Comparison of key skills specifications 2000/2002 with 2004 standardsX015461July 2004Issue 1
GCSE in Mathematics Specification A
Higher Tier
Paper 1 (Non-Calculator)
General Marking Guidance
• All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. • Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. • All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme. • Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. • Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. • Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows:
i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear. Comprehension and meaning is clear by using correct notation and labelling conventions.
ii) select and use a form and style of writing appropriate to purpose and to complex subject matter. Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning.
iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used.
|Guidance on the use of codes within this mark scheme |
|M1 – method mark |
|A1 – accuracy mark |
|B1 – working mark |
|C1 – communication mark |
|QWC – quality of written communication |
|oe – or equivalent |
|cao – correct answer only |
|ft – follow through |
|sc - special case |
Specification A: Paper 1 Higher Tier
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|1. | |32 ÷ 80 × 100 |40 |2 |M1 for 32 ÷ 80 × 100 oe |
| | | | | |A1 cao |
|Total for Question 1: 2 marks |
|2. | |300 × 0.7 |210 |2 |M1 for 300 × 0.7 |
| | | | | |A1 cao |
|Total for Question 2: 2 marks |
|3. |(a) | |2 × 2 × 2 × 3 × 5 |2 |M1 for correct method seen |
| | | | | |A1 cao |
| |(b) | |30 |1 |B1 cao |
|Total for Question 3: 3 marks |
|4. |(a) |24 ÷ 12 = 2 |360 |2 |M1 for 24 ÷ 12 (= 2) |
|FE | |2 × 180 | | |A1 cao |
| |(b) |18 ÷ 12 (=1.5) |300 |2 |M1 for 18 ÷ 12 (=1.5) |
| | |1.5 × 200 | | |A1 cao |
|Total for Question 4: 4 marks |
|5. | | |Shape enlarged ×3 in |3 |B3 shape enlarged × 3 in correct position |
| | | |correct position | |(B2 shape enlarged ×3 but in wrong position or shape enlarged by a different scale factor |
| | | | | |correctly) |
| | | | | |(B1 shape enlarged by a different scale factor and in wrong position) |
|Total for Question 5: 3 marks |
|6. |(a) | |20 |2 |M1 for substitution into formula |
| | | | | |A1 cao |
| |(b) | |m13 |1 |B1 cao |
| |(c) | |1 |1 |B1 cao |
| |(d) | |4y3 |2 |B2 for 4y3 |
| | | | | |(B1 for ay3 or 4yn or 161/2(y3)1/2) |
|Total for Question 6: 6 marks |
|7. | | |Question and response |2 |B1 for suitable question |
|FE | | |boxes | |B1 for response boxes |
|Total for Question 7: 2 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|8. |(i) | |0.39 |3 |B1 cao |
| | | | | | |
| |(ii) | |0.41 | |M1 for 1 – (0.2 + 0.16 + 0.23) |
| | | | | |A1 cao |
|Total for Question 8: 3 marks |
|9. | | |49 |4 |M1 for 100 – 38 (=62) |
| | | | | |M1 for 23 – 7 (-16) |
| | | | | |M1 for “62” – 18 – “16” |
| | | | | |A1 cao |
| | | | | |NB : working may be in a table or diagram |
|Total for Question 9: 4 marks |
|10. | | |2 |4 |M1 for attempt to find LCM of any 2 of 12, 8 and 9 |
|FE | | | | |M1 for attempt to find LCM of 8, 9 and 12 |
| | | | | |A1 for 72 |
| | | | | |A1 for 2 |
|Total for Question 10: 4 marks |
|11. | |15000÷100×40 (=6000) |3000 |4 |M1 for 15000 – 15000÷100×40 oe (=6000) |
|FE | |15000 – “6000” (=9000) | | |M1 for “9000” ÷ (3 + 1 + 2) (=1500) |
| | | | | |M1 for “1500” × 2 |
| | | | | |A1 cao |
|Total for Question 11: 4 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|12. |(a) | |12x + 3y |2 |M1 for 3×4x + 3×y or 12x or 3y |
| | | | | |A1 cao |
| |(b) | |5p2 – 15p |1 |B1 cao |
| |(c) | |y2 + 5y – 24 |2 |M1 for all 4 terms correct with or without signs or 3 out of no more than four terms correct with |
| | | | | |signs or y(y – 3) + 8(y – 3) or y(y + 8) – 3(y + 8) |
| | | | | |A1 cao |
| |(d) | |4t2 – 12t + 9 |2 |M1 for all 4 terms correct with or without signs or 3 out of no more than four terms correct with |
| | | | | |signs or 2t(2t – 3) - 3(2t – 3) |
| | | | | |A1 cao |
|Total for Question 12: 7 marks |
|13. | | |m = (p – h) ÷ 6 |2 |M1 for p – h = 6m |
| | | | | |A1 |
|Total for Question 13: 2 marks |
|14. | | |Region shaded |4 |M1 for line parallel to AB, 2 cm ±2mm from AB |
|FE | | | | |M1 for circle, centre T, radius 3 cm ±2mm |
| | | | | |M1 for bisector of angle DCB ±2o |
| | | | | |A1 for correct region shaded within guidelines |
|Total for Question 14: 4 marks |
