Foundation November 2024 Paper 3 Q6
6
(a) By rounding each value to one significant figure, estimate the cost of 4.9 kg of carrots at 73p per kg. [2]
(b) A student works out an estimate for this calculation.\[\dfrac{13.7 + 1.28}{5.099}\]
Their method is to:
- round each number correct to the same number of significant figures and
- work out the approximation.
The student writes
\[\dfrac{14 + 1}{5} = \dfrac{15}{5} = 3.\]What error has the student made in using their method? [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(5\ [\times]\ 70\) or \(5\ [\times]\ 0.7\) | M1 | Not from \(73 \times 4.9\) and rounded to 360 or truncated 350 Accept e.g. 70+70+70+70+70 for M1 Condone units included in product Condone answer 350p with £ crossed through or £3.50p | |
| and 3.5[0] | A1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Recognition that the figures are not all to the same number of sig fig e.g. They’re not all the same accuracy oe | 1 | See appendix Allow complete and correct example(s) | |
Appendix
Question 6b
| Response | Mark | |
|---|---|---|
| 13.7 rounded to the same number of significant figures would be 10 | Mentions “same number of sig fig” and the correct number chosen with correct example | 1 |
| 1.28 and 5.099 have not been rounded to the same number of sig fig as 13.7 | Correct, but only because of the mention of 13.7 (because they have been rounded to the same number of sig fig as each other) | 1 |
| They should have rounded 13.7 to 10 | Accept correct example as illustrating the error | 1 |
| They should have rounded 1.28 to 1.3 and 5.099 to 5.1 | Accept the two correct examples as illustrating the error | 1 |
| They should have rounded 1.28 to 1.30 and 5.099 to 5.1 | Condone the use of 1.30 for 1.3 | 1 |
| He should have rounded 13.7 to the first significant figure | Condone “first” for “1” | 1 |
| They should have rounded 1.28 to 1.3 | Recognises only one of the incorrectly rounded figures. If using 1.28 and 5.099 must describe both | 0 |
| The numerator is bigger than the denominator | Not a comment on the method | 0 |
| He did not round each number to its correct significant figure | A comment about the method BUT does not mention the same number of significant figures | 0 |
| They did not round each number to the correct amount of significant figures | A comment about the method BUT does not mention the same number of significant figures | 0 |
| 1.28 rounded to the same number of significant figures would be 2 | Does mention same number of sig fig but the wrong figure chosen and example is incorrect | 0 |
| They have rounded 13 wrong | Not explained what “wrong” means | 0 |
| He didn’t round 1.28 and 5.099 down properly | Does not explain the error. Might just be suggesting an arithmetic error | 0 |