Download [PDF] October 2021 CAIE P2 Mark Scheme 1112 Mathematics Cambridge Lower Secondary Checkpoint.

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This document has 11 pages. Any blank pages are indicated. IB21 05_1112_01/4RP © UCLES 2021 [Turn over Cambridge Lower Secondary Checkpoint MATHEMATICS 1112/02 Paper 2 October 2021 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Markers were instructed to award marks. It does not indicate the details of the discussions that took place at a Markers’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the End of Series Report. Cambridge will not enter into discussions about these mark schemes.

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED 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

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 3 of 11 Question Answer Marks Further Information 1 62.5 [%] 1 Accept 62 5 6 [%] 2 [ =] 40 and [ =] 5 2   At least 3 multiples of 8 less than 45 or 3 factors of 15 or for [ =] 5 and [ =] 40 M1 3 (a) 12.5 [cm] 1 Accept 12 5 6 [cm] (b) 125 [cm 2] 1 FT from their answer in part (a) × 10 correctly evaluated. 4 7 x + 3 + 2x – 6 2 In correct order one correct answer B1 5 3 : 5 1 6 (a) 17:07 1 Accept 5:07 [pm], accept space, dot etc. in place of the colon e.g 17 07, condone 17:07pm (b) 52 [minutes] 1 (c) 14:35 1 Accept 2:35 [pm], accept space, dot etc. in place of the colon e.g 1435, condone 14:35pm 7 (a) –25, –5 1 In correct order. 

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 4 of 11 Question Answer Marks Further Information (b) 1 Correct straight line joining (- 1, -25) to (3,15) Use template as a rough guide only, mark generously due to poor printing of graph ± 1 square tolerance. 8 (a) 28 [%] 2 For indication of a correct method. e.g. (16 000 – 12 500) ÷ 12 500 oe or 0.28 or (16 000 ÷ 12 500) × 100 oe or 128 [%] M1 or better, e.g. 7 9 4 4 5 6 9 4 4 [× 100] or better, e.g. 1.28 × 100 [– 100] (b) ($) 15 200 2 For sight of 0.95 or 95% or = 9 5 4 4 or 9 5 4 4 × 16 000 oe or 800 or answer 11875 M1 This is 95% reduction on $12500 9 (a) (2, 1) 1 20 10 5 15 0 Ð 10 1 2 3 Ð 20 Ð 5 Ð 15 Ð 25 Ð 30 Ð 1 y x

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 5 of 11 Question Answer Marks Further Information (b) [D=] (5, –1) 1 10 9 ? ; and 7 6 ? 2 Accept 9 ;������ Do not accept 7 6������ or 1.5c Take care as common incorrect answer is 6 7 ? 1 correct answer B1 11 6 2   A correct conversion between kg and tonnes, e.g. • 17 000 [kg] • 0.12 [tonnes] • 102 [tonnes] or correct method oe or digit 6 in final answer M1 Stating 1 tonne = 1000 kg is not enough oe e.g. 5 4 6 4 4 4 5 ; J1000, 6000 J1000 e.g. 0.006, 6000 12 180 [cm] 1 Accept 1.8 m as long as unit is given.  13 Ticks ‘No’ with 210[cm] and 200[cm] 2 Accept:  Ticks ‘No’ with 200  [cm] and –10  [cm] oe, 17 1000120 850  

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 6 of 11 Question Answer Marks Further Information or Ticks ‘No’ with 2.1[m] oe e.g. 10 [cm] short (repeated subtraction method)  Ticks ‘No’ with 210 [cm] and 10 [cm] more needed (200 implied) 2 × 45 + 2 × 60 oe M1 Implied by 210[cm] or 2.1[m] or –10[cm] oe for M1 e.g.  200 – 45 – 60 – 45 – 60  2 × 0.45 + 2 × 0.6 14 34 2 5 5 9 7 : 4 H144 oe or 46 or : 4 7 : 4 H480 oe or 80 M1 oe e.g. 115 J@ 360 144 A, 115 ÷ 2.5, 115 H@ 144 360 A, 115 × 0.4 144 ÷ (360 ÷ 115) oe e.g. 60 J@ 360 480 A, 60 ÷ 0.75, 60 H@ 480 360 A, 60 × 1.33 480 ÷ (360 ÷ 60) 15 (a) and Add 2 [to x] then multiply by 9 or Multiply [x] by 9 then add 18 2 Accept any equivalent algebraic expression e.g. (x + 3) ÷ 7 Do not accept e.g. x + 3 ÷ 7 Accept + 2 then  9 or  9 then +18 Accept multiply x and 2 by 9 then add [them] 3 7  x

