Higher June 2017 Paper 5 Q3
3 Last year, Katie earned £16 200.
Her total loan repayments were £6400.
Katie estimates that the ratio of her loan repayments to her earnings is approximately 3 : 8.
Is she correct?
Show your reasoning. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| A - Yes with appropriate reasoning involving rounding and correct simplification to 3 : 8 or 3 :11 or 8 : 11 or ratios reversed OR B - Yes it is approximately correct oe and simplification of 6400 : 16200 to 32 : 81 OR C - Yes with a correctly evaluated calculation using e.g. ratio 3 : 8 with a comparison comment OR D - Yes and e.g. 16200 ÷ 8 and 6400 ÷ 3 correctly evaluated | 3 | M2 eg for showing 6000 : 16000 and reducing to 3 : 8 or for appropriate rounding at some stage in correctly simplifying ratio leading to 3 : 8 isw or reduces 6400 : 16200 to 32 : 81 isw or reduces 6400 : 22600 to 32 : 113 isw or for ratio calculation leading to one of the following values seen 6075, 6163 to 6165, 16436 to16440, 17066 to 17067 or 22 275 or 23 463 to 23 467 seen isw or for 2025 and 2133 to 2134 seen isw or 2025 and 2054 to 2055 seen isw or 2133 to 2134 and 2054 to 2055 seen isw Or M1 for 6000 or 16 000 or 20 000 or 22 000 or 23 000 seen or for appropriate rounding of one number at some stage in simplifying ratio or for intention to find \(\frac{3}{8}\) of 16 200 or for \(\frac{8}{3}\) of 6400 or \(\frac{3}{11}\) of (16 200 + 6400) or \(\frac{8}{11}\) of (16 200 + 6400) isw or for 6400 ÷ 3 and one of 16 200 ÷ 8 or (6400 + 16 200) ÷ 11 seen isw or 16 200 ÷ 8 and (6400 + 16 200)÷ 11 seen isw | For all marks accept method with equivalent fractions or decimals [3sf or better] Allow equivalent methods working with the totals e.g. 3 : 11, condone 22600 rounded to 22000 For 3 or M2, allow clear ‘reverse’ methods working from e.g. 3 : 8 to 6000 and 16000 Accept clear working if not in ratio form e.g. 3.2 and 8.1 shown not in ratio The figures in the part marks column are guidance on accuracy required for 3 marks or M2 SEE APPENDIX |
Appendix: Exemplar responses for Q3
| Response | Mark | ||
|---|---|---|---|
| 1 | 6400 : 16200 = 64 : 162 = 32 : 81 which is roughly 30 : 80 = 3 : 8 so yes | 3B | |
| 2 | 6000 + 16000 = 22000, 22000 ÷ (3 + 8) = 2000 3 × 2000 = 6000 , 8 × 2000 = 16 000 so yes she is correct | Method C but better | 3C |
| 3 | 3.2 and 8.1 in working. Close as he can round the decimals to nearest whole number. | Decision not clear | M2B |
| 4 | 3 : 8 = 6 : 16 = 6000 : 16000 yes Katie is correct if she rounds to the nearest 1000 | Reverse method | 3A |
| 5 | 16 200 ÷ 8 = 2040, 2040 × 3 = 6120 she is not correct | Error made in calculation M2 not available | M1C |
| 6 | 16 200 ÷ 8 = 2025, 2025 × 3 = 6075 which is close to 6400 so yes she is approximately correct | 3C | |
| 7 | 16200 + 6400 = 22600, 22600 ÷ 11 =2540, 2540 × 3 | Intention to find 3/11 with errors | M1C |
| 8 | 16200 + 6400 = 22600 = 22000, 22000 ÷ 11 = 2000 | M1 for one correct rounding | M1D |
| 9 | 16200 ÷ 8 × 3 = 6075 No it is not correct | Correctly evaluated calculation with ratio 3 : 8 | M2C |
| 10 | 16200 : 6400 = 81 : 32 = 8.1 : 3.2 which is approximately 8 : 3 so she is correct | 3B | |
| 11 | 6000 ÷ 3 = 2000 and 16000 ÷ 8 = 2000 so yes | Equivalent to 4th the method but better | 3D |
| 12 | 16000÷8 = 2000, 6400÷3 = 2138.3×11 = 23466. Approximately 400 off so No. | Error in calculation | M1C/D |
| 13 | 16200 × 3/8 =6075. No not correct as for ratio to be correct her loan would have to be £6075. | M2C | |
| 14 | 6400÷3 = 2133.33, 16200÷8 = 2025. Not correct as ratio parts are not equal. | M2D | |
| 15 | 16200 – 6400 = 9800, 9800 ÷ 5 × 3 = 5880 No | M2C | |
| 16 | 6400 × 8 = 51200, 16200 x 3 = 48600 No they are different | M2C |