Mark scheme (Foundation) : Paper 2 Calculator - November …

1 GCSE Mathematics Paper 2 Foundation Tier Mark scheme 8300 November 2017 Version: Final MARK scheme GCSE MATHEMATICS 8300/2F November 2017 Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation events which all associates participate in and is the scheme which was used by them in this examination. The standardisation process ensures that the mark scheme covers the students responses to questions and that every associate understands and applies it in the same correct way. As preparation for standardisation each associate analyses a number of students scripts. Alternative answers not already covered by the mark scheme are discussed and legislated for. If, after the standardisation process, associates encounter unusual answers which have not been raised they are required to refer these to the Lead Assessment Writer.

2 It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of students reactions to a particular Paper . Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination Paper . Further copies of this mark scheme are available from Copyright 2017 AQA and its licensors. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even for internal use within the centre. MARK scheme GCSE MATHEMATICS 8300/2F November 2017 3 Glossary for Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible.

3 Thus, for GCSE Mathematics papers, marks are awarded under various categories. If a student uses a method which is not explicitly covered by the mark scheme the same principles of marking should be applied. Credit should be given to any valid methods. Examiners should seek advice from their senior examiner if in any doubt. M Method marks are awarded for a correct method which could lead to a correct answer. A Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. B Marks awarded independent of method. ft Follow through marks. Marks awarded for correct working following a mistake in an earlier step. SC Special case. Marks awarded for a common misinterpretation which has some mathematical worth. M dep A method mark dependent on a previous method mark being awarded. B dep A mark that can only be awarded if a previous independent mark has been awarded. oe Or equivalent. Accept answers that are equivalent.

4 Eg accept as well as 21 [a, b] Accept values between a and b inclusive. [a, b) Accept values a value < b .. Accept answers which begin eg , , Use of brackets It is not necessary to see the bracketed work to award the marks. MARK scheme GCSE MATHEMATICS 8300/2F November 2017 4 Examiners should consistently apply the following principles Diagrams Diagrams that have working on them should be treated like normal responses. If a diagram has been written on but the correct response is within the answer space, the work within the answer space should be marked. Working on diagrams that contradicts work within the answer space is not to be considered as choice but as working, and is not, therefore, penalised. Responses which appear to come from incorrect methods Whenever there is doubt as to whether a student has used an incorrect method to obtain an answer, as a general principle, the benefit of doubt must be given to the student. In cases where there is no doubt that the answer has come from incorrect working then the student should be penalised.]

5 Questions which ask students to show working Instructions on marking will be given but usually marks are not awarded to students who show no working. Questions which do not ask students to show working As a general principle, a correct response is awarded full marks. Misread or miscopy Students often copy values from a question incorrectly. If the examiner thinks that the student has made a genuine misread, then only the accuracy marks (A or B marks), up to a maximum of 2 marks are penalised. The method marks can still be awarded. Further work Once the correct answer has been seen, further working may be ignored unless it goes on to contradict the correct answer. Choice When a choice of answers and/or methods is given, mark each attempt. If both methods are valid then M marks can be awarded but any incorrect answer or method would result in marks being lost. Work not replaced Erased or crossed out work that is still legible should be marked. Work replaced Erased or crossed out work that has been replaced is not awarded marks.

6 Premature approximation Rounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 mark unless instructed otherwise. Continental notation Accept a comma used instead of a decimal point (for example, in measurements or currency), provided that it is clear to the examiner that the student intended it to be a decimal point. MARK scheme GCSE MATHEMATICS 8300/2F November 2017 5 Question Answer Mark Comments 1 135 B1 2 2 B1 3 1003 B1 4 A = 2B B1 5a y B1 5b 4a + 11 B2 B1 for each term Additional Guidance 4a or 11 or 4a + 11 seen and answer eg 15a B1 4a + 11 seen and then solves B1 11 and 11 seen (without 4a seen) B0 MARK scheme GCSE MATHEMATICS 8300/2F November 2017 6 Question Answer Mark Comments 6 Linear scale starting at 0 and increasing in 1s on vertical axis Vertical axis labelled frequency or f or number Title given or horizontal axis labelled (types of) bird(s) Bars labelled with four bird names (allow R, S, W, L)

7 Four bars with equal widths Equal gaps or no gaps between four bars All heights correct B3 Bar chart could be horizontal B3 for all criteria met B2 for 5 or 6 criteria met B1 for 3 or 4 criteria met correct or ft their increasing scale Additional Guidance Mark intention throughout If grid is blank, allow axes to be transposed If axes and labels do not match the orientation of the bar chart then only the marks for crtieria 3 (must be a title), 5, 6 and 7 may be awarded B1 max All values not needed for axis scale eg 0 can be implied but spacing must be linear Scale of 2 units per square does not meet the first criterion Allow words after number on axis label eg number seen , number of birds . Also allow eg Amount of birds Title must include the word bird Condone different gap between the vertical axis and the first bar with other gaps equal or no other gaps If no axis scale, bars with heights 2, 5, 3, 1 meet heights criterion Points only or vertical lines can score the marks for criteria 1, 2, 3, 4 and 7 B2 max MARK scheme GCSE MATHEMATICS 8300/2F November 2017 7 Question Answer Mark Comments 7 Alternative method 1 2 + 1 + 50p + 20p + 20p + 5p + 2p or ( ) or 1 + 50p + 2p + 1p or ( ) or 2 + 1 + 50p + 20p + 20p + 5p + 2p + 1 + 50p + 2p + 1p or ( ) (0) or 2 + 1 + 50p + 20p + 20p + 5p + 2p 1 50p 2p 1p or ( ) M1 Accept incorrect or missing units Totals either set of coins or Totals all coins or Works out difference (their + their ) 2 or their ( ) (0) 2 or ( ) or (their their ) 2 or their ( ) 2 or ( )

