T-shirts at £7.95 each £ 20 blank CDs at £2.49 per pack of 5 £ Total £ ....................................................................................................................................... ....................................................................................................................................... (b) The online store gives free delivery when the total cost is £50 or over. How much more does Lisa need to spend to get free delivery? [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (c) The music store also has a special offer on music-video downloads. Download one music-video for £1.99 SPECIAL OFFER TODAY 3 for the price of 2 What is the cost of 9 music-video downloads with this special offer? [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 104 2. Circle the numbers that are multiples of both 3 and 4. [2] 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 105 3. Seven numbered cards are placed face down. 1 2 7 8 9 11 15 One card is chosen at random. What is the probability that the card chosen will have: (a) an odd number? [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) a number greater than 8? [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 106 4. In a school, 3 of the pupils are girls. 5 There are 390 girls in the school. Calculate the total number of pupils in the school. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 107 5. A square ABCD has sides of length 5 units. Find the coordinates of point C. [2] x O Diagram not drawn to scale Coordinates of C = (………………. , ………………) © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 108 6. Charlie has x pens. [4] Lisa has 3 more pens than Charlie. Julian has twice as many pens as Lisa. How many pens do Charlie, Lisa and Julian have altogether? Simplify your answer as far as possible. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 109 7. A single lap of an athletics track is 400 metres. [2] How many laps will a person run in a two kilometre race? ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 110 8. A fashion store buys 200 bracelets for £6.30 each. [6] The store sells 60% of the bracelets for £10 each. The remaining bracelets are later sold at a reduced price of £4 each. How much profit or loss did the fashion store make? You must show all your working. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 111 9. (a) Solve 4x  16. [1] ....................................................................................................................................... ....................................................................................................................................... (b) Solve y  4. [1] 5 ....................................................................................................................................... ....................................................................................................................................... (c) Solve 5a 8 17. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 112 10. Angela plays netball for her local team. The number of goals she has scored in her first seven games is 3, 4, 5, 5, 6, 8 and 9. (a) Explain why the mode is 5. [1] ....................................................................................................................................... ....................................................................................................................................... (b) Angela’s coach thinks that it is possible for Angela to achieve a median of 6 and a range of 7 after two more games are completed. Give a possible number of goals scored in each of the next two games that would allow Angela to achieve this. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 113 11. Using the formula below, find the value of k when p = 50 and q = 10. [3] You must show all your working. 2q = p – 10k ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 114 12. Kyle and Ethan play a game using a spinner. A player wins when the spinner stops on their chosen colour. A player can choose from the colours Yellow (Y), Black (B) or Red (R). Kyle always chooses Red. Ethan always chooses Yellow. Which of the following spinners should Ethan choose so that he has the greatest chance of beating Kyle? Give a reason for your answer. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 115 13. Martin prefers to measure distances in kilometres rather than miles. The following table shows the number of miles and the number of kilometres for each of three distances. Miles 5 30 42·5 Kilometres 8 48 68 (a) Use the data in the table to draw a conversion graph. [3] © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 116 (b) The distance between Martin’s house and his favourite bicycle shop is 70 miles. Explain how he can use the graph to find this distance in kilometres. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Complete the following sentence: 70 miles is approximately ................................................ km. [2] © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 117 14. To fill in a block, you must add the values on the two blocks directly below it. [2] Some values are already displayed. Fill in the empty blocks. You must simplify your answer. (a) 8x 3x 2x x (b) [3] 9x –2x+y 5x © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 118 15. On 1 January 2014, Jasmine weighed 84 kg and was overweight for her height. By eating healthy food and exercising she lost 6% of her body weight during the first three months of 2014. Her weight then remained the same for the next two months. During June, Jasmine cycled every day and, by doing so, she lost 2·8% of her April body weight. (a) Calculate Jasmine’s body weight at the end of June. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) What percentage of her original body weight did Jasmine lose in these six months? [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 119 16. On an island there are two companies that hire out fishing boats to visitors. Fishing Boats R Us Ocean Blue Boats Hire charges Hire charges £45 for first hour £32 per hour then £30 per hour (or part of an hour) (or part of an hour) Robert wants to hire a boat to go fishing with his friends. He needs the boat from 9:15 a.m. to 5:30 p.m. Which company would you advise Robert to use? Show all your working and a give a reason for your answer. [5] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 120 17. Faizal has £400. He spends 1 of it on rent and 2 of it on food. 45 What fraction does he have left? Write your answer in its simplest terms. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 121 18. (a) What percentage is £95 of £250? [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) The total cost of 6 copies of a magazine and 4 copies of a newspaper is £29.04. The magazines cost £4.12 each. Find the cost of one newspaper. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 122 19. A cuboid with length 45 cm, width 20 cm and height 35 cm is completely filled with water. The water is then poured into a larger cuboid with length 100 cm and width 15 cm. Calculate the height of the water in the larger cuboid. Show all your working. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 123 20. A team of examiners has 48 000 examination papers to mark. It takes each examiner 1 hour to mark approximately 16 papers. (a) The chief examiner says that a team of 25 examiners could mark all 48 000 papers in 8 days. What assumption has the chief examiner made? You must show all your calculations to support your answer. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) Why is the chief examiner’s assumption unrealistic? What effect will this have on the number of days the marking will take? [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 124 21. Nancy makes two statements about the probability of events based on throwing fair dice. For each of her statements below, decide whether or not Nancy is correct. You must explain your decisions using probabilities. The probability of throwing a three on a dice is half the probability of throwing a six. Is Nancy correct? ........................... Explanation: [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... The probability of throwing a double six on two dice is 2 . 6 Is Nancy correct? ........................... Explanation: [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 125 22. Complete the table below. After a decrease of Original amount 40% 2% £ ……..…. £492 £ ……..…. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 126 23. Eliza makes this sketch of a pond. Diagram not drawn to scale The shortest distance across the pond is 6 m. The longest distance across the pond is 20 m. Eliza estimates that the surface area of the pond is 120 m2. (a) Explain how Eliza arrived at her estimate. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) Calculate an estimate for the surface area of the pond that would be more accurate than Eliza’s estimate. Explain how you have decided to calculate your estimate. You must justify your decision. Show all of your working. [5] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 127 24 A survey is carried out by asking people questions as they come out of a juice bar. A section of the questionnaire is shown below. (a) Explain why this is a biased survey. [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) State two criticisms of the design of question 1. [2] First criticism of question 1: ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... Second criticism of question 1: ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 128 25. The diagram shows a square. All the lengths are measured in centimetres. Diagram not drawn to scale Use an algebraic method to find the length of one side of the square. [5] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 129 26. Find the nth term of the sequence 6, 13, 20, 27, … [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 130 27. (a) When visiting a hat shop, each customer had the circumference of their head measured. The table shows the results for the customers who bought a hat during December. Head circumference, c (cm) Number of customers 50 < c < 54 12 54 < c < 58 32 58 < c < 62 14 62 < c < 66 2 Calculate an estimate for the mean head circumference. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) The hat shop sells 4 different sizes of hats. The conversion table from head circumference to hat size is shown below Head circumference, c (cm) Hat size 50 < c < 54 1 54 < c < 58 2 58 < c < 62 3 62 < c < 66 4 A salesman places an order for new stock for the hat shop. The salesman’s order form shows that about half of the hats ordered are size 2. The owner of the shop says the order should show that about a quarter of the hats ordered are size 2. Who is more likely to be correct, the salesman or the owner of the shop? You must give a reason for your answer. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 131 28. A statue is on display inside a glass cuboid. A scale drawing of the plan view (bird’s eye or aerial view) of the cuboid is shown below. Scale 1 cm : 20 cm A barrier is built around the cuboid so that no one can stand within 60 cm of the cuboid. Using the given scale, draw accurately the barrier on the scale drawing shown below. [4] © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 132 29. A man is working out the height of a vertical tree. The man is able to measure the angle of elevation of the top of the tree from his measuring instrument. The measuring instrument is 1∙8 m above ground level. When the man is standing 19 m from the base of the tree, the angle he measures is 56°. A sketch of this situation is shown below. Diagram not drawn to scale Calculate the full height of the tree. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 133 30. (a) A cube of weight 10 N rests on horizontal ground. The area of each face of the cube is 0·2 m2. Calculate the pressure exerted by the cube on the ground. State the units of your answer. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) A different cube also has a weight of 10 N. The area of each face of this cube is x m2. Find an expression for the pressure exerted by this cube on the ground. Give your answer in terms of x. [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.



