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Cambridge Lower Secondary Progression Test Mathematics mark scheme Stage 7 MATHS_S7_MS_7RP © UCLES 20182 M/S7/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/S7/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/S7/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/S7/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/S7/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/S7/MS © UCLES 2018 [Turn over Stage 7 Paper 1 Mark scheme Question 1 Part Mark Answer Further Information (a)1 Walk (b)2 True False 12 girls walk to school. More girls than boys travel to school by car. The same number of boys and girls travel to school by bus. For all 60 students the least common method of transport is bicycle. Award 1 mark for three correct. Total 3 Question 2 Part Mark Answer Further Information 11.4 0.4 25% 40% 0.25 4% Rings 25% and 0.25 only Total 1 Question 3 Part Mark Answer Further Information (a)1 2050 (b)1 100 Total 2 Question 4 Part Mark Answer Further Information 110 Total 1
8 M/S7/MS © UCLES 2018 Question 5 Part Mark Answer Further Information 1 3 5 = 6 10 = 9 15 Both correct for 1 mark. Total 1 Question 6 Part Mark Answer Further Information 1 ($)105 Total 1 Question 7 Part Mark Answer Further Information 1 64 (g) Total 1 Question 8 Part Mark Answer Further Information 1 One quarter of 5 2 is 1 3 or One quarter of 7 2 is 1 8 Both boxes correctly completed for 1 mark. Total 1
9 M/S7/MS © UCLES 2018 [Turn over Question 9 Part Mark Answer Further Information 1 mirror line Image does not have to be shaded. Accept slight inaccuracies in drawing as long as the intention is clear. Total 1 Question 10 Part Mark Answer Further Information 1 3 8 9 10 100All three correct for 1 mark. Total 1 Question 11 Part Mark Answer Further Information (a)1 Acute Right Obtuse Reflex (b)1 317(°) Accept angles in the range 316–318°. Total 2 Question 12 Part Mark Answer Further Information (a)1 2.7 (b)1 5.76 Total 2
10 M/S7/MS © UCLES 2018 Question 13 Part Mark Answer Further Information (a)118 (b)12 (c)1 402 Allow a follow-through as 400 + their answer to (b). Total 3 Question 14 Part Mark Answer Further Information (a)1 –1 in correct position on table (b)1 7 (°C) (c)1 5 (°C) Total 3 Question 15 Part Mark Answer Further Information 2 2 9 or equivalent fractionAward 1 mark for two correct fractions with a common denominator of a multiple of 9. Total 2 Question 16 Part Mark Answer Further Information (a)2 36(%) Award 1 mark if any of the following are seen: 36 100 (or 36 out of 100) 18 50 (or 18 out of 50) 0.36 (b)2 1 : 3 Award 1 mark for any of the following: 3 : 1 2 : 6 4 : 12 Total 4
11 M/S7/MS © UCLES 2018 [Turn over Question 17 Part Mark Answer Further Information 1 7 3 20 or 7.15Accept equivalent mixed fractions, e.g. 6 7 40 or 15 7 100 . Total 1 Question 18 Part Mark Answer Further Information 2 94 (m) 1.255 (l ) 0.465 (tonnes)Award 1 mark for any 2 correct. Total 2 Question 19 Part Mark Answer Further Information 2 9 40 Award 1 mark for 225 1000 seen or equivalent fraction, e.g. 45 200 . Total 2 Question 20 Part Mark Answer Further Information (a)1 A correct explanation e.g. There are 6 lengths, each of length h. Each square has a perimeter of 4h but two sides are not part of the perimeter.Condone without sentences, e.g. h + 2h + h + 2h = 6h 4h + 4h – 2h = 6h h + h + h + h + h + h Do not accept 6 × h unless there is indication on the diagram that each exterior side is marked as h. (b)1 20 Ignore any units. Total 2
12 M/S7/MS © UCLES 2018 Question 21 Part Mark Answer Further Information (a)1 9 20 Accept equivalent fraction, decimal or percentage, e.g. 0.45. Do not accept answer as a ratio (9:20) or in words. (b)1 Whole number values in the ratio 7:3, e.g. 7 (red) and 3 (green) 14 (red) and 6 (green) 21 (red) and 9 (green) 70 (red) and 30 (green)Do not accept 3 red and 7 green or 7 10 and 3 10 . Total 2 Question 22 Part Mark Answer Further Information (a)17 (b)120 Total 2 Question 23 Part Mark Answer Further Information 2 3 2 5 Award 1 mark for answer given not in simplest form, e.g. 33 2 55 or for 13 5 seen. Total 2
13 M/S7/MS © UCLES 2018 [Turn over Question 24 Part Mark Answer Further Information 3 $14.10 Award 2 marks for (their 6 slabs) × $2.35 correctly calculated or for 6 × $2.35 plus incorrect answer. Award 1 mark for (their 6 slabs) × $2.35 incorrectly calculated or 6 seen. Total 3