8 M1dep oe Accept incorrect or missing units 1, 20p and 2p A1 oe eg , , Correct units must be given Alternative method 2 Moves 3 coins from Eve to Ola and correctly evaluates one set of coins M1 Accept incorrect or missing units Moves a different set of 3 coins from Eve to Ola and correctly evaluates both sets of coins M1dep Accept incorrect or missing units 1, 20p and 2p A1 oe eg , , Correct units must be given Additional Guidance Answer of 1, 20, 2 with some or all units incorrect or missing M1M1A0 Do not accept eg A0 MARK scheme GCSE MATHEMATICS 8300/2F November 2017 8 Question Answer Mark Comments 8 (0) + (0) 2 or (0) + or (0) or M1 oe Cost of 2 suits 4 or 32 6 or (0) 6 or 39(.00) M1 oe eg 6 2 or (0) Cost of 6 dresses their + their 39(.00) M1dep dep on at least M1 awarded Must be adding their suit(s) and their dress(es) May be implied by final answer A1 Accept Additional Guidance + 6 M0M0M0dep + 39 M0M1M1dep 2 + 39 M0M1M1dep + 2 M1M0M1dep MARK scheme GCSE MATHEMATICS 8300/2F November 2017 9 Question Answer Mark Comments 9 Alternative method 1 18 4 or 14 seen M1 oe eg 4 + 14 = 18 39 2 their 14 or 39 28 or 11 M1dep oe eg 14, 14, 11 15 A1 Alternative method 2 39 + 3 4 or 39 + 12 or 51 M1 their 51 2 18 or their 51 36 M1dep 15 A1 Additional Guidance 14 may be implied by eg twins = 28 (but not just 28 seen)

9 M1 10 Fully correct table B4 B1 for each correct decision in a row Additional Guidance Must be true Cannot be true Might be true The triangle is equilateral The triangle has at least one other acute angle The triangle is right-angled The other two angles are each less than 60 Mark intention if crosses used eg if a cross is the only mark in a row assume that is the answer More than one tick in a row is choice for that decision B0 for that row MARK scheme GCSE MATHEMATICS 8300/2F November 2017 10 Question Answer Mark Comments 11 7 B1 12 B1 13a 752 951 or 752951 or 752,951 B1 Allow commas even if positioning incorrect eg 75,2951 or 752 951 B1 Additional Guidance B0 13b 20 000 and 400 and 10 and 800 000 and Yes B3ft ft correct decision for their answer to (a) oe decision eg it is sensible B2 20 000 and 400 and 10 B1 20 000 or 400 or 10 Additional Guidance 800 000 (and Yes) with no other values B0 If answer to (a) is 800 000 to 1sf then the correct ft decision in (b) is Yes eg1 (a) 770 000 (b) decision should be Yes eg2 (a) 1762 (b) decision should be No eg3 (a) (b) allow decision to be Yes or No MARK scheme GCSE MATHEMATICS 8300/2F November 2017 11 Question Answer Mark Comments 14a Alternative method 1 Two of the three totals correct (2016 =) 136 (2015 =) 143 (2014 =) 132 or 17 + 64 + 50 + 5 and 9 + 72 + 61 + 1 and 19 + 58 + 53 + 2 M1 Totals may be seen by table Correct totals may be implied by means (2016 34, 2015 , 2014 33)

10 Addition signs must be shown for horizontal addition but may be implied by a column of numbers in their working 136 and 143 and 132 and 2015 or 34 and and 33 and 2015 A1 Totals may be seen by table Alternative method 2 8 and 8 and 11 and 4 or 7 and 10 and 14 and 8 and 1 or 11 M1 Difference between 2016 and 2015 Difference between 2015 and 2014 Differences may be seen in table 7 and 11 and 2015 A1 Differences may be seen in table Additional Guidance Differences may have consistently opposite signs for either comparison Ignore totals for quarters shown Allow Year 2 for 2015 136 and 143 and 132, answer 143 M1A0 136 and 143 and 132, answer 143 in 2015 M1A1 14b Quarter 2 B1 MARK scheme GCSE MATHEMATICS 8300/2F November 2017 12 Question Answer Mark Comments 15 Alternative method 1 80 or 44 or 120 or 84 M1 oe 80 + 120 or 44 + 84 or 128 M1dep Correct method for both (80 + 120) or 130 or their 128 (80 + 120) 100 or their 128 2 or 64 M1 65% of total marks available or their total score for Riya as a percentage of full marks 128 and 130 and No or 64 and No A1 oe eg No, she needed 130 but was 2 marks short oe eg and and No Alternative method 2 marks not scored 80 or 36 or 120 or 36 M1 oe 80 + 120 or 36 + 36 or 72 M1dep Correct method for both (80 + 120) or 70 or their 72 (80 + 120) 100 or their 72 2 M1 35% of total marks available or their total score for Riya as a percentage of full marks 72 and 70 and No or 36 and 35 and No A1 oe eg No, she failed by 2 marks oe eg and and No Alternative methods 3 and 4 and additional guidance continue on the next two pages MARK scheme GCSE MATHEMATICS 8300/2F November 2017 13 Question Answer Mark Comments 15 cont Alternative method 3 80 or 44 M1 oe (80 + 120)