GCSE MATHEMATICS Sample Assessment Materials 135 COMPONENT 1: NON-CALCULATOR MATHEMATICS, HIGHER TIER GENERAL INSTRUCTIONS for MARKING GCSE Mathematics 1. The mark scheme should be applied precisely and no departure made from it. Marks should be awarded directly as indicated and no further subdivision made. When a candidate follows a method that does not correspond to the methods explicitly set out in the mark scheme, marks should be awarded in the spirit of the mark scheme. In such cases, further advice should be sought from the Team Leader or Principal Examiner. 2. Marking Abbreviations The following may be used in marking schemes or in the marking of scripts to indicate reasons for the marks awarded. CAO = correct answer only MR = misread PA = premature approximation bod = benefit of doubt oe = or equivalent si = seen or implied ISW = ignore subsequent working F.T. = follow through ( indicates correct working following an error and indicates a further error has been made) Anything given in brackets in the marking scheme is expected but, not required, to gain credit. 3. Premature Approximation A candidate who approximates prematurely and then proceeds correctly to a final answer loses 1 mark as directed by the Principal Examiner. 4. Misreads When the data of a question is misread in such a way as not to alter the aim or difficulty of a question, follow through the working and allot marks for the candidates' answers as on the scheme using the new data. This is only applicable if a wrong value, is used consistently throughout a solution; if the correct value appears anywhere, the solution is not classed as MR (but may, of course, still earn other marks). 5. Marking codes  ‘M' marks are awarded for any correct method applied to appropriate working, even though a numerical error may be involved. Once earned they cannot be lost.  ‘m’ marks are dependant method marks. They are only given if the relevant previous ‘M’ mark has been earned.  ‘A' marks are given for a numerically correct stage, for a correct result or for an answer lying within a specified range. They are only given if the relevant M/m mark has been earned either explicitly or by inference from the correct answer.  'B' marks are independent of method and are usually awarded for an accurate result or statement.  ‘S’ marks are awarded for strategy  ‘E’ marks are awarded for explanation  ‘U’ marks are awarded for units  ‘P’ marks are awarded for plotting points  ‘C’ marks are awarded for drawing curves © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 136 COMPONENT 1: NON-CALCULATOR MATHEMATICS, HIGHER TIER Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to AOs 1. (a) 9 B1 1.3a (b) –6 B1 1.3a (c) –3 B1 1.3a (3) (3)AO1 (0)AO2 (0)AO3 2. (a) 68000 B1 1.2 (b) 8∙53  10-5 B1 1.2 (c) 1∙5  109 B2 1.3b B1 for correct value not in standard form e.g. 15 × 108 or 1500 000 000 (4) (4)AO1 (0)AO2 (0)AO3 3. Correctly engaging with ratios to find M1 2.3a values that can be used on the graph e.g. Finding the ratio of red : white to be Seen or implied. 