Foundation June 2024 Paper 2 Q16
16 The table shows how much Amaya earns per hour.
| Work done on Monday to Friday | £20.15 per hour |
| Work done on Saturday or Sunday | £30.23 per hour |
One week Amaya works for \(40\frac{1}{3}\) hours between Monday and Friday and then for \(4\frac{1}{4}\) hours on Saturday.
(a) Amaya says
I will earn at least £900 for my work this week.
By rounding each value to the nearest integer, use estimation to show that Amaya may be correct. [5]
(b) Give one reason why your working in part (a) shows that Amaya can be certain of earning at least £900 for her work in this week. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Three of 20[.00], 30[.00], 40 and 4 seen | B1 | B1 seen as rounding | |
| \(40 \times 20\) | M1 | for their 40 x their 20 | their 40 can be \(40\frac{1}{3}\), \(40.\dot{3}\), 40.33[3…] or 41 their 20 can be 20.15 or 21 their 4 can be \(4\frac{1}{4}\), 4.25 or 5 their 30 can be 30.23 or 31 |
| \(4 \times 30\) | M1 | for their 4 x their 30 | |
| 920 or 800 and 120 | A2 | A2 dep on B1M1M1 or A1 dep on B1M1 for 800 or 120 | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| The calculation is an underestimate | 1 | All values were rounded down oe Mark best response as long as not contradictory or incorrect See Appendix 1 | |
Appendix
APPENDIX 1 Question 16(b)
We want the candidate to say WHY they are certain of the figure being at least £900.
If TOTAL is used then this MUST be £920. IF rounded figures are used then all four must be rounded down correctly (20,30,40,4)
| Response | Mark | |
|---|---|---|
| 1 | It is an Underestimate | 1 |
| 2 | All Values were rounded down | 1 |
| 3 | This is correct because at minimum she will make 920 (‘at minimum’ implies rounding and is correct) | 1 |
| 4 | The values are rounded down meaning she earnt more than this | 1 |
| 5 | (40 x 20) + (4 x 30) already equal over £900 | 1 |
| 6 | The underestimation is over £900 | 1 |
| 7 | If you round the earnings you get over £900 (this is true for rounding both up and down) | 1BOD |
| 8 | Because in my working not adding the minutes, it’s still over £900 as it’s £928.80 (incorrect) | 0 |
| 9 | Because I estimated it meaning she’d probably got more (probably does not mean certain) | 0 |
| 10 | As it has gone over £900 (not describing rounding or underestimate) | 0 |
| 11 | This is correct because she will make 920 (the candidate is not telling us WHY they are certain) | 0 |
| 12 | Because £20.15x40=£806 and £30.23 x4=120.92 + them = 926.92 not including the minimum (All rounded values not used) | 0 |
| 13 | If you added everything without a fraction it adds up to almost £900 (incorrect) | 0 |
| 14 | Because it works out that all of her work will add to over 900 (no reference to underestimate) | 0 |
| 15 | Because it’s over 900 (not enough, need to say WHY it is certainly over £900) | 0 |
| 16 | The estimation is over £900 (not enough, need to say WHY estimation is certainly over £900) | 0 |
| 17 | Because I rounded down (not enough- needs to be e.g. rounded all numbers down) | 0 |