[PDF] Cambridge Lower Secondary Progression Test - Mathematics 2018 Stage 9 - Mark Scheme.pdf | Plain Text

Cambridge Lower Secondary Progression Test Mathematics mark scheme Stage 9 MATHS_S9_01_MS_8RP © UCLES 2018

2 M/S9/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/S9/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/S9/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/S9/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/S9/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/S9/MS © UCLES 2018 [Turn over Stage 9 Paper 1 Mark scheme Question 1 Part Mark Answer Further Information 2 9.3 −2.1 −18.9Award 1 mark for two correct. Total 2 Question 2 Part Mark Answer Further Information 1 0.6 × 0.6 0.64 × 0.4 0.64 ÷ 0.4 0.4 ÷ 0.640.36 1.6 0.625 0.256 All lines correct for the mark. Total 1 Question 3 Part Mark Answer Further Information (a)1 7.1 14 7.5 7.9 28 (b)1 2 3 5 8 Total 2 Question 4 Part Mark Answer Further Information 1 Triangular prism Total 1

8 M/S9/MS © UCLES 2018 Question 5 Part Mark Answer Further Information 1     Total 1 Question 6 Part Mark Answer Further Information (a)16 (b)1 Any correct description of the relationship, e.g. • Positive correlation. • Heavier cakes take longer to cook. • As the mass increases, the cooking time increases.Do not accept simply ‘positive’. (c)1 Any correct explanation, e.g. • 80 minutes is too long for a cake that only has a mass of 800 grams. • 80 minutes would be the cooking time for a heavier cake. • Cakes that have a mass of 800g only take about 40 minutes to cook.Accept any indication that the cooking time is too long for the size of the cake. Do not accept • Not many cakes take that long to cook. Total 3 Question 7 Part Mark Answer Further Information 2 29 − 5nAccept equivalent expressions, e.g. 24 − 5(n − 1) Award 1 mark for −5n seen. Do not award the mark for just 5n. Total 2

9 M/S9/MS © UCLES 2018 [Turn over Question 8 Part Mark Answer Further Information 2 164.52 Award 1 mark either for • sight of the digits 16452 in the answer or • a correct method leading to an answer with 2 decimal places with no more than one arithmetic error. e.g. 4 5 7 × 3 6 2 6 4 2 1 3 7 1 0 1 6 3 5 2 so 163.52 Total 2 Question 9 Part Mark Answer Further Information (a)11 (b)1 1 8 Do not accept 3 1 2 Total 2

10 M/S9/MS © UCLES 2018 Question 10 Part Mark Answer Further Information (a)1 15.2 (km) Allow a tolerance of ±0.2 km. (b)2 087° 083° 57° 53° AN N C B Award 2 marks if C is within both sets of tram lines (tram lines should allow for a ±2° tolerance). Award 1 mark if C is within one set of tram lines. Total 3 Question 11 Part Mark Answer Further Information (a)1 x –1 0 2 y –1 15Both required for the mark. (b)2 Straight line graph correctly drawn extending at least from x = –1 to x = 2. –1 1 2 3 4 5 –2 –3 – 4 – 4 –3 –2 –10x y 1 2 3 4 5 6 Award 1 mark for correctly plotting their 3 points. Total 3

11 M/S9/MS © UCLES 2018 [Turn over Question 12 Part Mark Answer Further Information 215 Award 1 mark for sight of 9 2 and 10 3 or answer of 90 6 or for a correct method allowing one arithmetic error. Total 2 Question 13 Part Mark Answer Further Information 2x 2 − 2x − 15 Award 1 mark for at least three of these four terms seen or implied: x 2, −5x, 3x, −15 or for two correct out of x 2, −2x and −15 in final answer. Total 2 Question 14 Part Mark Answer Further Information 2 135 (cm 3) Award 1 mark for sight of a fully correct method for the area of the trapezium, e.g. • 2 × 3 + 0.5 × 2 × 3 • 0.5 × (2 + 4) × 3 • 3 × 4 − 0.5 × 2 × 3 implied by 9 × 15 seen or for sight of their area × 15. Total 2

12 M/S9/MS © UCLES 2018 Question 15 Part Mark Answer Further Information 2 True False 10 −1 = 0.1  400 × 10 4 = 400 000  0.3 ÷ 10 −2 = 0.003  0.8 × 10 3 = 0.8 ÷ 10 −3  Award 1 mark if 3 ticks are correctly placed. Total 2 Question 16 Part Mark Answer Further Information 2 30 (cm 2) Award 1 mark for 10 2 or equivalent or for an attempt at an algebraic solution, e.g, • 12 + 2 x or similar, which may be part of an equation • 2y = 2 x + 10. Total 2 Question 17 Part Mark Answer Further Information (a)1 Any correct explanation, e.g. • The probabilities do not add to make 1. • 0.35 + 0.25 + 0.3 = 0.9, not 1. • The total of the probabilities is 0.1 too small.0.35 + 0.25 + 0.3 = 0.9 on its own is not sufficient for the mark. (b)1 0.05 or equivalent Total 2

