PRACTICE PAPER SET 3 - Maths at BCS

1 PRACTICE Papers - Set 1- Teacher Booklet GCSE MATHEMATICS PRACTICE PAPER SET 3 Higher Tier PAPER 1 Mark Scheme 8300/1H Version Page 2 Version Further copies of this Mark Scheme are available from 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.

2 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 within the scheme 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 as well as 21 [a, b] Accept values between a and b inclusive.

3 [a, b) Accept values a value < b .. Allow answers which begin eg , , Use of brackets It is not necessary to see the bracketed work to award the marks. MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER 1 HIGHER Version Page 3 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.]

4 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.

5 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.

6 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. Q Answer Mark Comments Page 4 Version 1 18 B1 2 6x3 15x2 B1 3 x > 2 B1 4 50 3 B1 5 3x = 12 + 9 or 3x = 21 or x 9 3 = 12 3 or x 27 = 36 M1 12 + 9 3 or (12 + 9) 3 63 A1 Additional Guidance 12 + 9 3 = 39 M0A0 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER 1 HIGHER Q Answer Mark Comments Version Page 5 6(a) Alternative method 1 or M1 12 A1 Alternative method 2 at least eight or + at least eight M1 12 A1 Alternative method 3 or 36 and or 24 M1 12 A1 Additional Guidance Q Answer Mark Comments Page 6 Version 6(b)

7 It will take fewer days B1 oe the answer would be lower eg it will be less than 12 Additional Guidance Quicker/faster than 12 days B1 Quicker/faster alone B0 7 DAE = 180 65 72 or 43 or ABC = 65 or DAB = 72 or EDB = 180 65 or 115 or BAE = 180 65 or 115 M1 May be on diagram in correct position BAC = 180 65 65 or 50 or ADB = 115 72 or 43 and ACD = 115 or BAC = 50, BAE = 115 and ADB = 115 72 or 43 or CAE = 65 and DAE = 43 or DAB = 72 and BAC = 50 M1 May be on diagram in correct position oe 72 50 = 22 or 180 115 43 = 22 or 115 50 43 = 22 or 65 43 = 22 A1 Additional Guidance eg 115 or A = 50 is ambiguous Written work takes precedence over diagrams if contradictory.

8 M0 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER 1 HIGHER Q Answer Mark Comments Version Page 7 8(a) Alternative method 1 43 28 or 15 seen M1 15 13 (= 2) or 2, 13 and 15 A1 Alternative method 2 x + 2y = 28 and 2x + 3y = 43 M1 oe equations Solves equations correctly obtaining x = 2 A1 Additional Guidance If setting up two equations, they must be correct 8(b) b a M1 Second term 2b a M1dep oe Fourth term 3b a A1 Additional Guidance Q Answer Mark Comments Page 8 Version 9 The method will sometimes give an answer which is a whole number B1 64= 8 or correctly evaluated example where the answer is a whole number B1 eg 5 4 = 9 and 9 is a square number or 5 4 = 3 oe Correctly evaluated example where the answer is not a whole number B1 eg 3 2 = 5 and 5 is not a square number oe Additional Guidance 1 or 2 marks can be gained for example(s)

9 Even if the decision is incorrect 32 22 = 5 and 5 is between 4 and 9, implies 5 is not square B0B0B1 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER 1 HIGHER Q Answer Mark Comments Version Page 9 10(a) Alternative method 1 25 50 ( 60) or 30 minutes or 12 h or 20 30 ( 60) or 40 minutes or 23 h or 30 40 ( 60) or 45 minutes or 34 h M1 oe Two of 25 50 ( 60) or 30 minutes or 12 h and 20 30 ( 60) or 40 minutes or 23 h and 30 40 ( 60) or 45 minutes or 34 h M1 oe 25 50 ( 60) or 30 minutes or 12 h and 20 30 ( 60) or 40 minutes or 23 h and 30 40 ( 60) or 45 minutes or 34 h M1 oe C with all working correct A1 oe Additional Guidance Condone missing units, but note that 30 is given as both a distance and a speed in the question Mark scheme for 10(a) continues on the next page Q Answer Mark Comments Page 10 Version 10(a) Alternative method 2 20 30 ( 60) or 40 minutes or 23 h 30 40 ( 60) or 45 minutes or 34 h M1 25 50 ( 10) or 30 minutes or 21 h 50 23 or 33(.)

10 Miles or 40 23 or 26(. ) miles or miles 50 34 or miles or 30 34 or miles M1 30 21 or 15 miles or 40 21 or 20 miles 50 23 or 33(. ) miles and 40 23 or 26(. ) miles or miles 50 34 or miles and 30 34 or miles M1 C with all working correct A1 oe Additional Guidance Condone missing units, but note that 30 is given as both a distance and a speed in the question and 40 appears as both a time and a speed MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER 1 HIGHER Q Answer Mark Comments Version Page 11 10(b) time = 30 minutes or 12 h or 15 minutes difference or scale factor 2 B1 oe 30 2 or 30 12 or 60 M1 20 mph faster A1 Additional Guidance 20 mph with no box ticked B1M1A0 20 mph with slower ticked B1M1A0 11(a) 16 and 56 on each pair of branches B1 In correct order Additional Guidance 11(b)