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

GCSE MATHEMATICS Sample Assessment Materials 150 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to B1 Look for angles shown on diagram. 17. AB^C = 50(°) M1 AOs F.T 180(°)  80(°)  ‘their 50(°’) BA^C = 180(°)  80(°)  50(°) A1 = 50(°) E1 2.2 Convincing statement 2.2 2.2 2.2 (4) (0)AO1 (4)AO2 (0)AO3 18.(a) (i) A comment that states or implies B1 2.5b that we do not know the actual numbers. (ii) A comment that states or implies that B1 2.5b we do not know the pass rate between 2005 and 2010. (b) False AND a counter example B1 2.5a given. (3) (0)AO1 19. Attempt to repeatedly divide by 2 (3)AO2 (0)AO3 M1 3.1c At least 2 divisions needed for M1 105 cm or 52∙5 cm seen from correct A1 1.3a working A1 3.3 After 4 bounces. (3) (1)AO1 (0)AO2 20. (a) (i) Area of B = (4 × 3) × 3 M1 (2)AO3 F.T. ‘their area for B’. 36 (cm2) A1 F.T. ‘their area for B’. B1 3.2 Two values whose product is 36 B1 1.3a 3.1a (ii) Two different values whose product 1.3a is 36. (b) NO (because) their sides are not in E1 2.4a Accept convincing statement. a common ratio. (5) (2)AO1 (1)AO2 (2)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 151 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to M1 Accept alternative appropriate diagram. 21. Setting up a Venn diagram with a AOs rectangle containing two intersecting circles and placing either 17 or 6 correctly. 3.1c Alternative method (without a diagram): 20 – 3 = 17 OR 9 – 3 = 6 M1 Finding the other of 6 or 17. M1 3.1c 17 + 9 = 26 OR 20 + 6 = 26 1.3a OR 17 + 3 + 6 = 26 M1 1.3a Neither French nor German = 10 A1 F.T. ‘their 10’ Probability (neither) = 10 A1 36 (4) (2)AO1 (0)AO2 22. (a) 2x(3x + 4) B2 (2)AO3 B1 for a correct partially factorised (b) (x – 10)(x + 10) expression OR sight of 2x(3x ……) or B1 1.3a 2x(……+4) (3) 1.3a Accept 30  10  8p = 2400 23. (a) 2400  8  10 or equivalent. M1 Unsupported 30 is awarded M1A0 A1 (3)AO1 Statement that 30 bulbs must have been (0)AO2 used M1 (0)AO3 A1 (b) 2400  400 or equivalent E1 3.1d 6p or £0.06 (5) 2.1b (c) Correct conclusion e.g. ‘the cost of a bulb must be between 6p and 8p’. 3.1d Units required. 1.3a F.T their ‘6p’ 24.(a) Correctly completing the tree B2 diagram 0∙6, 0∙3. 0∙3, 0∙7 2.1a B1 for any one pair of branches correct M1 (total 1) (b) 0∙4  0∙7 A1 (1)AO1 = 0∙28 M1 (2)AO2 Or other complete method. A1 (2)AO3 FT for their P(walk to college) P(walk (c) 0∙6  0∙7 home) correctly evaluated, or by = 0∙42 (6) 2.3b alternative method 2.3a 1.3a 2.3a 1.3a (2)AO1 (4)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 152 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to M1 25. Correctly engaging with ratios to find AOs values that can be used on the graph e.g. Finding the ratio of red : white to be 2.3a 4:5 OR Seen or implied. Reducing the ratio of 4 : 9 to enable use on graph Ignore incorrect use of 4 : 9 as red : white e.g. 2 : 4·5 or 1 : 2·25 for this M1 Using a value for white paint to find a non- M1 3.1b The value must be one that can be read zero value of red paint. off 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 CAO numbers on the red paint axis: (4) (0)AO1 0, 0·5, 1, 1·5, 2, 2·5 (2)AO2 (2)AO3 26. Method to form two correct equations and eliminate one variable M1 3.1d Allow 1 error in one term, not one with First variable found correctly equal coefficients Substitute to find the second variable Tin = £5 and Brush = £2 A1 1.3a m1 3.1d Tin = £5 or Brush = £2. A1 3.3 F.T. ‘their first variable’ (4) (1)AO1 (0)AO2 (3)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 153 Specimen Assessment Materials Mark Elements Comments Non-calculator Foundation linked to S1 For the strategy and finding the need for 3 27. 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. 28. 1∙5  109 Must state which method is cheaper for 29. (a) 24× 45 their costs 30 (5) (1)AO1 10 (0)AO2 (4)AO3 × 15 B2 1.3b B1 for correct value not in standard form e.g. 15  108 or 1500 000 000 (2) (2)AO1 (0)AO2 (0)AO3 M1 3.1c Or equivalent. 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. 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 3.4a other site’ or ‘all workers will work at the E1 same rate’ or similar. Stating an impact E1 3.5 e.g. ‘if the work is harder or the workers are slower, then more workers will be (5) (1)AO1 needed.’ (0)AO2 (4)AO3 © WJEC CBAC Ltd.



