GCSE MATHEMATICS 8300/3H Higher Tier Paper 3 Calculator Mark scheme June 2022 Version: 1.0 Final *226g8300/3H/MS* MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 2 Mark schemes a... re 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 aqa.org.uk Copyright information 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. Copyright © 2022 AQA and its licensors. All rights reserved. MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 3 Glossary for Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. 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. eg accept 0.5 as well as 2 1 [a, b] Accept values between a and b inclusive. [a, b) Accept values a ⩽ value < b 3.14… Accept answers which begin 3.14 eg 3.14, 3.142, 3.1416 Use of brackets It is not necessary to see the bracketed work to award the marks. MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 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. 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. 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 – 8300/3H – JUNE 2022 5 Q Answer Mark Comments 1 4.301 B1 Q Answer Mark Comments 2 − 10 7 B1 Q Answer Mark Comments 3(a) D B1 Q Answer Mark Comments 3(b) B B1 MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 6 Q Answer Mark Comments 4 Alternative method 1 tan identified M1 oe eg tan–1 tan x = 4 10 or tan x = 2 5 or tan x = 2.5 M1dep oe eg tan–1 4 10 or 90 – tan–1 10 4 [68, 68.2] A1 SC1 [21.8, 22] Alternative method 2 sin x = 2 2 4 10 10 + or cos x = 2 2 4 10 4 + M2 oe eg sin x = 116 10 or sin–1 2 2 4 10 10 + or cos x = 4 116 or cos–1 2 2 4 10 4 + or 90 – sin–1 2 2 4 10 4 + or 90 – cos–1 2 2 4 10 10 + [68, 68.2] A1 SC1 [21.8, 22] Additional Guidance Accept 10.77 or 10.8 or 2 29 for 116 Tan can be identified by, for example, circling TOA in SOHCAHTOA Answer from accurate drawing M0M0A0 sin x = 10 sin 90 116 M2 (x =) tan 2.5 or (x =) tan 0.4 or (x =) tan − 1 10 4 unless recovered M1M0A0 tan = 10 4 or tan = 4 10 or tan x = 4 10 with no further correct working M1M0A0 MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 7 Q Answer Mark Comments 5 3 + 2 or 5 and 5 2 1 + 3 2 1 or 9 or 5 2 1 – 3 or 2 2 1 and 3 2 1 – 2 or 1 2 1 or 4 M1 oe eg 180 + 120 or 300 and 330 + 210 or 540 implied by 5 2 1 + 3 2 1 – 3 – 2 9 5 − 5 or + + 1 1 2 1 2 2 3 2 or 5 4 or 0.8 or 3 2 2 1 3 2 1 5 + + (× 100) or 5 9 (× 100) or 1.8 (× 100) or 180 M1dep oe eg 3 2 3 2 2 1 3 2 1 5 + + − − eg 540 300 300 − or 240 300 or 1.8 – 1 80 A1 Additional Guidance Allow working fully in minutes but units must be consistent in a single calculation eg 2 h 30 and 1 h 30 eg 3 + 2 = 5 and 330 + 210 = 540 eg 3 + 120 and 330 + 3 2 1 unless recovered M1 M1 M0 3 + 2 = 6, 5 2 1 + 3 2 1 = 9, 9 – 6 = 3, 3 = 50% M1M1A0 3 + 2 = 6, 5 2 1 + 3 2 1 = 9, answer 50% (3 is implied) M1M1A0 9 – 6 = 3, 3 = 50% (no method shown for 6) M0M0A0 MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 8 Q Answer Mark Comments 6(a) –1 and 5 B1 either order Additional Guidance Ignore x = written before answers (–1, 0) or (5, 0) B0 Q Answer Mark Comments 6(b) (2, –9) B2 B1 x = 2 or (2, …) or y = –9 or (…, –9) or (x – 2)2 – 9 B1ft correct y-coordinate for their xcoordinate with x ≠ –1, 0 or 5 SC1 (–9, 2) Additional Guidance If answer line is blank, check diagram for indication of x or y values (3, –9) B1 (3, –8) B1ft (1, –8) B1ft (2.5, –8.75) B1ft (0, –5) B0ft MARK SCHEME – GCSE MATHEMATICS – 8300/3H – JUNE 2022 9 Q Answer Mark Comments 7 (8th term =) 2 8 or 256 M1 oe may be implied Common difference of A indicated as 3 M1 may be implied eg 3n … or … + 3(n – 1) 3n + 10 = their 256 or (their 256 – 10) ÷ 3 or (their 256 – 13) ÷ 3 or 81 M1dep oe equation eg 13 + 3(n – 1) = 2 8 dep on 2nd M1 their 256 may be any number and may be in index form 82 A1 Additional Guidance n + 3 implies 2nd M1 Do not award M1 for 256 if it is in a list of powers of 2 unless it is indicated or it is the highest power evaluated Common difference of 3 may be shown on the progression for the 2nd M1 10, (13, 16, 19, 22), 25 without comm [Show More]
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