[PDF] Cambridge Lower Secondary Progression Test - Mathematics 2018 Stage 8 - Mark Scheme.pdf | Plain Text

Cambridge Lower Secondary Progression Test Mathematics mark scheme Stage 8 MATHS_03_S3_MS_7RP © UCLES 2018

2 M/S8/MS © UCLES 2018 General guidance on marking Difference in printing It is suggested that schools check their printed copies for differences in printing that may affect the answers to the questions, for example in measurement questions. Brackets in mark scheme When brackets appear in the mark scheme this indicates extra information that is not required but may be given. For example: Question 1 Part Mark Answer Further Information 1 19.7 or 19.6(58…) Total 1 This means that 19.6 is an acceptable truncated answer even though it is not the correct rounded answer. The … means you can ignore any numbers that follow this; you do not need to check them. Accept • any correct rounding of the numbers in the brackets, e.g. 19.66, • truncations beyond the brackets, e.g. 19.65 Do not accept • 19.68 (since the numbers in brackets do not have to be present but if they are they should be correct).

3 M/S8/MS © UCLES 2018 [Turn over These tables give general guidelines on marking learner responses that aren’t specifically mentioned in the mark scheme. Any guidance specifically given in the mark scheme supersedes this guidance. Number and place value The table shows various general rules in terms of acceptable decimal answers. Accept Accept omission of leading zero if answer is clearly shown, e.g. .675 Accept tailing zeros, unless the question has asked for a specific number of decimal places or significant figures, e.g. 0.7000 Accept a comma as a decimal point if that is the convention that you have taught the learners, e.g. 0,638 Units For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be given in the answer. Units are provided on the answer line unless finding the units is part of what is being assessed. The table shows acceptable and unacceptable versions of the answer 1.85 m. Accept Do not accept If the unit is given on the answer line, e.g. ............................ mCorrect conversions, provided the unit is stated unambiguously, e.g. ......185 cm...... m (this is unambiguous since the unit cm comes straight after the answer, voiding the m which is now not next to the answer)......185...... m ......1850...... m etc. If the question states the unit that the answer should be given in, e.g. ‘Give your answer in metres’1.85 1 m 85 cm185; 1850 Any conversions to other units, e.g. 185 cm

4 M/S8/MS © UCLES 2018 Money In addition to the rules for units, the table below gives guidance for answers involving money. The table shows acceptable and unacceptable versions of the answer $0.30. Accept Do not accept If the amount is in dollars and cents, the answer should be given to two decimal places.$0.30 For an integer number of dollars it is acceptable not to give any decimal places, e.g. $9 or $9.00$0.3 $09 or $09.00 If units are not given on the answer lineAny unambiguous indication of the correct amount, e.g. 30 cents; 30 c $0.30; $0-30; $0=30; $00:3030 or 0.30 without a unit $30; 0.30 cents Ambiguous answers, e.g. $30 cents; $0.30 c; $0.30 cents (as you do not know which unit applies because there are units either side of the number) If $ is shown on the answer line All unambiguous indications, e.g. $......0.30......; $......0-30......; $......0=30......; $......00:30......$......30...... Ambiguous answers, e.g. $......30 cents......; $......0.30 cents...... unless units on the answer line have been deleted, e.g. $ ......30 cents...... If cents is shown on the answer line......30......cents ......0.30......cents Ambiguous answers, e.g. ......$30 ......cents; ......$0.30 ......cents unless units on the answer line have been deleted, e.g. ......$0.30......cents