13 M/S9/MS © UCLES 2018 [Turn over Question 18 Part Mark Answer Further Information 1 2 5a or any equivalent fraction, e.g. a 4 10’ a 10 25 Total 1 Question 19 Part Mark Answer Further Information 2 39 304 Award 1 mark for an attempt to work out 4913 × 2 × 2 × 2. Total 2 Question 20 Part Mark Answer Further Information 3 Correct algebraic method seen leading to (x =) 2 (y =) −1 Correct methods include: • rearranging one of the equations to make one variable the subject and then substituting into the other equation, • making the coeffi cients of x or y equal followed by addition/subtraction of the equations.Do not accept trial and improvement as a method here. Award 2 marks for an algebraic method leading to either x = 2 or y = −1. Award 1 mark for 2 and −1 with no/incorrect working or for eliminating either x or y, allowing one arithmetic error, e.g. • rearrange one of the equations to make one variable the subject and then substituting into the other equation, • making the coeffi cients of x or y equal, followed by addition/subtraction of the equations. Total 3

14 M/S9/MS © UCLES 2018 Question 21 Part Mark Answer Further Information 2 ($) 9.60 Award 1 mark for 2.40 × 4 or 2.40 ÷ 0.25. Total 2 Question 22 Part Mark Answer Further Information 3(a =) 2 Award 2 marks for a 2 + 9 2 = 6 2 + 7 2. This may be implied by (a 2) = 6 2 + 7 2 − 9 2 (= 4). Award 1 mark for 6 2 + 7 2 (= 85) or a 2 + 9 2 seen. Total 3

15 M/S9/MS © UCLES 2018 [Turn over Stage 9 Paper 2 Mark scheme Question 1 Part Mark Answer Further Information 2 ($)87.12 Award 1 mark for a valid method, e.g. 48.40 ÷ 20 × 36 or 2.42 seen or 1.8 seen. Total 2 Question 2 Part Mark Answer Further Information (a)1 6(3a − 2) (b)1 c(2c + 5) Total 2 Question 3 Part Mark Answer Further Information (a)136 (b)1 144Accept 180 – their (a). Total 2 Question 4 Part Mark Answer Further Information 1 A minimum of four intervals in the range 100–200(cm) without gaps or overlapsIgnore additional intervals outside of this range. Condone unequal intervals. Total 1 Question 5 Part Mark Answer Further Information 1 True False  True  False Both correct for 1 mark. Total 1

16 M/S9/MS © UCLES 2018 Question 6 Part Mark Answer Further Information (a)1n 3 (b)1nAccept n 1 Total 2 Question 7 Part Mark Answer Further Information (a)1 (12, 5) (b)1 (5, 1) Total 2 Question 8 Part Mark Answer Further Information 1 12.4(…) (km / l) Total 1 Question 9 Part Mark Answer Further Information 2 2 4 61 2 4 63 6 12 185 10 20 30 Rows and columns can be transposed. The numbers 1, 3, 5 can be in any order. The numbers 2, 4, 6 can be in any order. Award 1 mark for row and column labels correct. Total 2

17 M/S9/MS © UCLES 2018 [Turn over Question 10 Part Mark Answer Further Information (a)1 Sales are expected to increase as the price goes down.Accept equivalents, e.g. • Less sales as the price goes up. • As one goes down the other goes up. (b)2 4 (thousand) Condone 4000. Award 1 mark for sight of 7 (thousand) or 3 (thousand). This can be implied by the correct lines drawn on the graph. Total 3 Question 11 Part Mark Answer Further Information 3 A complete trial and improvement method leading to the answer x = 3.4. This consists of at least one correct trial of 3.4 or lower and a correct 2 decimal place trial to confirm the first decimal place.Award 1 mark for any trial of a number between 3 and 4 correctly evaluated. Award 1 mark for a trial of x correctly evaluated where 3.35 G x G 3.38. Award 1 mark for 3.4 in the answer space. xx 2 + 4x (Accept rounded or truncated answers) 3.1 22.01 3.2 23.04 3.3 24.09 3.35 24.6225 3.36 24.7296 3.37 24.8369 3.38 24.9444 3.39 25.0521 3.4 25.16 3.5 26.25 3.6 27.36 3.7 28.49 3.8 29.64 3.9 30.81 Total 3