GCSE MATHEMATICS Sample Assessment Materials 155 COMPONENT 2: CALCULATOR-ALLOWED 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 156 COMPONENT 2: CALCULATOR-ALLOWED MATHEMATICS, HIGHER TIER Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to M1 Or equivalent full method 1. (a) 28416/38400)  100 A1 AOs 74(%) 1.3a 1.3a (b) 766 + 766  12/100 OR 766  1.12 M1 1.3a Or equivalent full method A1 1.3a 2. (a) Reason, e.g. ‘outside the juice bar’, (4) (4)AO1 ‘mostly younger people use juice bars’ (0)AO2 (0)AO3 E1 2.5b (b) Two appropriate criticisms E2 2.5b e.g. ‘No under 15s’, ’30 appears in two boxes’, ‘may object to giving their age’ (3) (0) AO1 (3) AO2 3. 6x – 2 = 4x + 5 (0) AO3 2x = 7 x = 7/2 (3.5) B1 2.2 B1 1.3a Length of side of square = B1 1.3a 4 × 3.5 + 5 or 6 × 3.5 - 2 =19 (cm) M1 2.2 A1 1.3a 4.(a) Reasonable straight line of best fit by (5) (3) AO1 eye, some points above and below (2) AO2 (0) AO3 (b) Suitable description of the relationship e.g. ‘higher the number of visitors, higher B1 1.3a the donations’ B1 2.1b Accept ‘positive correlation’ but not just ‘positive’ (c) Indicates Sunday (12, 100) B1 2.3a (d) (i) Valid explanation E1 2.1a e.g. \"By using the line of best fit\" or \"By using the relationship shown in the graph\" (ii) Valid explanation E1 2.5a e.g \"You can't say for definite how many donations the centre will receive on a (5) (1) AO1 particular day\" (4) AO2 (0) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 157 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to B1 Accept embedded answers in (a) and (b) 5. AOs Accept 3/12. (a) (x =) ¼ or 0∙25 or equivalent B1 Mark final answer B1 1.3a (b) 9x – 4 = 7x + 14 B1 2x = 18 or equivalent 1.3b FT until 2nd error x=9 1.3b 1.3b 6.(a) 7n – 1 (b) a+a+7+a+14+a+21=6 or equivalent (4) (4) AO1 (0) AO2 a = –9 or lowest number = –9 (0) AO3 –9, –2, 5, 12 B2 1.3a B1 for 7n ± … 7. (Height of tree =) Tan 56°  19 + 1∙8(m) Allow change of letter (Height of tree =) 29∙968658….. (m) M1 3.1a A1 1.3a 8.(a) Midpoints 52, 56, 60 and 64 5212 + 5632 + 6014 + 642 (=3384) B1 1.3a /60 OR sight of at least 3 trials keeping to 56.4 (cm) either difference criterion or sum criterion (b) Strategy to look back that 32 out of 60 (5) (4) AO1 are size 2, e.g. ‘(table shows) about half (0) AO2 customers are size 2 (1) AO3 Conclusion to give Salesman is correct M3 3.1d Award M2 for tan 56°  19 OR sight of 28∙168658….(m) Award M1 for tan 56° = opposite/19 Accept rounded or truncated from working A1 1.3b Accept rounded or truncated from working F.T from their rounded or truncated 28∙168… (4) (1) AO1 (0) AO2 (3) AO3 B1 1.3b M1 1.3b F.T. their midpoints, provided within interval m1 1.3b A1 1.3b F.T. their sum of products, division by 60 S1 2.5a E1 2.5a (6) (4) AO1 (2) AO2 (0) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 158 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to B1 9.(a) 8 (mm) AOs 2.3a (b) (i) Method e.g. M1 1.3a Or idea of alternative complete method increase in L / increase in M Accept sight of quotient based on misread of the scale for M1 only. e.g. 12/150 (= 0∙08) A1 1.3a Mark final answer. (ii) Full explanation, e.g. ‘rate of change of E1 2.3a length with mass’, ‘for every 1 g increase 0∙08 mm increase’ E1 2.3a (c) Plausible explanation, e.g. ‘no more data recorded’, ‘spring snaps’, ‘broken (5) (2) AO1 spring’, ‘spring now completely straight’, (3) AO2 etc (0) AO3 10. Straight lines parallel to all 4 sides and B2 2.3b B1 for straight lines parallel to 2 sides 3cm away (+2mm) and 3cm away (+2mm), OR straight lines parallel to all 4 sides but not at 3cm Arcs with radius 3cm (+2mm) at all 4 vertices joining the straight lines B2 2.3b B1 for arcs with radius 3cm (+2mm) at least 2 vertices but not joined to straight 11. (a) x + 3x + 16x = 1 lines, OR x = 1/20 or 0∙05 or equivalent ISW arcs at all 4 vertices but not