Download [PDF] April 2020 CAIE P2 Mark Schemes 1112 Mathematics Cambridge Lower Secondary Checkpoint

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[PDF] April 2020 CAIE P2 Mark Schemes 1112 Mathematics Cambridge Lower Secondary Checkpoint.pdf | Plain Text

This document has 14 pages. Blank pages are indicated. 05_1112_02 ©UCLES 2020 [Turn over Cambridge Lower Secondary Checkpoint MATHEMATICS 1112/02 Paper 2 Apri l 2020 MARK SCHEME Maximum Mark : 50 Published This mark scheme is published as an aid to teachers and learners, to indicate the requirements of the examination. However, we h ave not been able to adjust it to reflect the full range of answers that would have been seen as a part of the normal moderation and marking process, and it does not necessarily contain all the possible alternatives that might have arisen. Cambridge will n ot enter into discussions about the mark scheme.

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 2 of 14 G eneral guidance on marking This section gives general guidelines on marking learner responses that are not specifically mentioned in the mark scheme. Any guidance specifically given in the mark scheme supersedes this guidance. Difference in printing It is suggested that schools check their printed copies for di fferences in printing that may affect the answers to the questions, for example in measurement questions. Mark scheme annotations and abbreviations M1 method mark A1 accuracy mark B1 independent mark FT follow through after error dep dependent oe or equivalent cao correct answer only isw ignore subsequent working soi seen or implied 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 Answer Mark Further Information 5 19.7 or 19.6(58) 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).

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 3 of 14 Number and place value The table shows various general rules in terms of acceptable decimal answers. Decimal Answers 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 show s 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. ............................ m Correct conversions, provided the unit is stated unambiguousl y, 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 cm 185; 1850 Any conversions to other units, e.g. 185 cm

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 4 of 14 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 no t given on the answer line Any unambiguous indication of the correct amount, e.g. 30 cents; 30 c $0.30; $0-30; $0=30; $00:30 30 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

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 5 of 14 Duration In addition to the rules for units, the table below gives guidance for answers involving time durations. The table shows acceptable and unacceptable vers ions 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 corr ect conversion with appropriate units, e.g. 2.5 hours; 150 mins unless the question specifically asks for time given in hours and minutes Incorrect 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 of an hour - i.e. 18 minutes - rather than 30 minutes) 02:30 (as this is a 24-hour clock time, not a time interval) 2.5; 150 T ime The table below gives guidance for answers involving time. It shows acceptable and unacceptable versions of the answer 07:30 Accept Do not accept If the answer is required in 24-hour format Any 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; 0730 7:30 7:30 am 7 h 30 m 7:3 730 7.30 pm 073 07.3 If the answer is required in 12-hour format Any 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

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 6 of 14 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 ambiguit÷ = = = Accept extra brackets when factorising, e.g.= 5(x + (3 + y )). Teachers must mark the final answer given. If a correct answer is seen in working but final answer is given incorrectly then the final answer must be marked. If no answer is given on the answer line then the final line of the working can be taken to be the final answer. Inequalities The table shows acceptable and unacceptable versions of various answers. For the following Accept Do not accept For 6 ≤ x < 8 [6, 8) < x < For x ≤ –2 (–∞, –2] x < –2 For x > 3 (3, ∞) 3 < x Just ‘3’ written on the answer line, even if x > 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

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 7 of 14 Question Answer Mark Further Information 1 8.6 1 Accept – 8.6 or ±8.6 2 4f and y + 7 or 7 + y 2 Accept 4 × f and f × 4 4f or== y + 7 or 7 + y B1 3 2 : 5 cao 1 4 (t = ) 10 r 1 Accept 10 × r and r x 10 5 3.22 2 Condone 3.2 Only allow 3 if correct method or more accurate answer seen in working. 1 × 9 + 2 × 14 + 3 × 2 + 4 × 12 + 5 × 8 + 6 × 5 M1 soi by 161 6 420 and cm 3 2 Allow 0.00042 m 3 420 or cm 3 B1 7 5 1 8 (V =) 36 1