|15. | |2x +1 + 3x – 2 + 3x + 1 + 2x = 38 |80 |5 |M1 for 2x +1 + 3x – 2 + 3x + 1 + 2x = 38 |
| | |10x – 2 = 38 | | |M1 for correct method to solve linear equation |
| | |x = 4 | | |A1 for x = 4 |
| | | | | |M1 for substitution of x = 4 into any expression for side |
| | |7; 8; 13 | | |A1 cao |
| | |½ ×(7 + 13) × 10 | | | |
|Total for Question 15: 5 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|16. | |180 – (360÷ 5) oe (=108) |84 |4 |B1 for 60o seen |
| | |360 – “60” – 2×”108” | | |M1 for 180 – (360÷ 5) oe (=108) |
| | | | | |M1 for 360 – “60” – 2×”108” |
| | | | | |A1 cao |
|Total for Question 16: 4 marks |
|17. | |4000 × 1.032 |Bank B |5 |M2 for 4000 × 1.032 oe |
|QWC | | | | |(M1 for 1.03 × 4000 oe or 120 seen) |
|FE | | | | |M1 for 3.2 × 4000 ÷ 100 oe |
| | | | | |A1 for 256 and 243.60 |
| | | | | |C1 for clear working conclusion following on from candidate’s working |
| | | | | |QWC : Working must be clearly laid out and conclusion must link to working |
|Total for Question 17: 5 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|18. |(a) |6 ÷ 4 = 1.5 |13.5 |2 |M1 for 6 ÷ 4 (=1.5) or 2 ÷ 3 |
| | |1.5 × 9 | | |A1 cao |
| |(b) |10.5 ÷ 1.5 |7 |2 |M1 for 10.5 ÷ 1.5 oe |
| | | | | |A1 cao |
|Total for Question 18: 4 marks |
|19. | | |x = 2, |4 |M1 for correct process to eliminate either x or y (condone one arithmetic error) |
| | | |y = -1.5 | |A1 for either x = 2 or y = -1.5 |
| | | | | |M1 (dep on 1st M1) for correct substitution of their found variable |
| | | | | |A1 cao for both x = 2 and y = -1.5 |
|Total for Question 19: 4 marks |
|20. |(a) | |Points plotted and|2 |B1 ft for at least 5 of 6 points plotted correctly ± ½ sq at end of |
| | | |cf graph drawn | |B1 ft (dep on previous B1) for points joined by curve or line segments provided no gradient is |
|FE | | | | |negative – ignore any part of graph outside range of their points |
| | | | | |(SC B1 if 5 or 6 pts plotted not at end but consistent within each interval and joined) |
| | | | | | |
| | | | | | |
| |(b) | |Box plot drawn |3 |B1 for median drawn correctly (ft from graph) |
| | | | | |B1 for UQ and LQ drawn correctly (ft from graph) |
| | | | | |B1 for whiskers correct |
| |(c) | | |2 |B2 ft for any comparison of spread in context |
| | | |Comparison | |(B1 ft for any comparison not in context) |
|Total for Question 20: 7 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|21. | |(14 – 2)/2 (=6) |19 |3 |M1 for (14 – 2)/2 (=6) |
| | |“6” ( 3 (=18) | | |M1 for “6” ( 3 |
| | |“18” + 1 | | |A1 cao |
| | | | | | |
| | | | | |or |
| | | | | | |
| | | | | |M1 for (k – 1)/12 = 3/2 |
| | | | | |M1 for 2(k – 1) = 12 × 3 |
| | | | | |A1 cao |
|Total for Question 21: 3 marks |
|22. | | |96 |4 |M1 for Angle ABC = 0.5 × 168 (= 84) |
| | | | | |M1 for Angle ADC = 180 – 0.5×168 |
| | | | | |A1 cao |
| | | | | |C1 for Angle at centre is twice angle at circumference and Opposite angles of a cyclic |
| | | | | |quadrilateral sum to 180o |
| | | | | | |
| | | | | |or |
| | | | | | |
| | | | | |M1 for reflex angle AOC = 360 – 168 (= 192) |
| | | | | |M1 for 0.5 × 192 |
| | | | | |A1 cao |
| | | | | |C1 for Angle at centre is twice angle at circumference and angles at a point add up to 360( |
|Total for Question 22: 4 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|23. | | |[pic] |4 |B1 for[pic] |
| | | | | |M1 for [pic] or [pic] or [pic] or [pic] or [pic] or [pic] |
| | | | | |M1 for [pic] + [pic] + [pic] + [pic] + [pic] +[pic] |
| | | | | |A1 for [pic] oe |
| | | | | | |
| | | | | |or |
| | | | | |B1 for[pic] |
| | | | | |M1 for [pic] or [pic] or [pic] |
| | | | | |M1 for 1 – ([pic] + [pic] + [pic]) |
| | | | | |C1 for [pic] oe |
|Total for Question 23: 4 marks |
|24. | | |5 , - 0.5 |5 |M1 for common denominator on LHS or clearing fractions |
| | | | | |M1 for multiplying out brackets |
| | | | | |A1 for 2x2 – 9x + 5 = 0 |
| | | | | |M1 for (2x ± 1)(x ± 5) or substitution into quadratic formula |
| | | | | |A1 for 5 and - 0.5 |
|Total for Question 24: 5 marks |
|1MA0/1H |
|Question |Working |Answer |Mark |Additional Guidance |
|25. |(i) | |2b + a |2 |M1 for [pic] oe |
| | | | | |A1 cao |
| | | | | | |
| | | | | |M1 for [pic]oe |
| | | | | |M1 for [pic] oe |
| |(ii) | |½b + a |3 |A1 for ½b + a oe |
| | | | | | |
|Total for Question 25: 5 marks |
April 2010
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Mark Scheme
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