at 3cm or not joined to straight lines (b) (Statement that Stephen is incorrect and) a correct explanation e.g. fraction (4) (0) AO1 (proportion) of tickets bought would be the (4) AO2 same. (0) AO3 M1 1.1 Use of ‘total probability = 1’ A1 1.3a Accept 5% only if specified as a percentage. E1 2.5a Accept alternative explanations such as ‘It may decrease his chance of winning a prize as more people may be tempted to buy tickets’ (3) (2) AO1 (1) AO2 (0) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 159 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to M3 M2 for sight of 560  455  37∙8, OR 12.(a) All three stages of the appropriate AOs M1 for sight of 560  37∙8, 4∙55  37∙8, calculation 37∙8  4∙55, or 4∙55  1∙48 560  (4∙55  37∙8 )  1∙48 3.1d Note: 560  37∙8 (= 14∙814814… gallons)  4∙55 (= 67∙407… litres) Use of 14∙8 gives 67∙34, use of 15 gives 68∙25 (£)99.76 A2 1.3a Depends on M3 A1 for (£)99.7629.. or 99.6632 or 101.01 or other amount from premature approximation (b) 560 / 10∙75 or 560 / 10 ¾ M2 3.1d M1 for 560/10∙45 or 560/675 or 560/645 52(∙093 mph) A1 1.3a C.A.O C selected or implied with a reason, E1 2.1b Only F.T. provided e.g. ‘C because 52 mph average means travels fast’ 50  their average speed  70 (9) (3) AO1 13.(a) 2∙3 1030 / 25 or equivalent (1) AO2 7∙2 1028 (5) AO3 M2 3.1c M1 for an attempt to divide 2∙3 1030 by 2 more than once A1 1.2 (b) r = 0∙75t  x B3 2.3a B2 for correct expression 0∙75t  x B1 for 0∙75x, x –1/4 x, 0∙752x, … 14 (a) 45 / 120 (×100) SC2 for r= 0.25t x or SC1 for 0∙25t  x 37∙5(%) rounded or truncated (6) (1) AO1 or equivalent (3) AO2 (2) AO3 M1 1.3b Accept values from 44 to 46 inclusive A1 1.3b leading to 36∙66.. to 38∙33..(%) rounded or truncated. (b) 70 seconds means ≈ 100 × 85/120 M1 3.1c (OR 100 × 84/120 = 70%). 70 seconds gives 84 to 86 inclusive so OR accept 70% to 72%. 80% calls means (0∙8 × 120 =) 96 calls 70∙833..% OR 71% OR ≈75 seconds A1 2.1b Alternative solution to (b): AND ‘You can’t tell’, with full supported interpretation ‘No’ (target not met stated working for reasoning, gains M1 A1. or implied) e.g. percentage of calls answered in 70 seconds could be anything between Stating an assumption made E1 3.4a 50% and 91.6666…% e.g. “ assumed that the times between 60 Assumption: e.g. ‘you don’t know how and 80 are evenly distributed” the calls are distributed in the 60-80 group’ gains E1. (5) (2) AO1 (1) AO2 (2) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 160 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to B1 15. Use of A : B is 2 : 3 or sight of 2/5 B1 AOs Area circle = π × 1∙52 M1 Area A = (2/5) × π × 1∙52 A1 3.1a = 2∙8(27.. cm2) 1.1 3.2 1.3a 16. x  3  (32  (4  2)  3)  / (2 2) (4) (2) AO1  (0) AO2 (2) AO3 M1 1.3a Allow one slip  3  33 / 4 A1 1.3a 0∙69 and – 2∙19 A1 1.3a CAO. Must be correct to 2 decimal 17. (a) Sight of 305(cm) or 3·05(m) places AND 3·95(cm) or 0·0395(m) (3) (3) AO1 305 or 3·05 (0) AO2 3·95 0·0395 (0) AO3 B1 3.1d The B1 may be awarded if these values are seen in (a) or in (b) and need not be of the same units. M1 3.1d F.T. ‘their 305’, provided it is > 300 and < 310 AND ‘their 3·95’, provided it is > 3 and < 4 = 77 A1 1.3a 77·2.... is A0. (b) (If container has height=) B1 2.4a The B1 may be awarded if these values 295(cm) or 2·95(m) AND are seen in (a) or in (b) and need not be of the same units. (each metal plate has thickness=) 4·05(cm) or 0·0405(m) 295 or 2·95 M1 2.4a F.T. ‘their 295’, provided it is > 290 and 4·05 0·0405 < 300 AND ‘their 4·05’, provided it is > 4 and < 5 = 72·8... A1 2.4a Alternative methods: 73 × 4·05 M1 = 295·6(5) AND ‘this is >295’ A1 OR 295/73 M1 = 4·04 AND ‘this is less than 4·05’ A1 (6) (1) AO1 (3) AO2 (2) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 161 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to B1 Dependent on B1, unless correct 18. (a) (x =) 