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 8 of 14 Question Answer Mark Further Information 9 Correct working, e.g. : • 75 miles is 120-121 km • 115 km is 71-72 miles • a conversion factor and comparison to 8 5=or= 5 8= 1 = e.g. 75 115 == 1.533 which is less than 1.6(09) = 115 75 == 0.652 which is greater than 0.625 (or 0.621)= = 10 = 4ab ? 6a2 2 One correct term in the expansion i.e. 4ab or ? 6a2 B1 11 30= = and 400 2 One correct answer B1 12 8 (kg) 2 a correct complete method e.g.:= • 256 ÷ 48 × 1.5 •=256 ? 32 = M1

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 9 of 14 Question Answer Mark Further Information 13 0.045 and 17 000 2 One correct answer B1 14 25.1(…) (cm) 2 Accept 25 cm for 2 marks if accompanied by working. π × 8 oe M1 15 (x = ) ?2 1 Do not accept 9 ?2 16 D C A E B 2 3 correct B1 17 b(5b −=3)= 1 18 3 1

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 10 of 14 Question Answer Mark Further Information 19(a) D = 12 T oe 1 D = 12 × T 12D T = , 12 D T = = C ondone= 36 3 =in place of 12 = 19(b) = 5.5 = 1FT FT is from their linear formula connecting T and D 19(c) Straight line between (0, 0) and (10, 120) ±=half a square = 1 Follow through their (a) or (b) as long as the line is through the origin. = e.g. a straight line from (0, 0) to (10 × their 12) e.g. a straight line from (0, 0) to ( their 5.5, 66) and extending this line across full range 0 ≤=T ≤=10 = 20 = At least 5 more of the quadrilaterals drawn so that they= tessellate e.g. 1 They must fit together with no gaps that could not be filled with the same quadrilateral.

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 11 of 14 Question Answer Mark Further Information 21 X beside ( −2, −7) 1 No mark if there is a cross in more than one box. Allow any unambiguous indication. 22 Use of the range to m ake a correct explanation, e.g. The range for Mondays (or 14) is smaller than the range for Thursdays (or 20) 1 Condone mention of the mean if the values of the ranges are compared. Do not accept • the range is better on Monday • an explanation that simply repeats the values of the range without a comparison. 23 4.29 cao 1 24 2.65 (tonnes) 1 25 5n ? 2 2 Do not accept n = 5 n ? 2 Allow equivalents e.g. 3 + ( n ? 1)5 5n + c where c is a constant B1 c may be 0 26 189.43 (NZ dollars) 2 Allow 189 or 189.4 or 189.43? 1000 ? 7.76 or 1.47 ? 7.76 M1 M1 implied by 129 or 128.865 (correctly rounded or truncated to 4sf or better) or 0.189(4?)

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 12 of 14 Question Answer Mark Further Information 27 150(°) 2 4 × 180 ÷ 6 or 180 – 6 360 = or 90 + 6 360 = M1 Implied by 120 seen (allow 60 and 60 on diagram).

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 13 of 14 Question Answer Mark Further Information 28 67.3 (%) or 67.2...(%) 3 × × −× × (38 49) + (12 40) (50 28) (50 28) =oe= = = = or ×× × (38 49) + (12 40) (50 28) oe M2 − 1862 + 480 1400 1400 = = −− ×× 38 49 28 12 40 28 () +() 50 28 50 28 = = Implied by 0.672...= = 1862 + 480 1400 = = ×× 38 49 12 40()+()50 28 50 28 = = Implied by 1.672... = − 49 28 28 =oe= or − 40 28 28 =oe= or (38 × 49) + (12 × 40) oe M1 Implied by 0.75 = = Implied by 0.428...= = Implied by=2342= = Only award M1 if M2 not given. =

1112/02 Lower Secondary Checkpoint Mathematics – Mark Scheme April 2020 PUBLISHED © UCLES 2020 Page 14 of 14 Question Answer Mark Further Information 29(a) (x =) 0.2 oe 2 A correct method, e.g. • 2x + 2x + x = 1 oe •= 1 ? 5 = M1 29(b) 0.6 oe 1 e.g.= 5 3, 10 6 = = Condone 3x Follow through as 3 times their answer to (a), provided this gives a value between 0 and 1. 30 (y =) 3x oe 1 31 (p −=8,= q) 2 p −=8 or q B1