4:5 OR Reducing the ratio of 4 : 9 to enable use on Ignore incorrect use of 4 : 9 as red : white graph for this M1 e.g. 2 : 4·5 or 1 : 2·25 Using a value for white paint to find a non- M1 3.1b The value must be one that can be read off zero value of red paint. the graph. This may be implied from markings on the e.g. 2 litres of white paint gives 1·6 litres diagram but the value does not need to be of red paint. indicated on the diagram. Do NOT F.T. from incorrect interpretation OR (4·5 – 2 =) 2·5 litres of white paint of 4 : 9 as red paint : white paint gives 2 litres of red paint. OR 1·25 litres of white paint gives 1 litre of red paint. Using the red paint value found to fill in A1 3.1b This mark depends on both previous M one of the non-zero values required on the marks. red paint axis. Some correct working must be shown. e.g. 1·6 found from conversion, then 1·5 (This could be in the diagram.) indicated on the axis. (The values are 0·5, 1, 1·5, 2, 2·5.) Correctly filling in all the remaining A1 2.3b C.A.O. numbers on the red paint axis: (4) (0)AO1 0, 0·5, 1, 1·5, 2, 2·5 (2)AO2 (2)AO3 4.(a) Correctly completing the tree diagram B2 B1 for any one pair of branches correct 0∙6, 0∙3. 0∙3, 0∙7 2.3b (total 1) (b) 0∙4  0∙7 M1 2.3a = 0∙28 A1 1.3a M1 2.3a Or other complete method. (c) 0∙6  0∙7 A1 1.3a F.T. for their P(walk to college) P(walk = 0∙42 home) correctly evaluated, or by © WJEC CBAC Ltd. (6) (2)AO1 alternative method (4)AO2 (0)AO3

GCSE MATHEMATICS Sample Assessment Materials 137 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to M1 2 correct before 2nd error 5. Method to find prime factors A1 AOs Ignore 1s for A1, but not for B1 2, 2, 2, 2, 3, 3, 5, 5 B1 F.T. provided index >1. Accept \".\" 24  32  52 1.1 1.3a 1.2 (3) (3)AO1 (0)AO2 6. Method to form two correct equations M1 (0)AO3 Allow 1 error in one term, not one with and eliminate one variable equal coefficients First variable found correctly A1 3.1d Substitute to find the second variable m1 Tin = £5 or Brush = £2. Tin = £5 and Brush = £2 A1 1.3a F.T. ‘their first variable’ (4) 3.1d 3.3 Allow  0·2cm 7. An arc, centre P, of radius 5 cm B1 (1)AO1 B1 for drawing by eye or using a Correctly constructing a perpendicular B2 (0)AO2 protractor bisector (3)AO3 2.3a 2.3a Correct shading B1 2.3b F.T. for an arc centre P and a line 8. 5 parts = (£)30 OR 30  5 OR crossing PQ. Shading needs to be on both 7x – 2x = 30 OR equivalent sides of line PQ (1 part) = (£)6 (4) (0)AO1 (Amount shared =) 6  9 (4)AO2 =(£)54 (0)AO3 9. (a) 2x(3x + 4) M1 3.1d Accept 5/9 = 30 (b) (x – 10)(x + 10) A1 1.3b m1 3.1d F.T their 1 part, provided M1 awarded A1 1.3b Award M1A1m1A0 for answers of £12 and £42 (4) (2)AO1 (0)AO2 (2)AO3 B2 1.3a B1 for a correct partially factorised expression OR sight of 2x(3x ……) or 2x(……+4) B1 1.3a (3) (3)AO1 (0)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 138 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to S1 For the strategy and finding the need for 3 10. Setting up one of two models (needing AOs or 5 strips of carpet as appropriate 3 strips along 8m or 5 strips along 13m) 3.1d (Cost along 8 m side =) 13 × 3 × (£) 25 M1 3.1d Finding the cost of the carpet for their 3.1d model (Cost along 13 m side =) 8 × 5 × (£) 25 M1 1.3a F.T. their number of strips Finding the cost of the carpet for their model F.T. their number of strips (£) 975 AND (£) 1000 A1 8 m method is cheaper by (£) 25 A1 3.4b F.T. for their costs provided at least S1 awarded. 