5 M/S8/MS © UCLES 2018 [Turn over Duration In addition to the rules for units, the table below gives guidance for answers involving time durations. The table shows acceptable and unacceptable versions of the answer 2 hours and 30 minutes. Accept Do not accept Any unambiguous indication using any reasonable abbreviations of hours (h, hr, hrs), minutes (m, min, mins) and seconds (s, sec, secs), e.g. 2 hours 30 minutes; 2 h 30 m; 02 h 30 m Any correct conversion with appropriate units, e.g. 2.5 hours; 150 mins unless the question specifically asks for time given in hours and minutesIncorrect or ambiguous formats, e.g. 2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3; 2.3 h (this is because this indicates 0.3 (i.e. 18 minutes) of an hour rather than 30 minutes) 02:30 (as this is a 24-hour clock time, not a time interval) 2.5; 150 Time The table below gives guidance for answers involving time. The table shows acceptable and unacceptable versions of the answer 07:30. Accept Do not accept If the answer is required in 24-hour formatAny unambiguous indication of correct answer in numbers, words or a combination of the two, e.g. 07:30 with any separator in place of the colon, e.g. 07 30; 07,30; 07-30; 07307:30 7:30 am 7 h 30 m 7:3 730 7.30 pm 073 07.3 If the answer is required in 12-hour formatAny unambiguous indication of correct answer in numbers, words or a combination of the two, e.g. 7:30 am with any separator in place of the colon, e.g. 7 30 am; 7.30 am; 7-30 am 7.30 in the morning Half past seven (o’clock) in the morning Accept am or a.m.Absence of am or pm 1930 am 7 h 30 m 7:3 730 7.30 pm

6 M/S8/MS © UCLES 2018 Algebra The table shows acceptable and unacceptable versions of the answer 3x – 2. Accept Do not accept x3 – 2; 3 × x – 2 3x + –2 if it is supposed to be in simplest form Case change in letters Changes in letters as long as there is no ambiguity Accept extra brackets when factorising, e.g. 5(x + (3 + y)). Inequalities The table shows acceptable and unacceptable versions of various answers. For the following Accept Do not accept For 6 G x 1 8[6, 8) 6 1 x 1 8 For x G –2(–∞,–2] x 1 –2 For x 2 3(3, ∞) 3 1 xJust ‘3’ written on the answer line, even if x 2 3 appears in the working Plotting points The table shows acceptable and unacceptable ways to plot points. Accept Do not accept Crosses or dots plotted within ± 1 2 square of the correct answer The graph line passing through a point implies the point even though there is no cross.A horizontal line and vertical line from the axes meeting at the required point

7 M/S8/MS © UCLES 2018 [Turn over Stage 8 Paper 1 Mark scheme Question 1 Part Mark Answer Further Information 1 15.79 Total 1 Question 2 Part Mark Answer Further Information 2 2 1 50% 5 2 35% 107 28% 257 40% 207 70% Award 1 mark for two additional correct lines. Total 2 Question 3 Part Mark Answer Further Information (a)1 x–1 0 2 y11 8 2Award 1 mark if both are correct. (b)2 Straight line drawn with a ruler extending at least between (–1, 11) and (2, 2)Award 1 mark if all three points from their table are plotted correctly. Total 3

8 M/S8/MS © UCLES 2018 Question 4 Part Mark Answer Further Information 2 64 16 .......4 square cube....... Award 1 mark for 4 correct or for their 16 equal to the square of their 4. Total 2 Question 5 Part Mark Answer Further Information (a)1 0.3 (b)112 Total 2 Question 6 Part Mark Answer Further Information 1 45 75 9 25 3 15 5 3.6 Total 1

9 M/S8/MS © UCLES 2018 [Turn over Question 7 Part Mark Answer Further Information (a)1 18 (cm 2) (b)1(a =) 4 Total 2 Question 8 Part Mark Answer Further Information 1 60.5 (m) 2 5700 (cm) 2 0.0509 (km)Accept correct conversions to the same unit. Total 1 Question 9 Part Mark Answer Further Information (a)115x 2 (b)25y + 12 Award 1 mark for 5y or +12 correct. Total 3 Question 10 Part Mark Answer Further Information 2 1.5 (km) Award 1 mark for correct conversion between metres and kilometres e.g. 40 lengths = 1 km or 25 m = 0.025 km or correct conversion of their total length in metres to kilometres or for 1500 m seen. Total 2

10 M/S8/MS © UCLES 2018 Question 11 Part Mark Answer Further Information (a)1 A B Accept shorter mirror line as long as the section between A and B is present. Accept solid mirror line. (b)1 A C B Condone lack of label if the position is clear. (c)1 1 (unit) right and 4 (units) up Accept   1 4 . Accept 4 up and 1 right. Total 3 Question 12 Part Mark Answer Further Information (a)112 (b)1 ($)6 Total 2