35° E1 AOs workings seen but with 1 error in their Angles in same segment, (angles in calculation triangle) 2.3a Accept, e.g. ‘angles from same chord’ 2.3a (b) 40 B1 Dependent on B1, unless correct Angle at the centre is twice the angle at E1 2.3a workings seen but with 1 error in their circumference 2.3a calculation (c) Angle CAB = x AND stating alternate B1 2.4b May be indicated on the diagram segment theorem B1 2.4b Stating triangle CAB isosceles AND (6) (0) AO1 (180 – x)/2 (6) AO2 (0) AO3 19. Radius of the cylinder = 0.5 cm OR B1 Maybe shown on the diagram diameter = 1 cm S1 3.1d Idea height of cylinder approximately M1 circumference of ring M1 3.1d Maybe internal, external or somewhere A1 Ring C = 2 π  value between 8 and 9 E1 in between. inclusive E1 Accept sight of 8π or 9 π for S1 Volume = π 0∙52 ring C 3.1d Volume in the range 39∙5 to 44∙4 (cm3) (7) inclusive 3.1d C.A.O. E.g. 41∙95 (cm3) from use of 8∙5 Statement about assumption, e.g. volume 1.3a of cylinder used to calculate volume of dog toy, use of mid value for radius. 3.5 Accept ‘circumference of the ring is the Justification e.g. 3.4a same as the length of plastic’, ‘radius used smaller radius so volume will be doesn’t change as bend around’ greater, or used larger radius so volume will be less, or Do not accept ‘radius is 0.5’ used 8∙5 cm as height of cylinder is clearly between 8 cm and 9 cm. 20.(a) Sight of h  u2 or h =ku2 B1 (1) AO1 May be implied in later working 5 = k  102 M1 (0) AO2 A1 (6) AO3 F.T. non-linear only in all parts k = 0∙05 3.1d Or equivalent. h = 0∙05  122 M1 3.1d Ignore incorrect use of . h = 7∙2 (m) or equivalent A1 1.3a NOTE: working for finding k (first three marks) may be seen in (b) not (a). 3.1d Award the marks in (a) if this is the case. 1.3a F.T. ‘their k ‘ (b) 16 / 0∙05 = u2 (=320) M1 1.3a u = 17∙88854… (m/s) A1 1.3a Accept rounded or truncated (7) (4) AO1 (0) AO2 (3) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 162 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to M1 21. Use of scale factor 1∙5 or 2/3 as AOs appropriate, or angles in ABC correctly as (60,) 80 and 40 3.1b DE/sin 60 = 9/sin 40 M1 3.2 or AB/sin60 = 6/sin40 m1 1.3a DE = 12(∙126 cm) DE = 9 × sin60/sin40 or AB = 6 ×sin60/sin40 AB = 8(∙084 cm) or 8.1(cm) A1 1.3a (4) (2) AO1 C.A.O. (0) AO2 Alternative: 22.(a) Reasonable tangent drawn S1 (2) AO3 M1 CD/sin80 = 9/sin40 Gradient = difference v / difference t M1 Calculated gradient for their tangent A1 2.3a or CD = sin80×9/sin40 U1 1.3a Units given m/s2 or ms-2 1.3a OR AC/sin80 = 6/sin40 S1 1.1 or AC = sin80×6/sin40 (b) Attempt to find area by splitting up. M2 M1 AC = ⅔CD or AC =9.19 Suitable area sections with at least 2 correct (CD=13∙79) areas. m1 AB2 = 62 + AC2 - 2×6×AC×cos60 (F.T. their AC but not their CD used) A1 AB = 8(∙084cm) or 8∙1(cm) C.A.O. With or without tangent (Answers may be in the range 25 to 37) Independent of other marks 3.1c 3.1c M1 Suitable area sections with at least 1 1.3a correct area. Allow tolerance in reading the velocity, as estimation required. Units not required Answers in the range 134 (m) to 158 (m) A1 3.4a from correct working E1 (9) (c) Appropriate improvement suggested e.g. “working with more trapeziums of narrower widths” (4) AO1 (1) AO2 (4) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 163 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Higher linked to B1 F.T ‘their f(4)’ 23. (a) f(4) = 8 B1 AOs Alternative method: gf(4) = 19 gf(x) = 3 + 2(2x) OR 3 + 4x M1 1.3a gf(4) = 19 (b) fg(x) = 2(3 + 2x) A1 1.3a fg(x) = 6 + 4x M1 A1 B1 6 + 4x = 14 B1 x=2 3.1b 1.3a 3.1b Allow F.T. from ‘their 6 + 4x', provided it is a linear expression, for M1 only 1.3a C.A.O. Alternative method: fg(x) = 2(3 + 2x) M1 2(3 + 2x) = 14 M1 3 + 2x = 7 A1 C.A.O. or equivalent without brackets x=2 A1 C.A.O. (6) (4) AO1 (0) AO2 (2) AO3 © WJEC CBAC Ltd.



