Unit 5 Mathematics for programmers

Level 3 Technical Level IT: PROGRAMMING Y/507/6469 Unit 5 Mathematics for programmers Mark scheme June 2019 Version: 1.0 Final *196AY/MS* 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 Examiner. 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 information For confidentiality purposes acknowledgements of third-party copyright material are published in a separate booklet which is available for free download from after the live examination series. Copyright © 2019 AQA and its licensors. All rights reserved. Level of response marking instructions Level of response mark schemes are broken down into levels, each of which has a descriptor. The descriptor for the level shows the average performance for the level. There are marks in each level. Before you apply the mark scheme to a student’s answer read through the answer and annotate it (as instructed) to show the qualities that are being looked for. You can then apply the mark scheme. Step 1 Determine a level Start at the lowest level of the mark scheme and use it as a ladder to see whether the answer meets the descriptor for that level. The descriptor for the level indicates the different qualities that might be seen in the student’s answer for that level. If it meets the lowest level then go to the next one and decide if it meets this level, and so on, until you have a match between the level descriptor and the answer. With practice and familiarity you will find that for better answers you will be able to quickly skip through the lower levels of the mark scheme. When assigning a level you should look at the overall quality of the answer and not look to pick holes in small and specific parts of the answer where the student has not performed quite as well as the rest. If the answer covers different aspects of different levels of the mark scheme you should use a best fit approach for defining the level and then use the variability of the response to help decide the mark within the level, ie if the response is predominantly level 3 with a small amount of level 4 material it would be placed in level 3 but be awarded a mark near the top of the level because of the level 4 content. Step 2 Determine a mark Once you have assigned a level you need to decide on the mark. The descriptors on how to allocate marks can help with this. The exemplar materials used during standardisation will help. There will be an answer in the standardising materials which will correspond with each level of the mark scheme. This answer will have been awarded a mark by the Lead Examiner. You can compare the student’s answer with the example to determine if it is the same standard, better or worse than the example. You can then use this to allocate a mark for the answer based on the Lead Examiner’s mark on the example. You may well need to read back through the answer as you apply the mark scheme to clarify points and assure yourself that the level and the mark are appropriate. Indicative content in the mark scheme is provided as a guide for examiners. It is not intended to be exhaustive and you must credit other valid points. Students do not have to cover all of the points mentioned in the Indicative content to reach the highest level of the mark scheme. An answer which contains nothing of relevance to the question must be awarded no marks. The following annotation is used in the mark scheme: ; - means a single mark // - means alternative response / - means an alternative word or sub-phrase A. - means acceptable creditworthy answer R. - means reject answer as not creditworthy NE. - means not enough I. - means ignore DPT. - in some questions a specific error made by a candidate, if repeated, could result in the candidate failing to gain more than one mark. The DPT label indicates that this mistake should only result in a candidate failing to gain one mark on the first occasion that the error is made. Provided that the answer remains understandable, subsequent marks should be awarded as if the error was not being repeated. Question Guidance Mark 01 A Mark is for AO1 ; R. more than one box ticked 1 02 C Mark is for AO2 A OR B; R. more than one box ticked 1 03 A Mark is for AO4 1 ; x2 R. more than one box ticked 1 04 B Mark is for AO3 {7, 11} ; R. more than one box ticked 1 05 A Mark is for AO3 1 ; 64 R. more than one box ticked 1 Question Guidance Mark 06 Mark is for AO3 1 mark for the correct difference, eg: (with an independent event) the outcome of the first event does not influence the outcome of the second event whereas with a dependent event it does; (with a dependent event) the outcome of the first event influences the outcome of the second event but this is not true of an independent event; Independent event: (Two events are independent if) the outcome of the first event does not influence the outcome of the second event // the probability that one event occurs in no way affects the probability of the other event occurring. Dependent event: (Two events are dependent if) the outcome of the first event influences the outcome of the second event // the probability of one event occurring influences the likelihood of the other event. 1 07.1 Mark is for AO4 120; 1 07.2 2 marks for AO4 2 marks if answer is correct 30;; If answer given is not correct then award working marks as follows: Maximum of 1 from: sight of 1 x 2 x 3 // 1 x 2 x 3 x 4 // 6 // 24; 1 x 2 x 3 x 4 crossed out on the numerator and denominator; incorrect answer that has been correctly worked out using the answer to Question 7.1; 2 Question Guidance Mark 08 3 marks for AO5 1 mark for each correct matrix [ 1 1 x = 6 -3 � �y� � � 1 2 A. 3 marks if the correct matrices are given but the rows in each matrix are the other way around. A. answer written outside the matrix lines so long as the meaning is clear. A. If not fully correct award a maximum of 2 marks for the question, eg: • The first matrix is correct; and the second and third matrices are correct but are the wrong way around; • 1 mark for each correct matrix in the wrong position; • 1 mark if the final matrix is given as �2� 6 and there is nothing written in the first or second matrices; 3 Question Guidance Mark 09.1 Mark is for AO2 OR; 1 09.2 3 marks for AO2 3 1 mark for each correct column X Y L M P 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 A. Follow through for column P based on complete but incorrect columns L and M. A. Follow through for column P based on incorrect answer to Question 9.1. 09.3 3 marks for AO2 3 marks if answer is correct P = (X + Y ) + (X . Y) // P = (X ∨ Y ) ∨ (X