Practice Papers Set 1 Teacher Booklet GCSE MATHEMATICS Practice Papers Set 4 Paper Higher - Mark Scheme 8300/H Version 1.0
Principal Examiners have prepared these mark schemes for specimen papers. These mark schemes have not, therefore, been through the normal process of standardising that would take place for live papers. Further copies of this Mark Scheme are available from aqa.org.uk 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 A B ft SC M dep B dep Method marks are awarded for a correct method which could lead to a correct answer. Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. Follow through marks. Marks awarded for correct working following a mistake in an earlier step. Special case. Marks awarded within the scheme for a common misinterpretation which has some mathematical worth. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous independent mark has been awarded. Or equivalent. Accept answers that are equivalent. eg accept 0.5 as well as 1 [a, b] [a, b) Accept values between a and b inclusive. Accept values a value < b 3.14 Allow answers which begin 3.14 eg 3.14, 3.14, 3.1416 Use of brackets It is not necessary to see the bracketed work to award the marks. Page Version 1.0
MARK SCHEME GCSE MATHEMATICS PRACTICE PAPERS SET 4 PAPER HIGHER 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 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 gs 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 candidate intended it to be a decimal point. Version 1.0 Page 3
5 11 1 1 10 3 4n 1 1 4 1000 3 or 333.( ) 5 18.(5 ) or 18.6 or 18.3 19(th) (term) For A mark to be awarded any calculations shown must be correct Page 4 Version 1.0
MARK SCHEME GCSE MATHEMATICS PRACTICE PAPERS SET 4 PAPER HIGHER Alternative method 1 1.015 seen or 4000 1.015 or 4060 4000 1.015 = 410.90 6(a) Alternative method 0.015 4000 or 60 or 4060 or 0.015 4060 or 60.9 4000 + 60 + 60.9 = 410.90 Allow 410.90p 410.9 1.014 or 410.9 0.014 or 57.696 or 57.69 or 57.70 410.9 + their 57.696 or 4178.596 dep 6(b) their 4178.596 0.0135 dep 56.4110001 or 56.41 or 56.4 and 57.696 or 57.69 or 57.70 and Less Version 1.0 Page 5
sin 0 = 1 x or 1 sin 0 7 4.1 Accept 4 with working shown ( ) 70 or 5 ( ) 8 or 7 ( ) 0 May be on a diagram 8 5 7 Any order 5 7 Any order 3a 4 = 11 11 + 4 3a = 11 + 4 or 3a = 15 or a = 5 dep 11 + 4 3 9 6 4b = 14 14 6 or 6 14 4b = 6 14 or 4b = 8 dep 6 14 4 a = 5 and b = Page 6 Version 1.0
MARK SCHEME GCSE MATHEMATICS PRACTICE PAPERS SET 4 PAPER HIGHER Width of rectangle or radius of semicircle = 7 cm seen or implied eg 14 7 or 98 ( 1 ) π 7 or 49 π or 49 π or [153.8, 154] or [76.9, 77] 10 14 7 1 π 7 or 98 [76.9, 77] [1, 1.1] Accept 98 49 π Mid values seen 5, 15, 5 or 5.005, 15.005, 5.005 or 5.01, 15.01, 5.01 5 18 (+) 15 15 (+) 5 7 Accept use of mid values 5.005, 15.005, 5.005 or 5.01, 15.01, 5.01 Allow one error 11(a) eg one mid value incorrect or one calculation incorrect their 490 40 dep 1.5 or 1.6 SC for 7.5 or 7.6 or 17.5 or 17.6 Version 1.0 Page 7
11(b) Indicates lower Valid reason eg 4.50 is less than 5 and 3.40 is less than 5 ξ M F for two correct regions 1 9 3 15 14 13 6 1 4 8 5 7 8 10 11 B Condone omission of numbers in (M F) / 1 P(Multiple 3 / Factor 4) = 7 3 P(Factor 4 / Multiple 3) = 5 3 3 3 or 0.6 0.4(8 ) 5 7 or P(multiple of 3 ) P(multiple of 7 ) If Venn diagram not used, working must be clear y 1 x or y = k x 13(a) k = 3.5 4. or k = 14.7 or y = 14.7 x dep.65 Page 8 Version 1.0
MARK SCHEME GCSE MATHEMATICS PRACTICE PAPERS SET 4 PAPER HIGHER y 13(b) O x (.318 10 3 ) (3.8 10 6 ) 6.1 14(a) 4 A 10 7 A 10 6 14(b) where.0 < A < 3.0 B where 0 < A < 30 SC1 A 10 6 or A 10 8 where.0 < A < 3.0 Version 1.0 Page 9
1 = 5 + p p p p 4 (= 0) dep (p 6) (p + 4) (= 0) 15 or ( ) 4 1 4 p = 6 and p = 4 Allow use of q instead of p throughout 1.08 seen or 5.5 0.08 5.5 1.08 or 5.67 16 their 5. 67 0. 9 6.3(0) x + y = 9 17(a) ( 3, 4) 17(b) Page 10 Version 1.0
MARK SCHEME GCSE MATHEMATICS PRACTICE PAPERS SET 4 PAPER HIGHER T F B for correct and 1 incorrect or incomplete 17(c) T Alternative method 1 15 and 51 or 5 3 and 8 3 400 51 15 or 15 51 97.( ) or 0.4( ) 18 97.( ) and 100 and Yes 0.4( ) and Yes Alternative method 3 0. 5 0.69 or 0.63 5 8 0.65 and 0.63 and Yes Version 1.0 Page 11
π 10 5 or 50π or [785, 785.5] or 786 or π 5 1.5 or 6.5π or [196., 196.4] or 196 their 786 + their 196 or 31.5π or [981, 98] dep may be implied π 10 10 or 100π 19 or [314, 314.] or π 5 5 or 5π or [78.5, 78.6] or 79 their [314, 314.] their [78.5, 78.6] or 75π or [35.4, 35.7] dep dependent on third M 387.5π or [116, 118] x + x + 7x + 7 or x + 8x + 7 3x + 4x + 1 dep 0 4x + 10x + 10x + 5 or 4x + 0x + 5 x + 4x 4 (x ) so never positive Page 1 Version 1.0
MARK SCHEME GCSE MATHEMATICS PRACTICE PAPERS SET 4 PAPER HIGHER 3 choices for 1st digit 3 4 3 ( 1) dep 1 7 x 4 9x = or h = h 9 4 x 9x 4 1 4 3x 3x 3x 3 Show clearly that both are equal to 9 x 3 4 Version 1.0 Page 13
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