GCSE MATHEMATICS Sample Assessment Materials 165 COMPONENT 2:CALCULATOR-ALLOWED 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 166 COMPONENT 2:CALCULATOR-ALLOWED MATHEMATICS, FOUNDATION TIER Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to B1 F.T their values, provided that units 1. (a) (£)8.5(0) and (£)23.85 B1 AOs are consistent (£)9.96 B1 F.T 50 – ‘their 42.31’ (£)42.31 1.3a Or equivalent B1 1.3a SC1 for (9 × 1.99=)(£)17.91 (b) (£)7.67 M1 1.3a (c) 6 × 1.99 A1 1.3a (£)11.94 3.1c 1.3a 2. 12 and 24 indicated (6) (5)AO1 (0)AO2 3. (a) 5/7 (1)AO3 (b) 3/7 B2 1.1 B1 for 2 correct and 1 incorrect OR 4. 390 ÷ 3 1 correct and no more than 1 ×5 incorrect 650 (2) (2)AO1 (0)AO2 (0)AO3 B1 1.3a In Q3 as a whole, penalise -1 once B1 1.3a only if consistent use of incorrect notation. (2) (2)AO1 (0)AO2 (0)AO3 M1 1.3b Award M1 for sight of 130 or 1950 m1 1.3b Accept in either order × 5, ÷ 3 A1 1.3b CAO 5. Strategy attempting to add 5 to the x- (3) (3)AO1 coordinate or subtracting 5 from the y- (0)AO2 coordinate (0)AO3 e.g. B shown as (6, y) or D shown as (x, 3) M1 3.1a Evidence on diagram or if at least 1 (6, – 3) correct coordinate A1 2.1a 6. Lisa = x + 3 (2) (0)AO1 (1)AO2 (1)AO3 B1 2.3b Accept 2 × x + 3 or x + 3 × 2. Julian = 2(x + 3) B1 2.3b F.T. 2 × ‘their Lisa’ if Lisa ax + b, B1 Expansion of bracket = 2x + 6 B1 where b  (Total number of pens = x + x + 3+2x + 6=) 1.3a 0 4x + 9 F.T. if 2(ax ± b) 1.3a (4) (2)AO1 (2)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 167 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to M1 For conversion and division 7. (2 × 1000) ÷ 400 A1 AOs 5 (laps) 1.3a 8. (Cost of bracelets = 200  6.30) (£)1260 1.3a (number of bracelets sold at higher price) (2) (2)AO1 60/100  200 OR 120 (0)AO2 (sale of 120 bracelets =120  (£)10 =) (0)AO3 (£)1200 B1 3.1d (sale of 80 bracelets = 80  (£)4 =) B1 3.1d (£)320 (Profit =) B1 1.3a F.T. ‘their 120’ (£)1200 + (£)320 – (£)1260 B1 1.3a F.T. 200 –‘ their 120’ but not 120 (Profit of) (£)260 M1 3.1d F.T. ‘their 120  (£)10' 9. (a) x = 4 + ‘their 80 (but not 120)  (£)4' (b) y = 20 (c) 5a = 17 + 8 – ‘their (£)1260’ a=5 A1 1.3a 10. (a) Suitable explanation e.g. “5 occurs more often than any other (6) (3)AO1 number” (0)AO2 (3)AO3 (b) For 2 correct values that give a range of 7 AND a median of 6. B1 1.3a Allow embedded answers in all parts 11. 20 = 50 – 10k B1 1.3a OR 10k = p – 2q OR 2q – p = –10k B1 1.3a 10k = 50 – 20 OR –10k = 20 – 50 B1 1.3a F.T. from 1 error for equation in the k = 3 (seconds) form ma = n, m ≠ 1 (4) (4)AO1 (0)AO2 (0)AO3 E1 1.1 E.g. 5 is the most popular number B2 2.1b 6 &10, 7&10, 8 &10, 9 &10,10 & 10 B1 for 2 values that either give a range of 7 or a median of 6 (3) (1)AO1 (2)AO2 (0)AO3 M1 1.3a 20 must be evaluated if this method used. For isolating k term. M1 1.3a 20 must be evaluated. FT their equation or formula, if of equivalent difficulty. A1 1.3a (3) (3)AO1 (0)AO2 (0)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 168 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to B1 12. Spinner 1 E1 AOs Suitable explanation e.g. “Ethan has 50% chance of a yellow & 2.4a Kyle has 25% chance of a red” or 2.4a “probability of yellow (½) > probability of red (¼)” (2) (0)AO1 (2)AO2 13.(a) Uniform scale on kilometre axis (0)AO3 Plotting at least two correct points Correct straight line through points B1 1.2 P1 2.3b L1 2.3b (b) Full explanation given E1 2.1b e.g. “he could find what 35 miles is in km and then double it” Approximately 112 (km) B1 1.3a F.T. their graph or 14. (a) accept answers in the range 110 – 113 (km) (5) (2)AO1 (3)AO2 (0)AO3 B1 3.1a For the 5x B1 1.3a For the 4x F.T ‘their 5x’ – x (b) B1 1.3a For the 4x B1 1.3a For the 2x + y F.T ‘their 4x’ – 2x + y B1 1.3a For the 11x + y F.T 9x + ‘their 2x + y’ Must be in the form ax + by (5) (4)AO1 (0)AO2 (1)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 169 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to M1 15.