Foundation June 2017 Paper 1 Q8
8 Nadia has £5 to buy pencils and rulers.
| Prices | |
|---|---|
| Pencils | 8p each |
| Rulers | 30p each |
She says,
“I will buy 15 pencils.
Then I will buy as many rulers as possible.
With my change I will buy more pencils.”
How many pencils and how many rulers does she buy? [6 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(15 \times 8\) or 120 | M1 | |
| 500 \(-\) their 120 or 380 | M1dep | |
| their 380 \(\div\) 30 or 12(…) | M1dep | oe builds up in 30s to at least their 380 \(-\) 30 or builds up in 30s from their 120 to at least 470 allow one error in any build up method |
| their \(12 \times 30\) or 360 or their 12 chosen from a build up | M1dep | oe their 12 must either come from rounding down their 12.(…) or from choosing their 12 out of a build up or because they had an exact answer of their 12 from a correct method for the third mark |
| their 380 \(-\) their 360 or 20 or 500 \(-\) (their 360 \(+\) their 120) or their 360 \(+ 8 + 8\) (their correct number of 8s) or 376 or their 360 \(+\) their 120 \(+ 8 + 8\) (their correct number of 8s) or 496 | M1dep | their 20 must be \(0 \lt\) their \(20 \lt 30\) |
| 17 pencils, 12 rulers | A1 | |
| Alternative method 2 | ||
| \(15 \times 0.08\) or 1.2(0) | M1 | |
| 5 \(-\) their 1.2(0) or 3.8(0) | M1dep | |
| their 3.8(0) \(\div\) (0).3(0) or 12(...) | M1dep | oe builds up in (0).3(0)s to at least their 3.8(0) \(-\) (0).3(0)* allow one error or builds up in (0).3(0)s from their 1.2(0) to at least 4.7(0) allow one error |
| their \(12 \times 0.3(0)\) or 3.6(0) or their 12 chosen from a build up | M1dep | dep on previous mark their 12 must either come from rounding down their 12.(…) or from choosing their 12 out of a build up or because they had an exact answer of their 12 from a correct method for the third mark |
| their 3.8(0) \(-\) their 3.6(0) or (0).2(0) or 5 \(-\) (their 3.6(0) \(+\) their 1.2(0)) or their 3.6(0) \(+\) (0).08 \(+\) (0).08 (their correct number of (0).08s) or 3.76 or their 3.6(0) \(+\) their 1.2(0) \(+\) (0).08 \(+\) (0).08 (their correct number of (0).08s) or 4.96 | M1dep | their 0.20 must be \(0 \lt\) their \(0.20 \lt 0.30\) |
| 17 pencils, 12 rulers | A1 | |
Additional guidance
| Do not allow mixed units in working unless recovered | |
| For build-up, one arithmetic mistake counts as one error, even though more than one value may be affected eg, 30, 60, 90, 130, 160, 190, 220, 250, 280, 310, 340, 370 gets 3rd mark in alternative method 1 (error from 90 to 130, but 30 then added correctly throughout) | |
| If there is no change possible, or change is not considered after rulers are bought, it is maximum M4 | |
| Example \(\;15 \times 8 = 120 \qquad 500 - 120 = 360\) \(360 \div 30 = 12\) then 12 chosen as number of rulers but no further work (4th mark awarded despite no “remainder” but 5th mark has to consider change) | M1M1M1M1M0A0 |
| Example \(\;15 \times 8 = 120 \qquad 500 - 120 = 380\) \(380 \div 30 = 9.2\) and 9 chosen as the number of rulers (no further work) | M1M1M1M1A0A0 |
Notes
* Corrected from the printed mark scheme, which says “their 3.8(0) \(-\) 30”.