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Mathematics Mark Schemes Cambridge International Primary Achievement Test

Maths mark schemes — Achievement Test Guidelines for marking test papers These mark schemes are designed to provide you with all the information \ necessary to mark the Primary Progression Tests. As far as possible, the mark scheme\ s give you full guidance regarding acceptable and unacceptable alternative answers and, \ where appropriate, include examples of student work to illustrate the marking \ points. However, it is not always possible to predict all the alternative answers that may b\ e produced by students and there could be places where the marker will have to use the\ ir professional judgement. In these cases it is essential that such judgement be applie\ d consistently. The guidelines below should be followed throughout (unless the mark scheme states otherwise ):  A correct answer should always be awarded full marks even if the working\ shown is wrong.  Where more than one mark is available for a question the mark scheme exp\ lains where each mark should be awarded. In some cases marks are available fo\ r demonstration of the correct method even if the final answer is incorrec\ t. The method marks can be awarded if the correct method is used but a mistake \ has been made in the calculation, resulting in a wrong answer. Method marks\ can also be awarded if the calculation is set up and performed correctly but\ incorrect values have been used, e.g. due to misreading the question or a mistake \ earlier in a series of calculations.  If a question uses the answer to a previous question or part question th\ at the child got wrong, all available marks can be awarded for the latter question if\ appropriate calculations are performed correctly using the value carried\ forward. Places where such consideration should be made are indicated in the mark\ schemes. In these cases, it is not possible to provide all the alternat\ ive acceptable answers and the marker must follow the child’s working to determine w\ hether credit should be given or not.  Half marks should not be awarded (except in Paper 3) and at no point s\ hould an answer be awarded more than the maximum number of marks available, regardless of the quality of the answer.  If the child has given more than one answer the marks can be awarded if \ all the answers given are correct. However, if correct and incorrect answers ar\ e given together marks should not be awarded (marks for correct working out can\ still be gained).  If the answer line is blank but the correct answer is given elsewhere, e\ .g. an annotation on a graph or at the end of the working out, the marks can be\ awarded provided it is clear that the child has understood the requirements of t\ he question.  If the response on the answer line is incorrect but the correct answer i\ s shown elsewhere, full marks can still be awarded if the child has made the err\ or when copying the answer onto the answer line. If the incorrect final answer \ is the result of redundant additional working after the correct answer had been reache\ d the marks can be awarded provided the extra work does not contradict that al\ ready done.

 Each question and part question should be considered independently and m\ arks for one question should not be disallowed if they are contradicted by wo\ rking or answers in another question or part question.  Any legible crossed-out work that has not been replaced can be marked; b\ ut if work has been replaced the crossed-out part should be ignored.  If the child’s response is numerically or algebraically equivalent to\ the answer in the mark scheme, the mark should be given unless a particular form of answer\ was specified by the question.  Diagrams, symbols or words are acceptable for explanations or responses.\  Where students are required to indicate the correct answer in a specific\ way, e.g. by underlining, marks should be awarded for any unambiguous indication, \ e.g. circling or ticking.  Any method of setting out working should be accepted.  Standard rules for acceptable formats of answers involving units, money,\ duration and time are given below. Each question on the test paper has a box beside it for the teacher to r\ ecord the mark obtained. It is advisable to use these boxes so that students, and othe\ rs looking at the test papers, can clearly see where the marks have been awarded. It is also u\ seful to use the boxes because it makes the process of entering the data into the analysi\ s tool easier. The page total boxes can be used to aid addition but care must be taken not \ to accidentally enter these values into the analysis tool. Finally, it is advisable to use a pen of a different colour to that used\ by the students so that the marks and comments can be clearly seen. It should also be noted tha\ t marking in red ink and using the mark boxes is an essential requirement for the Achieve\ ment tests. General rules for alternative answers In most places on the mark schemes acceptable and unacceptable alternati\ ve answers are given in detail, however some general rules are given below and are \ not necessarily repeated in full for each question that they apply.

Number and Place value The table shows various general rules in terms of acceptable decimal ans\ wers. 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 numbe\ r of decimal places, e.g. 0.7000 Always accept appropriate tailing zeros, e.g. 3.00m; 5.000kg Accept a comma as a decimal point if that is that convention that you ha\ ve taught the children, e.g. 0,638 Units For questions involving quantities, e.g. length, mass, time or money, co\ rrect units must be given in the answer. The table shows acceptable and unacceptable versio\ ns of the answer 1.85m. Correct answer Also accept Do not accept Units are not given on answer line and question does not specify unit for the answer. 1.85m Correct conversions provided that the unit is stated, e.g. 1m 85cm 185cm 1850mm 0.00185km 1.85 185m If the unit is given on the answer line, e.g. ……………………………m …..1.85…… m Correct conversions, provided the unit is stated unambiguously, e.g. …..185cm….. m …..185……m …..1850.… m etc. If the question states the unit that the answer should be given in a specified unit, e.g. “Give your answer in metres” 1.85m 1.85 1m 85cm 185; 1850 Any conversions to other units, e.g. 185cm Note: if the answer line is left blank but the correct answer is given elsewh\ ere on the page it can be marked correct if the units match those on the answer line or are\ unambiguously stated.