(a) 84 – 0∙06  84 OR 0∙94  84 AOs (= 78∙96 kg or 79 kg) 3.1d 78∙96  0∙972 OR 78∙96 – 0∙028  78∙96 M1 3.1d F.T. their 78∙96 or 79 provided the OR 0.028  0∙94  84 value is < 84 76∙7(4912 kg) or 76∙7(88 kg) or 76∙8(kg) or A1 1.3a Or 76∙75 or 76∙74 77(kg) If no marks, then SC1 for an answer 1.3a of 76∙6(08) from a reduction of 8∙8%. (b) (84 – 76∙74912)/84  100 or M1 No F.T. to (b) A1 1.3a F.T. their ‘76.7’, provided ≠ 76∙6(08) equivalent full method from 8∙8% 8∙632% rounded or truncated from correct (5) (3)AO1 Accept an answer of 8∙333..% from (0)AO2 using 77kg, or working B1 (2)AO3 8∙69…% from using 76∙7, … M1 16. For use of 9 hours A1 3.1d F.T. their whole number of hours. (Fishing Boats R Us) 45 + 30 × 8 B1 3.1d Award M0 A0 for use of 8.15 E1 (Ocean Blue Boats ) (£) 285 (5) 1.3b F.T. their whole number of hours. (£)288 1.3b Award B0 for use of 8.15 F.T. their prices for Fishing Boats R Choice of company with valid reason 3.4b Us AND Ocean Blue Boats. e.g. “go with Fishing Boats R Us as they are cheaper “ or “could use either as there’s not (2)AO1 much between them” (0)AO2 (3)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 170 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to 17. AOs 12 M1 1.3b He spends (£)100 on rent OR + 45 and (£)160 on food leaving (£)140 13 A1 1.3b F.T. for second M1,A1 M1 OR A1 20 Frac. remaining 140/400 OR or 1 – 13 1.3b 20 7 1.3b Decimals or % equivalents 0∙25 + 0∙4(0) = 0∙65 I.S.W. (4)AO1 1- 0∙65 = 0∙35 First M1, A1 possible (0)AO2 F.T. for second M1,A1 20 (0)AO3 but must be fractions for second M1,A1. 35 7 M1 = A1 100 20 Incorrect method of Subtracting at each stage : Spends (£)100 on rent Leaving £300. 2/5 of £300 = 120 leaving (£)180 F.T. for second M1,A1 Frac. remaining 180  9 400 20 Possible 4 marks then 1 if any A marks awarded (4) 18. (a) 95  100 M1 1.3a 250 A1 38 (%) 1.3a M1 (b) Cost of newspapers = £29.04 – 4∙12 × 6 m1 1.3b Award M1 for sight of (£)4.32 Cost of 1 newspaper = 1.3b A1 (£29.04 – 4∙12 × 6)  4 1.3b C.A.O = (£) 1.08 (5) (5)AO1 (0)AO2 Seen or implied in further calculations 19. 35 × 45 × 20 M1 (0)AO3 F.T. their 31500 31500 A1 31500 ÷ (100 × 15) M1 3.1d 21 (cm) A1 1.3a 3.1d (4) 1.3a (2)AO1 (0)AO2 (2)AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 171 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to M2 M1 for dividing 48000 by two of 16, 20. (a) 48000 /16 /25 /8 AOs 25 or 8. Accept alternative methods involving 3.1c multiplication, e.g. 25 x 16 = 400 48000/400 (= 120) 120/8 (M1 for 2 of the 3 steps) = 15 A1 1.3a C.A.O. Correct interpretation of their answer: E1 3.3 e.g. (Assumption is) that each examiner E2 works for 15 hours a day. 3.4b F.T. ‘their 15’, if appropriate. (6) 3.5 Reason is AO3.4b, effect is AO3.5. (b) Reason: e.g. It is unlikely that all E1 for reason only. examiners will work for as long as 15 hours in one day. OR It is unlikely that the examiners will be able to work at the same rate for 15 hours in one go. AND Effect: e.g. 8 days is too short a time to complete the marking. 21. No AND reason (both the same) 1/6 B1 (1)AO1 1/6 must be seen. (0)AO2 Accept NO with appropriate sight of (5)AO3 1/6. Accept reference to 1/6 in words. 2.5a No AND reason (1/6  1/6=)1/36 B2 2.5a B1 for No AND reason may be based on sample space or, 22. Calculating original amount gives 1/61/6 without stating 1/36, or, e.g. sight of 492  100/ 60 OR ‘60% is 492’ gives 1/61/6 with an incorrect response, e.g. 2/36 (£) 820 or, sight of 1/36 with no conclusion Do not accept incorrect probability with statement ‘No’ without working (3) (0)AO1 (3)AO2 (0)AO3 M1 3.1b A1 1.3a 0∙98  ‘their 820’ M1 3.1b (£)803.6(0) A1 1.3a Amount After a decrease of (4) (2)AO1 40% 2% (0)AO2 (2)AO3 £820 £492 £803.6(0) © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 172 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to E2 Sight of the word rectangle and area 23. (a) Valid reason or explanation, e.g. AOs of 620 for E2. ‘approximates to a rectangle with an S1 Needs to be precise in reference to M1 2.1b rectangle, not vague referring to area of 620’ M1 edges or banks of the pond being 3.1d extra. (b) Correct strategy Award E1 for explanation without e.g. considers 2 semi-circles and a rectangle reference to 620. Method of calculating area Accuracy in establishing missing lengths / 3.1d Idea of splitting up the area dimensions 1.3b e.g. r2 + l  w e.g. Sight of diameter 6m or radius 3m AND length of rectangle =20–3–3 20–6(=14)m, or 32 + 146 Value for their area A1 1.3b e.g. 112(.27… m2) E1 3.4a Justification of their method e.g. “having a rectangle and 2 semi-circles is (7) (2)AO1 (2)AO2 more like the sketch than using a rectangle (3)AO3 as Eliza has done” 2.5b 24. (a) Reason, e.g. ‘outside the juice bar’, E1 ‘mostly younger people use juice bars’ E2 2.5b (3) (b) Two appropriate criticisms e.g. ‘No under 15s’, ’30 appears in two boxes’, ‘may object to giving their age’ 25. 