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 7 of 11 Question Answer Marks Further Information 1 box correct B1 (b) (x – 6) 2 1 Accept any equivalent algebraic expression e.g. (x – 6)(x – 6), x 2 –12x + 36 Do not accept without brackets e.g. x – 6 2 Do not isw incorrect expanding following a correct answer. 16 (a) 1 Must be number first then shape.   (b) 1 Accept equivalent fractions, decimals and percentages, 16.7%, 0.167. Do not accept truncation at 2sf i.e. 16%, 0.16 Do not accept ratio answers 1 : 6 or words 1 in 6   17 First box: inserts a number between 0 and 1 exclusive and Second box: inserts a number greater than 1 and 2 Accept fractions, decimals or powers of 10. e.g. 0.1, 5 5 4, 10 –1 NumberShape 111 222 333 4 1 2 3 444 61

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 8 of 11 Question Answer Marks Further Information Third box: inserts a number between 0 and 0.1 exclusive e.g. 0.01, 5 5 4 4, 10 –2 2 boxes correctly filled B1 18 9 1   19 1 Accept any unambiguous indication 20 Hexagon 1 21 A complete trial and improvement method leading to the answer x = 2.3 Must include all three marking points below. 3 Ignore the final column in the table when marking. x = 2y + 4x = (y + 4) ÷ 2 x = (y – 4) ÷ 2x = (y ÷ 2) – 4

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 9 of 11 Question Answer Marks Further Information Any correct trial of a number x, where 2 ˂ x ⩽ 3 M1 x x 3 + 3x Accept rounded or truncated answers provided they allow for comparison 2.1 15.5[61] 2.2 17.2[48] 2.25 18.1[40625] 2.3 19.0[67] 2.31 19.2[56391] 2.32 19.4[47168] 2.33 19.6[39337] 2.34 19.8[32904] 2.35 20.0[27875] 2.4 21.0[24] 2.5 23.1[25] 2.6 25.3[76] 2.7 27.7[83] 2.8 30.3[52] 2.9 33.0[89] 3 36 a different correct trial of x = 2.35 M1 Accept values between 2.3485… ⩽ x ⩽ 2.35 2.3 in answer space B1 22 (a) Any of the following, or equivalent:  You do not know which height corresponds to which hand span/the data is not paired 1 Do not accept You cannot draw a scatter diagram (without further explanation).

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 10 of 11 Question Answer Marks Further Information  The original data has been lost /we don’t know the numbers  The class data has been grouped See additional guidance for exemplars. (b) A usable data collection sheet that allows you to see which height corresponds to which hand span e.g. Height Hand span 1 Accept if data included. Do not accept diagrams e.g. stem-and-leaf (as data is still not paired). 23 (a) 54 [l] 2 Correct method : 4 H 7 4 H 7 4 5 4 4 4 or Digits 54 in final answer M1 e.g. 54000, 0.054 etc. (b) 26.5 [cm] 1 Do not allow answer in metres e.g. 0.265 m Accept FT for 8 ;. ; ? ? ? ? ? : ?; H30 or 5 8 7 5 ? ? ? ? ? : ?; correctly evaluated (and correctly rounded, if necessary, to 2sf or better or truncated to 3sf) 24 A correct reason e.g. the three probabilities add up to less than 1 or 100% or 1 Accept e.g.  the probabilities don’t add to 100 (BOD missing percent sign)  because it is not 1 (BOD the “it”)

1112/02 Lower Secondary Checkpoint – Mark Scheme October 2021 PUBLISHED Page 11 of 11 Question Answer Marks Further Information the three probabilities do not add up 1 or 100%  there must be one more colour with probability of 0.2 (even though there could be more than one extra colour)  it is only 0.8 (even though “it” is vague, the word “only” implies total probability is too low) Do not accept e.g.  the probabilities add up to 0.8 (no mention of this being less than 1/not equal to 1) 25 18.7 [cm] 3 Accept 18.6[9693…] accept truncated or rounded to 3sf or better or the exact answers 4 + √216 , 4 + 6 √6 Accept 19 only with correct working e.g. √15 6 F3 6 or better or 14.7 (or better)   √15 6 F3 6 or 14.7 or √5 6 F3 6 or 4 M2 or better e.g. √216 or better e.g. √16 For 14.7 accept 14.6[9693…] truncated or rounded to at least 3 figs MD 2 + 3 2 = 15 2 oe or better or MB 2 + 3 2 = 5 2 oe or better M1 or better, e.g. MD 2 = 216 where M is the midpoint of AC, other letters are possible or better e.g. MB 2 = 16