11 M/S8/MS © UCLES 2018 [Turn over Question 13 Part Mark Answer Further Information (a)1 (b)1 Total 2 Question 14 Part Mark Answer Further Information (a)1 2 × 2 × 7 or 2 2 × 7 Must see prime factors multiplied. Do not accept 1 × 2 × 2 × 7. (b)1 2 × 3 × 5 × 7 If 1 is given as prime in parts (a) and (b) penalise only on first occurrence. (c)114 (d)1 420 Total 4 Question 15 Part Mark Answer Further Information 1 100 Total 1

12 M/S8/MS © UCLES 2018 Question 16 Part Mark Answer Further Information 1 103 Total 1 Question 17 Part Mark Answer Further Information (a)1 8.6 Accept 3 8 5 or equivalent fraction. (b)1 180 Total 2 Question 18 Part Mark Answer Further Information 1 Square Rectangle Parallelogram Rhombus Kite Total 1 Question 19 Part Mark Answer Further Information (a)1 1904 (b)1 938 Total 2 Question 20 Part Mark Answer Further Information 23n + 1 Award 2 marks for any equivalent expressions, e.g. 1 + 3n or n + n + n + 1 Award 1 mark for 3n seen. Total 2

13 M/S8/MS © UCLES 2018 [Turn over Question 21 Part Mark Answer Further Information 2 o 0.41 6 Allow any clear indication of recurring 6, i.e. 6 with recurring symbol. Award 1 mark for any rounded or truncated answer to two significant figures or better, e.g. 0.416, 0.41 or 0.42. Total 2 Question 22 Part Mark Answer Further Information 2 1 25 Award 1 mark for 200 5000 seen or any equivalent fraction not in its simplest form. Total 2 Question 23 Part Mark Answer Further Information 2 1 11 14 or 25 14 Award 1 mark for finding two correct fractions with a common denominator. Total 2

14 M/S8/MS © UCLES 2018 Stage 8 Paper 2 Mark scheme Question 1 Part Mark Answer Further Information 1 2 : 4 : 1 Total 1 Question 2 Part Mark Answer Further Information 2 All 7 additional combinations shown, with no repetitions. Morning activity Afternoon activity ST SV SF CT CV CF AT AV AFCombinations can be listed in any order. Award 1 mark for at least 5 additional correct combinations with at most 1 repetition or error. Total 2 Question 3 Part Mark Answer Further Information (a)1 10:17 (b)2 15 (minutes) Award 1 mark for sight of either 14 (minutes) or 29 (minutes) or 7 (minutes) or 8 (minutes). Total 3

15 M/S8/MS © UCLES 2018 [Turn over Question 4 Part Mark Answer Further Information (a)1(C =) 18t + 3 (b)1 ($)147 Follow through from an incorrect answer to part (a) as long as it involves more than one arithmetical operation. Total 2 Question 5 Part Mark Answer Further Information (a)1 Any decimal strictly between 11.375 and 11.38, e.g. • 11.376 • 11.3751 • 11.37999Do not accept 11.375 or 11.38. (b)1 Any decimal strictly between 0.99 and 1, e.g. • 0.995 • 0.991 • 0.99996Do not accept 0.99 or 1. Total 2 Question 6 Part Mark Answer Further Information 2 10 13 5 7 107 and a comparative calculation, e.g. 5 7 = 0.71(4…) 7 10 = 0.7 10 13 = 0.76(9…) 650 910 and 637 910 and 700 910 Award 2 marks for 10 13 circled and correct comparison. Award 1 mark for two fractions correctly converted to comparable form, e.g. 10 14 and 10 13 . Award no marks for a decision with no calculation. Total 2

16 M/S8/MS © UCLES 2018 Question 7 Part Mark Answer Further Information (a)1 ($)640 (b)1 (£)185 to (£)190 inclusive (c)1 ($)1600 Allow follow through of 2.5 × their (a). Total 3 Question 8 Part Mark Answer Further Information 2 ($)15.66 Award 1 mark for sight of any of these: 0.08 × 14.50 8 100 × 14.50 1.16 1.08 108 100 108% Total 2 Question 9 Part Mark Answer Further Information 2 12 (cm 2) Award 1 mark for either 0.5 × 4 × 6 or sight of 9 or 21 or for any other complete method for finding the area. Total 2 Question 10 Part Mark Answer Further Information 1 0.0625 Accept 1 16 . Total 1