11. Attempt to find vector EF Must state which method is cheaper for e.g. ED + DF or  DE + DF their costs = a + 7b (5) (1)AO1 EF  – 3 (0)AO2 (4)AO3 3a 21b M1 3.1b Accept intention, i.e. missing brackets e.g. 3a  2b instead of 3a + 2b A1 1.3a C.A.O. M1 2.3a F.T. ‘their a + 7b’  – 3 M1 for sight of 3a + 21b or a  7b or 3 (a + 7b) A1 1.3a (4) (2)AO1 (1)AO2 (1)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 139 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to 12. (a) 24× 45 AOs 30 10 M1 3.1c Or equivalent. × 15 M1 3.1c Or equivalent (the 24 must have been used). M1 for correctly using two of the operators ‘45’, ‘30’, ‘10’ and ‘15’ with the 24. = 24 (workers) A1 1.3a C.A.O. 3.4a Do not penalise pre-approximations as long as 24 is given as the final answer. Alternative presentation: Area Time Workers 30 10 24 ….Award M1 for correct step(s) to 45 ….Award M1 for correct step(s) to 15 …. …. …. (b) Stating one assumption made 45 15 24 A1 C.A.O. e.g. ‘similar work will be carried out on the other site’ or ‘all workers will work at the E1 3.5 same rate’ or similar. E1 (5) (1)AO1 Stating an impact (0)AO2 e.g. ‘if the work is harder or the workers (4)AO3 are slower, then more workers will be 2.3a needed.’ 1.1 13.(a)(i) m1 = – 3 B2 3.1b B1 for evidence of interpreting the graph to find the gradient e.g. (9  0)/(0  3) or (ii) m2= 1 B1 equivalent or stating m1 = 3 3 M1 F.T. as long as m1 × m2 = –1 A1 (b) Method to find the intercept of line L2 M1 e.g. substituting m2, 1, 6 into y = mx + c A1 (7) c = 17 or equivalent 1.3a 3 3.1b Finding the equation of L2 e.g. substituting m2 and c into y = mx + c to give y  1 x  17 or equivalent 1.3a 33 (3)AO1 x – 3y +17 = 0 (2)AO2 (2)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 140 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to M1 14. (Distance =) 3 × 40 A1 AOs = 120 (miles) M1 A1 2.2 (Time =) 120  30 1.3a = 4 (hrs) M1 2.2 1.3a (average speed =) 120 + 120 3+4 2.2 F.T. ‘their calculated values’. OR 7 × 35 M1 OR 240 / 35 M1 = 34(·2…mph) ‘So not correct’. A1 2.5a = 245 (miles) A1 =6(·8..)(hrs) A1 Calculation AND statement required. 15. (For triaPnCg^lBes=BCQPB^aCnd(oCr BeQqu)ivalent) Base angles of an isosceles (6) (2)AO1 triangle. (4)AO2 (0)AO3 (So) PB^C = QC^B Angles were bisected. B1 2.4b B1 2.4b Side BC is common (BC = BC) B1 2.4b Reasons given E1 2.4b The first two reasons noted above must be given for E1 to be awarded. (So triangles BCP and BCQ are congruent) B1 2.1a For correctly giving the condition for congruence. ASA (5) (0)AO1 (5)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 141 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to B2 B1 for any 3 correct entries 16.(a) Entries 30, 30, 40, 35, 5 AOs F.T. for their entries for M marks only in B1 (b) (b) (Number of cars exceeding limit = 2.3a 40/100 × 140 =) 56 cars Accept 60/100 × 140 = 84. 3.1d 56 – 35 – 5 = 16 cars in 30-40 group. (OR 84 – 30 – 30 = 24) M1 3.2 16/40 × 10 = 4 mph For attempting to identify the number of (OR 24 /40 × 10 = 6 mph) ‘cars fined’ (or not fined) in the correct Estimate of speed = 40 – 4 = 36 mph single group. (OR 30 + 6 = 36 mph) M1 3.1d F.T. ‘their 56’ or ‘their 84’. (c) 3, 4, 2, 1∙5, 0∙5 For translating this number into a speed. Axes correct and labelled, no gaps between bars F.T. their number of cars Correct histogram A1 1.3a (d) Yes, with reason e.g. ‘there were more slower B1 1.3a speeds recorded’. M1 2.3b 17. Sight of y  1 or y  k Histogram needs to be attempted. xx A1 2.3b F.T. candidate’s frequency density if table completed incorrectly but the idea of frequency density is used. SC1 if correct but not labelled. B1 2.1b F.T from their histogram in (c) if necessary. Other reasons could include: ‘40 cars exceeded 40mph before but only 20 afterwards.’ ‘80 cars exceeded 30mph before but only 40 afterwards.’ (10) (2)AO1 ‘Only 28% exceeded 36mph instead of (5)AO2 40%.’ (3)AO3 B1 1.1 May be implied in further work 16  k k=8 M1 1.3b 1 2 A1 1.3b A1 1.3b F.T, ‘their 8’ y8 x (4) (4)AO1 (0)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 142 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to  18. 3 7  3 7 4  7 AOs    4  7 4  7 4  7 M1 1.3b Numerator 12 7  21 A1 1.3b A1 1.3b Denominator 9 A1 1.3b 4 77 3 (4) (4)AO1 C.A.O. (0)AO2 19. a = 6 (0)AO3 b =  22 B1 1.3a . B1 1.3a 20.(a) x = 0·7878…and 100x = 78·78.. (2) (2)AO1 with an attempt to subtract. (0)AO2 78 (= 26) (0)AO3 99 ( 33) M1 1.3a Or equivalent method. A1 1.3a (b) 1/9 × 3 B2 1.3a B1 for each. = 0·333… B1 1.1 Must be convincing as a recurring 21. Interpreting diagram to get formula decimal. for area of either rectangle (5) (5)AO1 e.g. x(x + 2) = y or equivalent OR (0)AO2 12(4 + x) = 4y or equivalent (0)AO3 B1 2.3a This B1 mark maybe implied by the correct quadratic, hence if M1 awarded also award this B1 mark. ISW Equating formulae M1 3.1b Allow 1 error, e.g. missing brackets, or e.g. x (x+ 2) = 12 + 3x OR from incorrect expansion. FT provided 12(4 + x) = 4x(x + 2) OR equivalent equivalent level of difficulty Deriving a quadratic equation A1 1.3b Must equate to zero e.g. x2 – x – 12 = 0 OR M1 3.1b FT provided equivalent level of difficulty 4x2 – 4x – 48 = 0 A1 1.3b Must have both solutions Factorising and solving their quadratic E1 3.4b F.T provided on +ve and one –ve solution equation A1 3.3 e.g. (x + 3)(x – 4) = 0 (7) (2)AO1 x = –3 or x = 4 (1)AO2 Statement about ignoring x = –3 as it (4)AO3 leads to negative lengths Dimensions 4 (cm) and 6 (cm) © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 143 Specimen Assessment Materials Mark Elements Comments Non-calculator Higher linked to B1 Allow appropriate marking of axes if 22.(a) AOs coordinates not given. Concave down curve translated 2.3a left Point (7,0) shown. B1 2.3b Point (1, 0) shown. B1 2.3b (b) Concave down curve B1 2.3a symmetrical about the y-axis. Stationary points at (0, 3). B1 2.3b (c) A comment regarding no scale B1 2.5b or coordinates shown. (6) (0)AO1 23.(a) (i) 0·7 × 0·7 × 0·3 (6)AO2 = 0·147 (0)AO3 (ii) Indicates three possible M1 3.1c situations A1 1.3a e.g.HMM or MHM or MMH M1 3.1c 0·441 Less than a 50% chance. May be indicated by 0·3×0·7×0·7 × 3 or equivalent. (b) (i) Evaluating the method used A1 1.3a F.T. ‘their 0·147’ 3 e.g. Indicates that the first ball A1 2.1a F.T. ‘their 0·441’. selected is returned to the box before the second ball is selected or 2 E1 3.4a attempts are independent. E1 3.5 (ii) Stating how the results would be different e.g. if the first ball was not (7) (2)AO1 returned then the probability of (1)AO2 winning would be less than 1/16. (4)AO3 24. ½ x (x + 3 ) sin60 = √300 M1 3.1d Allow missing brackets ½ x ( x + 3) √3 = √300 m1 3.2 Or similar progress 2 x2 + 3x – 40 = 0 A1 3.2 F.T. ‘their sin60’ (x + 8)(x – 5) = 0 M1 1.3a x=5 A1 3.3 BA2 = 82 + 52 – 2  8  5 cos60 M1 3.2 Accept BA2 = (x+3)2 + x2 -2 x  (x+3)cos60. Sight of cos60 = ½ BA = 7 (cm) B1 1.1 A1 1.3a (8) (3)AO1 (0)AO2 (5)AO3 © WJEC CBAC Ltd.



