Higher June 2022 Paper 1 Q8
8 In a week, Samir is paid
- a basic hourly rate for the first 30 hours worked
- an overtime hourly rate for any extra hours worked.
The graph shows his pay for working up to 40 hours in a week.
Work out the ratio basic hourly rate : overtime hourly rate
Give your answer in its simplest form. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: using different time periods | ||
| \(450 \div 30\) or 15 or \(250 \div 10\) or 25 | M1 | oe for any section of the basic rate or the overtime rate eg \(\dfrac{450 - 150}{30 - 10}\) |
| 15 and 25 | A1 | implied by any ratio equivalent to 3 : 5 do not allow as a ratio in the wrong order eg 25 : 15 |
| 3 : 5 or \(\dfrac{3}{5} : 1\) or \(1 : \dfrac{5}{3}\) | B1ft | oe fully simplified ft full simplification of their two values |
| Alternative method 2: using equal time periods | ||
| Four correct readings from equal time periods of at least 5 hours from the two sections of the graph | M1 | eg at 5 and 10 hours and at 35 and 40 hours if a reading from 30 is used, there may only be 3 readings a reading of 0 from 0 may be implied |
| 15 and 25 or correct totals for their equal time periods | A1 | eg 10 hours = 150 and 10 hours = 250 implied by any ratio equivalent to 3 : 5 must not be seen as a ratio in the wrong order eg 250 : 150 |
| 3 : 5 or \(\dfrac{3}{5} : 1\) or \(1 : \dfrac{5}{3}\) | B1ft | oe fully simplified ft full simplification of their two values |
Additional guidance
| In alt 2, only three readings are needed if a reading from 30 hours is included in both time periods or a reading of 0 is used eg readings of 300 from 20, 450 from 30 and 700 from 40 | M1 |
| Readings from 10, 20, 30 and 40 should be 150, 300, 450 and 700 For readings from other numbers of hours not giving a multiple of £10 allow the multiple of 10 above or below the reading or any value between, which can then be used to score all three marks eg allow [220, 230] for a reading at 15 hours | |
| eg alt 1 readings of 70 at 5 hours, 380 at 25 hours, 450 at 30 hours and 700 at 40 hours, followed by hourly rates of 15.50 and 25 and an answer of 31 : 50 | M1A1B1ft |
| eg alt 2 readings of 370 at 25 hours, 450 at 30 hours, 580 at 35 hours and 700 at 40 hours, followed by totals of 80 and 120 or hourly rates of 16 and 24 and an answer of 2 : 3 | M1A1B1ft |
| For \(1\dfrac{2}{3}\) allow 1.67 or better with correct rounding | |
| 450 : 250 = 45 : 25 does not get the mark for 25, but gets the final mark if simplified to 9 : 5 | |
| Ignore units throughout eg answer £3 : £5 | M1A1B1 |
| 15 : 25 | M1A1B0 |
| 25 : 15 or 25 : 10 not simplified | M1A0B0 |
| 25 : 15 with answer 5 : 3 or 25 : 10 with answer 5 : 2 | M1A0B1ft |
| Answer 5 : 3 without working implies | M1A0B1ft |
| 15 : 17.5 | M1A0B0 |
| 15 : 17.5 followed by 6 : 7 | M1A0B1ft |
| 20 : 25 | M1A0B0 |
| 20 : 25 followed by 4 : 5 | M1A0B1ft |
| 3 : 5 in working with answer 1.5 : 2.5 | M1A1B0 |
| 30 : 10 = 3 : 1 | M0A0B1ft |