Money For questions involving money, it is essential that appropriate units ar\ e given in the answer. The table shows acceptable and unacceptable versions. Accept Do not accept If the amount is in dollars and cents, the answer should be given to two decimal places. $0.30 $9 or $9.00 $09 or $09.00 If units are not given on answer line Any unambiguous indication of the correct amount, e.g. 30 cents; 30 c $0.30; $0.30c; $0.30cents $0-30; $0=30; $0:30 30 or 0.30 without a unit Incorrect or ambiguous answers, e.g. $0.3; $30; $30cents; 0.30cents If $ is shown on the answer line $....... 0.30……. $....... 0.30 cents…. Accept all unambiguous indications, as shown above $....... 30……. $....... 30 cents…. (this cannot be accepted because it is ambiguous, but if the dollar sign is deleted it becomes acceptable) If cents is shown on the answer line ....... 30…….cents ....... $0.30 …….cents ....... 0.30 …….cents ....... $30…….cents Duration Accept any unambiguous method of showing duration and all reasonable abb\ reviations of hours (h, hr, hrs), minutes (m, min, mins) and seconds (s, sec, sec\ s). 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; 2h 30m; 02h 30m 5 min 24 sec; 00h 05m 24s Incorrect or ambiguous formats, e.g. 2.30; 2.3; 2.30 hours; 2.30 min; 2h 3; 2.3h Any correct conversion with appropriate units, e.g. 2.5 hours; 150 mins 324 seconds 2.5; 150 304 Also accept unambiguous digital stopwatch format, e.g. 02:30:00 00:05:24; 05:24s Do not accept ambiguous indications, e.g. 02:30 5.24

Time There are many ways to write times, in both numbers and words, and marks\ should be awarded for any unambiguous method. Accept time written in numbers or w\ ords unless there is a specific instruction in the question. Some examples are give\ n in the table. Accept Do not accept Any unambiguous indication of correct answer in numbers, words or a combination of the two, e.g. 07:30, 19:00 0730; 07 30; 07.30; 07,30; 07-30; 7.30; 730 a.m.; 7.30am; 7.30 in the morning Half past seven (o’clock) in the morning Thirty minutes past seven am Also accept: O-seven-thirty 1900; 19 00; 19_00 etc. Nineteen hundred (hours) Seven o’clock in the afternoon/evening Accept correct conversion to 12-hour clock, e.g. 16:42 4:42 p.m. Sixteen forty two Four-forty-two in the afternoon/evening Four forty two p.m. Forty two (minutes) past four p.m. Eighteen (minutes) to five in the evening Also accept a combination of numbers and words, e.g. 18 minutes to 5 p.m. 42 minutes past 4 in the afternoon Incorrect or ambiguous formats, e.g. 07.3; 073; 07 3; 730; 73; 7.3; 7.3am; 7.30p.m 19; 190; 19 000; 19.00am; 7.00am 4.42am; 0442; 4.42 Forty two (minutes) past sixteen Eighteen (minutes) to seventeen

Cambridge International Primary Achievement Test – Mathematics Paper \ 2 Question Mark Answer Additional information 1 3Nn9 1 1757, 2018, 2187, 2508, 2575 2 3Nn11 1 1000 3a 3P8 1 3.75 b 3P8 1 1.05 4 3P1 1 55 5 3D1 1 24 6 3Ss3 1 c 7 3Sp2 1 W or west 8 3Sm7 1 2 hours 15 minutes. Accept 2 and a quarter hours, or the same in figures. Also accept 135 minutes. 9 4Nn16 1 Hundredths 10a 4Nc6 1 19 b 4Nc6 1 4 11a 4P5 1 374.97 b 4P5 1 37.50 Also accept: the answer to (a) × 10% 12a 4P2 1 14 b 4P2 1 81 13a 4D5 1 13 b 4D5 1 10 14 4Ss2 1 C 15 4Sp8 1 20 16a 4Sm5 1 39 b 4Sm5 2 78 cm 2 1 mark for 78 1 mark for cm 2

Question Mark Answer Additional information 17 5Nn15 1 1 5 3, 54, 10 5 , 52, 10 2 Fraction Decimal 51 0.20 52 0.40 51 0.80 18 5Nn20 2 1 mark for each correct answer. Accept 0.2 instead of 0.20 19 5Nc13 1 6460 20a 5P5 1 34 b 5P5 1 Accept any answer implying the two previous numbers are added to make the next number in the sequence. 21 5P1 1 8 22 6D5 1 78 23 5Ss5 1 A Shape correctly drawn, using ruler. 24 5Sp2 1 A

Question Mark Answer Additional information 25a 6D3 1 23 (accept 24) b 6D3 1 32 (accept answers in range 30, 31, 32) 26 5Ss2 2 A mirror line (a) Pattern completed as shown. (b) Point A is positioned at (5, 1) One mark for each part correctly completed. 27a 5Sp3 1 82 Accept 81 or 83 b 5Sp3 1 133 Accept 132 or 134