14 M/S7/MS © UCLES 2018 Stage 7 Paper 2 Mark scheme Question 1 Part Mark Answer Further Information (a)148 (b)119 (c)125 Total 3 Question 2 Part Mark Answer Further Information 2 52 Award 1 mark if 5 × 9 or 45 is seen. Total 2 Question 3 Part Mark Answer Further Information 14 Total 1 Question 4 Part Mark Answer Further Information (a)1 H(assan) J(amila)Both correct for 1 mark. (b)1 A(nastasia) Total 2
15 M/S7/MS © UCLES 2018 [Turn over Question 5 Part Mark Answer Further Information (a)1 A correct demonstration in any orientation, e.g. or (b)1 The correct demonstration in any orientation, e.g. Total 2 Question 6 Part Mark Answer Further Information 2 650 (grams) Award 1 mark for sight of 0.65 or incorrect reading from scale correctly converted to grams. Total 2
16 M/S7/MS © UCLES 2018 Question 7 Part Mark Answer Further Information 1 Triangular prism Total 1 Question 8 Part Mark Answer Further Information (a)16 (b)131 (c)18 Total 3 Question 9 Part Mark Answer Further Information 2 4 3 4 2 . 3 3 2 7 . 9 – 1 4 . 9 Award 1 mark for 2 correct digits. Total 2 Question 10 Part Mark Answer Further Information 2 (Order) 1 (Order) 6 (Order) 3 Award 1 mark if 2 are correct. Total 2
17 M/S7/MS © UCLES 2018 [Turn over Question 11 Part Mark Answer Further Information 2 7.5 (litres) Award 1 mark for 10 4 (= 2.5) or 3 4 of 10. Total 2 Question 12 Part Mark Answer Further Information 1 Correct ruled line extending across the entire grid. –3 –2 –1 0 1 2 3 4 – 4 – 4 –3 –2 –1 1 2 3 4y x Total 1 Question 13 Part Mark Answer Further Information 1 A correct explanation, e.g. 7T have a higher mean Having a higher range means 7P are less consistent not better; he should have looked at the means. 7T scored 4 more than 7P on average.Any equivalent statement making it clear that a higher mean is better. Do not accept just repeating the facts given in the question without comparison, e.g. 7P is 56 and 7T is 60. Total 1
18 M/S7/MS © UCLES 2018 Question 14 Part Mark Answer Further Information 2 4 (hours) 30 (minutes) and 21:40Award 1 mark for each correct answer. Total 2 Question 15 Part Mark Answer Further Information 1 9 Total 1 Question 16 Part Mark Answer Further Information 2 150 (cm 2) Award 1 mark for 5 × 5 × 6 or for 25 (cm 2) seen (this may be on the diagram). Total 2 Question 17 Part Mark Answer Further Information 1 (1, 2) Total 1
19 M/S7/MS © UCLES 2018 [Turn over Question 18 Part Mark Answer Further Information 1 No and a correct reason, e.g. Lily’s number could be 1900 and Aiko’s number could be 1568 Aiko’s number could be as low as 1500 (and Lily’s number must be larger than this) 1850 G LN 1 1950 and 1500 G AN 1 2500 Total 1 Question 19 Part Mark Answer Further Information 1 Days WeeksBoth correct for 1 mark. Total 1 Question 20 Part Mark Answer Further Information 1 (Angle COD =) 50(°) Total 1 Question 21 Part Mark Answer Further Information 1 Green and green. Both correct for 1 mark. Total 1
20 M/S7/MS © UCLES 2018 Question 22 Part Mark Answer Further Information 14q + 2pAllow unsimplified equivalent expressions. Total 1 Question 23 Part Mark Answer Further Information 2 4.1 Award 1 mark for correct method with one arithmetic error. Total 2 Question 24 Part Mark Answer Further Information 2 Shows that percentage of women who own a bicycle is 71(.42…)% and men is 73(.33….)%.Award 1 mark for 0.71 or 71% or 0.73 or 73%. Total 2 Question 25 Part Mark Answer Further Information 3 3.94 (m 2) Award 2 marks for 39 400 (cm 2) or for 2 2 – 0.3 × 0.2 or equivalent methods involving sub-division of the rectangle (working in metres). Award 1 mark for a correct area calculation in either centimetres squared or metres squared or for conversion to 0.3 m and 0.2 m. Total 3
21 M/S7/MS © UCLES 2018 [Turn over Question 26 Part Mark Answer Further Information 2 Complete accurate pentagon with sides of length 6 cm and internal angles of 108°.Allow a tolerance of 1 mm on the side lengths and 1° on the angles. Award 1 mark for one side and one angle correct. Total 2 Question 27 Part Mark Answer Further Information 1 0.075 Condone –0.075. Total 1
22 M/S7/MS © UCLES 2018 Stage 7 Paper 3 Mark scheme Question Mark Answer Further Information 1149 21–2 314 418 51 (3, –1) 61Certain 0 Impossible 0.5 Even chance 1 7120 81 7 20 Accept equivalent fractions or 0.35 or 35%. 91 8.35 101 1 5 Accept equivalent fractions or 0.2 or 20%. 111 50(°) 1214x = 28 131 60(%) 141 10 16 8 6 9 12 4 5 15117 161 20 (cm) 171Both correct for 1 mark. 181 105 (calories) 191 45 (cm 3) 201 0.4 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. 33 50 72 48 26