18 M/S9/MS © UCLES 2018 Question 12 Part Mark Answer Further Information 3 7.5 (%) Award 2 marks for a correct method for finding the fractional or percentage increase, i.e. – 0.08 ×1300 + (961 900) 2200 (= 0.075) or 1.08 × 1300 + 961 2200 (= 1.075) or 2365 2200 Award 1 mark for sight of any of these: • 0.08 × 1300 (=$104) oe • 1.08 × 1300 (=$1404) oe • ($)165 (increase over year) • ($)2365 (total for this year). Total 3 Question 13 Part Mark Answer Further Information 2(c =) −20 Award 1 mark for 5c + 160 = 60 or c + 32 = 12. Total 2

19 M/S9/MS © UCLES 2018 [Turn over Question 14 Part Mark Answer Further Information 3 3840 (bottles) Method 1 (Calculating the total number of litres produced). Award 2 marks for sight of 2880 (litres) or 180 × 40 2.5 or 7200 2.5 Award 1 mark for sight of 180 × 40 (= 7200) or 40 (= 16) 2.5 Method 2 (Calculating the number of bottles produced per tree). Award 2 marks for sight of 21.33… (bottles per tree) or 40 2.5 ÷ 0.75 (= 21.33 ...) Award 1 mark for 40 2.5 (= 16) Total 3

20 M/S9/MS © UCLES 2018 Question 15 Part Mark Answer Further Information (a)1 4.384615..…. Award the mark if these digits are seen. (b)1 4.4 Allow follow through from an incorrect answer in (a) as long as their (a) has 3 or more digits. Total 2 Question 16 Part Mark Answer Further Information 2 3.6 (litres) Award 1 mark for 3600 or for correct conversion to litres of an incorrect volume in cm 3. Total 2 Question 17 Part Mark Answer Further Information 1 Journey A: 180 km in 3 hours Journey C: 30 km in 0.5 hoursJourney B: 140 km in 2.5 hours Journey D: 10 km in 10 minutes Total 1

21 M/S9/MS © UCLES 2018 [Turn over Question 18 Part Mark Answer Further Information 1 A correct representation, i.e. or Accept a drawing with some visible edges of the individual cubes shown, e.g. Accept a drawing with hidden edges shown if hidden edges are dashed. Total 1 Question 19 Part Mark Answer Further Information 2 – r t (=) 3 7 or – r t21 (=) 7 Accept equivalent expressions, e.g. r ÷ 7 − 3 (r − 21) ÷ 7 Do not accept r − 21 ÷ 7 Award 1 mark for a correct first step, i.e. r =t+3 7 rt721 =+ Total 2

22 M/S9/MS © UCLES 2018 Question 20 Part Mark Answer Further Information (a)2 History Geography 86524 33 105 00 56 48 117 2478Award 1 mark if there is one omission in the 9 leaves or if there are 9 unordered, but otherwise correct, leaves. (b)1 A correct comparison, e.g. • There are more higher geography marks than history marks. • History has more marks in the 40s than geography. • Geography has more marks in the 70s than history.Do not accept just a description of one subject, e.g. history had lots of marks in the 40s. Do not accept references to averages alone. Total 3 Question 21 Part Mark Answer Further Information 2 (Manjit’s number =) 6 (Gabriella’s number =) 39Award 1 mark for one number correct or if a factor of 24 (other than 24) and a multiple of 13 (other than 13) are seen. Total 2 Question 22 Part Mark Answer Further Information 1 Any correct explanation that indicates that the original price of the trainers needs to be taken into account, e.g. There is a higher percentage/fractional discount on bargain trainers. There is a 12% discount on the Alpha trainers compared to a 20% discount on the Bargain trainers. 6 50 is less than 6 30 (or equivalent).Do not accept, e.g. • Bargain trainers are cheaper. • Alpha trainers are more expensive. Total 1

23 M/S9/MS © UCLES 2018 [Turn over Question 23 Part Mark Answer Further Information 2 The point should be plotted at (2012, 42). 0 2007 2006 2008 2009 2010 2011 2012 10 20 30 40 50 60 Award 1 mark if the value 42 is seen (28 + 14) or implied by the graph. or Award 1 mark for correct method. x + x 2 with x misread from the graph. Total 2

24 M/S9/MS © UCLES 2018 Stage 9 Paper 3 Mark scheme Question Mark Answer Further information 119 21 Square Triangle Hexagon Pentagon 31x → x − 3 41 Negative Ignore comments about strength. 5122 61 18 Answer may be written next to 13. 71 A B 81 122 200 or 61 100 or 61% or 0.61 91 20 (km) 101 3 2 or 1 1 2 or 1.5 Accept any equivalent fractions. 11118 1212 131 3.2 141 0510 Do not accept solid circle. 151 0.4 (m 3) 161 150(°) 171 72(°) 181 360 cm 3 1800 cm 3 180 cm 3 3600 cm 3 191 64 Do not accept 4 3. 201 1 250 000 (cm 3) 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.