GCSE MATHEMATICS Sample Assessment Materials 145 COMPONENT 1: NON-CALCULATOR MATHEMATICS, FOUNDATION TIER GENERAL INSTRUCTIONS for MARKING GCSE Mathematics 1. The mark scheme should be applied precisely and no departure made from it. Marks should be awarded directly as indicated and no further subdivision made. When a candidate follows a method that does not correspond to the methods explicitly set out in the mark scheme, marks should be awarded in the spirit of the mark scheme. In such cases, further advice should be sought from the Team Leader or Principal Examiner. 2. Marking Abbreviations The following may be used in marking schemes or in the marking of scripts to indicate reasons for the marks awarded. CAO = correct answer only MR = misread PA = premature approximation bod = benefit of doubt oe = or equivalent si = seen or implied ISW = ignore subsequent working F.T. = follow through ( indicates correct working following an error and indicates a further error has been made) Anything given in brackets in the marking scheme is expected but, not required, to gain credit. 3. Premature Approximation A candidate who approximates prematurely and then proceeds correctly to a final answer loses 1 mark as directed by the Principal Examiner. 4. Misreads When the data of a question is misread in such a way as not to alter the aim or difficulty of a question, follow through the working and allot marks for the candidates' answers as on the scheme using the new data. This is only applicable if a wrong value, is used consistently throughout a solution; if the correct value appears anywhere, the solution is not classed as MR (but may, of course, still earn other marks). 5. Marking codes  ‘M' marks are awarded for any correct method applied to appropriate working, even though a numerical error may be involved. Once earned they cannot be lost.  ‘m’ marks are dependant method marks. They are only given if the relevant previous ‘M’ mark has been earned.  ‘A' marks are given for a numerically correct stage, for a correct result or for an answer lying within a specified range. They are only given if the relevant M/m mark has been earned either explicitly or by inference from the correct answer.  'B' marks are independent of method and are usually awarded for an accurate result or statement.  ‘S’ marks are awarded for strategy  ‘E’ marks are awarded for explanation  ‘U’ marks are awarded for units  ‘P’ marks are awarded for plotting points  ‘C’ marks are awarded for drawing curves © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 146 COMPONENT 1: NON-CALCULATOR MATHEMATICS, FOUNDATION TIER Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to B1 1. 10 B1 AOs 13 B1 27 B1 1.1 8 1.1 1.1 1.1 2. Seven million five hundred thousand (4) (4)AO1 9000 (0)AO2 (0)AO3 3687 B1 1.2 Accept seven and a half million B1 1.1 Or 9 thousand. Accept thousand(s) but not 1000(s) B1 1.3a (3) (3)AO1 3. (a) Showing ‘20 to 24’ AND ‘25 (to 29)’ B1 (0)AO2 (0)AO3 2.1a Showing (6) 8 5 B1 1.3a F.T. their intervals, provided not 13 overlapping. For the 8, 5 and 13. (b) Uniform scale for the frequency axis B1 2.3b B0 for ambiguous placement of scale starting at 0. numbers. Four bars at correct heights. B1 2.3b F.T. their numbers in (a). If no scale shown, assume intervals of 1 from 0 to 15. Penalise uneven bar widths 1. (4) (1)AO1 (3)AO2 (0)AO3 4. (a) 2190 B1 1.1 54 000 B1 1.1 (b) Sensible estimates that would lead to M1 1.3a Accept 50 3∙9, 51 4 or 50 4 single digit multiplication. Correct answer from their estimates. A1 1.3a Award M1 A1 for unsupported answers of 200, 195 or 204 Award M0 A0 for (51 × 3.9 =) 198.9 (4) (4)AO1 (0)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 147 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to B2 B1 for each quadrant 5. AOs 1.3a (2) (2)AO1 (0)AO2 6. (a) 262 B1 (0)AO3 B2 (b) Thursday Tuesday E1 1.3a B1 for each. Allow SC1 if reversed. 