6x – 2 = 4x + 5 B1 (0) AO1 B1 (3) AO2 2x = 7 B1 (0) AO3 x = 7/2 (3·5) M1 2.2 Length of side of square = A1 1.3a 1.3a 4 × 3·5 + 5 or 6 × 3·5 – 2 (5) =19 (cm) 2.2 1.3a (3) AO1 (2) AO2 (0) AO3 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 173 Specimen Assessment Materials Mark Elements Comments Calculator-allowed Foundation linked to B2 B1 for 7n ± … 26. 7n – 1 AOs Allow change of letter 1.3a 27. (a) Midpoints 52, 56, 60 and 64 (2) (2) AO1 5212 + 5632 + 6014 + 642 (=3384) (0) AO2 (0) AO3 /60 B1 1.3b M1 1.3b F.T. their midpoints, provided within interval m1 1.3b 56.4 (cm) A1 1.3b F.T. their sum of products, division by 60 (b) Strategy to look back that 32 out of 60 are size 2, e.g. ‘(table shows) about half S1 2.5a customers are size 2 Conclusion to give Salesman is correct E1 2.5a 28. Straight lines parallel to all 4 sides and (6) (4) AO1 3cm away (+2mm) (2) AO2 Arcs with radius 3cm (+2mm) at all 4 (0) AO3 vertices joining the straight lines B2 2.3b B1 for straight lines parallel to 2 sides 29. (Height of tree =) Tan 56°  19 + 1∙8(m) and 3cm away (+2mm), OR straight lines parallel to all 4 sides but not at (Height of tree =) 29∙968658….. (m) B2 2.3b 3cm 30. (a) 10/0·2 B1 for arcs with radius 3cm (+2mm) = 50 at least 2 vertices but not joined to N/m2 straight lines, OR arcs at all 4 vertices but not at 3cm or (4) (0) AO1 not joined to straight lines (4) AO2 (0) AO3 M3 3.1d Award M2 for tan 56°  19 OR sight of 28∙168658….(m) Award M1for tan 56° = opposite/19 Accept rounded or truncated from working A1 1.3b Accept rounded or truncated from working F.T from their rounded or truncated 28∙168… (4) (1) AO1 (0) AO2 (3) AO3 M1 1.3a A1 1.3a U1 1.1 (b) 10/x (N/m2) B1 2.3b (4) (3)AO1 (1)AO2 (0)AO3 © WJEC CBAC Ltd.





COMPONENT 1: NON-CALCULATOR, HIGHER TIER Qu. Topic Max Num Alg mark 3 1 Substituting 3 4 3 2 Standard form 44 7 3 Cherry blossom paint ratio and graph 4 2 4 Tree diagram – Andy going to college 6 7 6 5 Prime factors in index notation 33 2 34 6 Simultaneous equations – paint and brushes 4 7 Loci 4 8 Ratio problem 4 9 Factorising 3 10 Carpet 52 11 Vectors 4 12 Building site 5 13 Gradients & perp. lines 7 14 Speed 6 15 Congruency 5 16 Histogram 10 17 Inverse proportion 4 18 Surds 44 19 Simplifying 2 20 Recurring decimals & Indices 55 21 Composite shape 7 22 Transformation of graphs 6 23 Probability 7 24 Trigonometry, algebra and surds 81 Totals 120 19 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 175 Ratio Geom Prob Stats AO1 AO2 AO3 Common 300 4 0 0 2 (C1 FT Q28) 4 0 2 2 4 (C1 FT Q25) 6 2 4 0 6 (C1 FT Q24) 300 1 0 3 4 (C1 FT Q26) 4 040 4 202 3 0 0 3 (C1 FT Q22) 3 1 0 4 5 (C1 FT Q27) 4 211 5 1 0 4 5 (C1 FT Q26) 322 6 240 5 050 10 2 5 3 4 400 400 200 500 214 060 7 214 5 305 23 21 23 51 35 34 29

GCSE MATHEMATICS Sample Assessment Materials 176 COMPONENT 1: NON-CALCULATOR, FOUNDATION TIER Qu. Topic Max Num Alg mark 3 1 Factors, primes, etc 44 5 2 2 Place value 33 3 3 Frequency table and bar graph 4 4 17 4 Rounding and simple estimate 44 5 Rotational symmetry 2 6 Car parking 11 11 7 Balancing weights 3 8 Scale drawing 5 9 Shopping estimate 44 10 Piece of wood 22 11 Simplifying 5 12 Perimeter rectangle problem 3 13 Sequences - diagrams 2 14 Sharing money and percentage 5 15 Temperature 6 16 Painting 4 17 Triangle 4 18 Evaluating presentation and validation 31 19 Bouncing ball 3 20 Area ratio 5 21 French German Venn 4 22 Factorising 3 23 Daffodil bulbs 5 24 Tree diagram – Andy going to college 6 25 Cherry blossom paint ratio and graph 4 26 Simultaneous equations - paint and brushes 4 27 Carpet 52 28 Standard form 22 29 Building site 5 Totals 120 33 © WJEC CBAC Ltd.