17 M/S8/MS © UCLES 2018 [Turn over Question 11 Part Mark Answer Further Information 2 8.7 Award 1 mark for a total of 174 or Award 1 mark for their total f × x correctly divided by 20; this can be implied by (42 + 16 + 36 + 80)/20 with at least 3 values in numerator correct. Total 2 Question 12 Part Mark Answer Further Information (a)2 1 2 3 ............ 10 1003 5 7 17 ............ 201 8 21 Award 1 mark for one correct value. (b)1x → 2x + 1 Total 3 Question 13 Part Mark Answer Further Information 2 2 pairs of arcs and a correct line AB Construction curves must be arcs and line must be shown with accuracy ± 2 mm from the midpoint of AB and ± 2°. Award 1 mark for a correct line within tolerance or for an attempt at a correct method demonstrated by two pairs of intersecting arcs. Total 2

18 M/S8/MS © UCLES 2018 Question 14 Part Mark Answer Further Information (a)14 (b)135 (c)127 (d)1 Ticks No and gives a correct reason based on the values of the medians, e.g. • The median was higher before the menu was changed. • The average number of customers was lower after the menu changed. • The average number of customers fell.Follow through from their (b). Do not accept ‘The average was higher/lower.’ (no reference to before or after). Total 4 Question 15 Part Mark Answer Further Information (a)144 (b)2 5 Award 1 mark for sight of correct method for finding the second term, e.g. (17 + 7) ÷ 3 = (8) or for identifying the 2 nd term as 8. Total 3 Question 16 Part Mark Answer Further Information (a)1 Answers in the range 75 to 75.4(…) (mm) (b)1 Answers in the range 452 to 453 (mm 2) Total 2 Question 17 Part Mark Answer Further Information 1 315 (g) Total 1

19 M/S8/MS © UCLES 2018 [Turn over Question 18 Part Mark Answer Further Information 2 128 (cm 2) Award 1 mark for a correct method with at most 1 arithmetic error or for 24 and 16 seen. Total 2 Question 19 Part Mark Answer Further Information 2 Correct triangle with side lengths equal to 6 cm and two correct arcs seen.Award 1 mark for one correct arc shown. Allow a tolerance of ± 2 mm for the length of the sides and position of the arcs. Total 2 Question 20 Part Mark Answer Further Information 2 4 green, 2 red and 3 blue Award 1 mark for beads in the correct unsimplified ratio, e.g. 8 green, 4 red and 6 blue or equivalent, e.g. 423 ,, 999 or if the number of green is double the number of red or if the number of blue is 1 3 of their total number of beads. Do not accept 1 3 for blue. Total 2

20 M/S8/MS © UCLES 2018 Question 21 Part Mark Answer Further Information 2 Ticks Earth and shows a correct conversion between kilometres and miles, i.e. one of (Earth) 12 760 km = 7975 miles or (Venus) 7560 miles = 12 096 kmAward 1 mark for sight of 7975 or 12 096 or for sight of a correct conversion factor between miles and km, e.g. • 8 km = 5 miles • 1 km = 0.625 miles • 1 mile = 1.6 km This may be implied as part of a calculation, e.g. 12 760 × 5 ÷ 8 Total 2

21 M/S8/MS © UCLES 2018 Stage 8 Paper 3 Mark scheme Question Mark Answer Further information 11 Any one of 1, 2, 4, 5, 10 or 20 214 31 ab b does not need to be labelled. 41 24.0 Do not accept just 24. 512 61– 4u + 2w or 2w – 4u 714 81 3 10 Accept equivalent fractions or 0.3 or 30%. 91 136 1012(n + 5) n (2 + 5) n + 5 × 2 2n + 5 5n + 2 111 2 (km) 121 0.92 131 16(%) 141 10 (children) 151(x =) 5 161 70(°) 1719 181 (3, 3) 191 2 : 1 201 260 (cm 2)

22 M/S8/MS © UCLES 2018 Copyright © UCLES, 2018 Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. BLANK PAGE