2.3a Accept valid and relevant equivalent (c) Comment regarding some cars B1 2.4a comments. B1 leaving and others taking their place. (d) (Total number of cars Mon-Fri) 538 1.3b F.T. 800 – ‘their (a)’ (538 × 2 =) (£)1076 1.3b F.T. ‘their 538’ Alternative method: 104×2 + 43×2 + 112×2 + 163×2 + 116×2 M1 (must show intent to add for the M1) (£)1076 A1 (e) (¼ of 800 =) 200 B1 1.3a F.T. (800 – 3 × ‘their 200’) (£)1.50 (Charge =)(800-200) ×(£)1.5(0) M1 3.1d F.T. their number of cars only if less than 800. Less and (£)900 A1 2.1b F.T. their values. (f) One assumption stated E1 3.4a e.g. “the car parking pattern was the same each week” OR “the week considered was typical” OR “the same amount was collected each week” OR “the car park was open for 52 weeks” Stating how the results would be different E1 3.5 e.g. “If the car park was not open for 52 (11) weeks the total could be lower” OR “some (4)AO1 (4)AO2 weeks could be much busier so the total (3)AO3 would be more” 1.3a 7. A = 14 B1 1.3a B = 15 B1 1.3a C=6 B1 (3)AO1 (3) (0)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 148 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to B1 Allow  0·2 cm 8. (a) Line measured as 7·6 (cm) M1 AOs F.T. ‘their length’. Evidence of multiplying by 10. A1 Must show units. 76 km 1.3b 1.3b 1.3b (b) Sight of 2 × 40 or 80 or 76/40 or 1∙9 B1 2.4a E1 YES and explanation 2.4a Any equivalent convincing argument. (5) F.T. ‘their 76’. e.g. because 2 × 40 > 76 or 76/40 < 2 or 1∙9 < 2 9. (a) Rounded values B2 (3)AO1 Award B2 for all 5 values rounded. B1 (2)AO2 Award B1 for 3 or 4 values rounded. (0)AO3 1.3a Item Cost Chicken curry £3 Pizza £3 Washing Powder £6 or £6.10 Butter £1 or £1.50 Bread £1 or 90p Approximate total = £14 or £13.90 or 1.3a F.T. their approximated values if at least B2 awarded. £14.10 or £14.50 or £14.60 or £14.40 2.5a If prices are added to give £14.12 and (3)AO1 approximate value of £14 given, award (b)Suitable explanation E1 (1)AO2 final B1. e.g. “shopkeeper added £89 not 89p”. (4) (0)AO3 Accept “he forgot the decimal point for the 89 pence” 10. (32 – 18) ÷ 2 M1 3.1c 7 (cm) A1 1.3a Or equivalent 11. (a) 9a + 8b (2) (1)AO1 3y  6 (0)AO2 (b) 6y2 (1)AO3 (c) (d) y4 B2 1.3a B1 for 9a +kb or B1 for ka  2b. 12. Missing side segment = 4 B1 1.3a (Perimeter=) 7+3+7+4+3+7+3+4+7+3 B1 1.2 = 48 (cm) B1 1.2 (5) (5)AO1 (0)AO2 (0)AO3 B1 2.3a May be implied by correct working M1 3.1a Attempt to all 10 sides of the shape F.T. their '4' but M0 if 7 OR 3 used instead of 4 A1 1.3a CAO (3) (1)AO1 (1)AO2 (1)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 149 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to M1 13. 2×60 + 1 OR 60 + 61 or A1 AOs equivalent 3.1a = 121 2.1a (2) (0)AO1 (1)AO2 (1)AO3 14. (a) 720  ½ × 720  2/5 × 720 or M1 1.3b Alternative method: equivalent (1  1/2  2/5) × 720 or equivalent M2 Sight of (£)288 B1 1.3b Award M1 for sight of 1/10 or equivalent (Amount left) (£)72 = (£)72 A1 A1 1.3b For A1, F.T. (£)720  ‘their (£)360’  ‘their (£)288’ Two amounts must be subtracted from (£)720. (b) 72 / 720 × 100 M1 1.3a F.T. ‘their £72’ = 10(%) A1 1.3a Alternative method: 100(%)  50(%)  40(%) (5)AO1 M1 (0)AO2 = 10(%) A1 (0)AO3 (5) Ignore notation for this B1 1.3a 15. (a) 10(:00) 1(:00) 4(:00) B1 OR 10(:)00 13(:)00 16(:)00 B1 B1 Correct notation ‘a.m./p.m.’ M1 1.2 A1 (b) 9(°C) E1 1.3a CAO (c) (14 + 18 + 23 + 19 + 16) / 5 (6) 1.3a = 18(°C) 1.3a (d) Any statement that refers to other 2.4a Must refer to other temperatures. possible temperatures, apart from the five ‘It was done every 3 hours’ is not sufficient recorded. (5)AO1 (E0). (1)AO2 16. (Area = ) ½(4 + 5)  6 or equivalent M1 (0)AO3 F.T. ‘their area’. 27(m2) A1 M1 3.1d (Cost =) 27 × 60 or equivalent 1.3a A1 3.2 18 (4) 1.3a = (£)90 (2)AO1 (0)AO2 (2)AO3 © WJEC CBAC Ltd.