Ratio Geom Prob Stats AO1 AO2 AO3 Common 400 300 4 130 400 2 200 443 300 5 320 310 101 500 3 111 011 5 500 2 4 510 22 202 4 040 2 030 3 102 32 212 4 202 3 0 0 3 (C1 HT Q9) 5 122 6 2 4 0 6 (C1 HT Q4) 4 0 2 2 4 (C1 HT Q3) 1 0 3 4 (C1 HT Q6) 3 1 0 4 5 (C1 HT Q10) 2 0 0 2 (C1 HT Q2) 5 1 0 4 5 (C1 HT Q12) 32 18 20 62 29 29 29

COMPONENT 2: CALCULATOR-ALLOWED, HIGHER TIER Qu. Topic Max Num Alg mark 1 Percentages 44 2 Questionnaire 3 3 Algebra square length 55 4 Animal rescue scatter diagram 5 4 5 Solving equations 4 5 6 Linear sequence + sequence problem 5 7 Trigonometry - man and tree 4 8 Mean hat circumference data 62 9 Spring graph interpretation 55 10 Locus statue 4 11 Probability 3 12 Fuel consumption 94 13 Bacteria growth decay rate 6 33 14 Cumulative frequency customer service 5 15 Ratio + circle 4 16 Quadratic formula 33 17 Lower and upper bounds - metal plates 66 18 Circle theorems 6 19 Dog toy 7 20 Stone in the air 74 21 Triangle between parallel lines 4 22 Travel acceleration area distance 96 23 Composite functions 66 Totals 120 19 41 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 177 Ratio Geom Prob Stats AO1 AO2 AO3 Common 400 3 0 3 0 3 (C2 FT Q24) 3 2 0 5 (C2 FT Q25) 5 140 400 4 0 1 2 (C2 FT Q26) 4 1 0 3 4 (C2 FT Q29) 4 4 2 0 6 (C2 FT Q27) 230 13 0 4 0 4 (C2 FT Q28) 3 210 5 315 132 2 3 212 31 202 300 132 6 060 7 106 3 403 22 202 3 414 402 19 23 18 52 34 34 24

GCSE MATHEMATICS Sample Assessment Materials 178 COMPONENT 2: CALCULATOR-ALLOWED, FOUNDATION TIE Qu. Topic Max Num Alg mark 1 Music bill question 66 2 Multiples of 3 and 4 22 3 Calculating probabilities 2 4 Fraction of girls in a school 33 5 Coordinates of a square 22 6 Collection of pens 44 7 Athletics track 22 8 Bracelets 65 9 Linear equations 44 10 Netball averages 3 11 Formula: Finding k 33 12 Spinners 2 13 Conversion graph 5 14 Algebra pyramid 55 15 Health weight loss 5 16 Fishing boat trip 55 17 Faizal's fractions 44 18 Percentage and cost of comic 53 19 Pouring water into cuboids 4 20 Exam marking 6 21 Probability statements 3 22 Percentage change with reverse 4 23 Pond shape area 7 24 Questionnaire 3 25 Algebra square length 55 26 Linear sequence 22 27 Mean hat circumference data 62 28 Locus statue 4 29 Trigonometry - man and tree 4 30 Pressure problem 4 Totals 120 32 25 © WJEC CBAC Ltd.

ER g Ratio Geom Prob Stats AO1 AO2 AO3 Common 1 2 501 3 (C2 HT Q2) 200 5 (C2 HT Q3) 5 3 200 2 (C2 HT Q6a) 2 300 6 (C2 HT Q8) 5 011 4 (C2 HT Q10) 3 220 4 (C2 HT Q7) 2 3 200 4 4 303 24 400 6 17 120 300 4 020 7 230 401 1 3 302 4 203 4 400 5 28 18 500 202 105 030 202 223 030 320 200 420 040 103 310 67 27 26

GCSE MATHEMATICS Sample Assessment Materials 179 GCSE Mathematics SAMs 2015/RH JW 26/6/15 © WJEC CBAC Ltd.