Foundation June 2017 Paper 3 Q18
18 A shop sells two brands of battery.
One brand A battery powers a toy for 5 hours.
One brand B battery powers the same toy for \(5\dfrac{1}{2}\) hours.
Which brand is better value?
You must show your working. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 of 6 – cost per hour | ||
| \(3.6(0) \div 8\) or (0).45 or \(2.94 \div 6\) or (0).49 | M1 | \(360 \div 8\) or 45 or \(294 \div 6\) or 49 |
| their (0).45 \(\div\) 5 or (0).09 or their (0).49 \(\div\) 5.5 or (0).08(9…) | M1dep | their 45 \(\div\) 5 or 9 or their 49 \(\div\) 5.5 or 8.(9…) |
| their (0).45 \(\div\) 5 and their (0).49 \(\div\) 5.5 | M1dep | their 45 \(\div\) 5 and their 49 \(\div\) 5.5 |
| (£)0.09 and (£)0.08(9…) | A1 | 9(p) and 8.(9…) (p) |
| brand B | A1ft | ft correct decision for their values with M3 scored |
| Alternative method 2 of 6 – cost per hour from price of pack | ||
| \(8 \times 5\) or 40 or \(6 \times 5.5\) or 33 | M1 | |
| \(3.6(0) \div\) their 40 or (0).09 or \(2.94 \div\) their 33 or (0).08(9…) | M1dep | \(360 \div\) their 40 or 9 or \(294 \div\) their 33 or 8.(9…) |
| \(3.6(0) \div\) their 40 and \(2.94 \div\) their 33 | M1dep | \(360 \div\) their 40 and \(294 \div\) their 33 |
| (£)0.09 and (£)0.08(9…) | A1 | 9(p) and 8.(9…) (p) |
| brand B | A1ft | ft correct decision for their values with M3 scored |
| Alternative method 3 of 6 – number of hours per unit cost from number of batteries | ||
| \(3.6(0) \div 8\) or (0).45 or \(2.94 \div 6\) or (0).49 | M1 | \(360 \div 8\) or 45 or \(294 \div 6\) or 49 |
| \(5 \div\) their (0).45 or 11.1(…) or \(5.5 \div\) their (0).49 or 11.2(…) | M1dep | \(5 \div\) their 45 or (0).111(…) or \(5.5 \div\) their 49 or (0).112(…) |
| \(5 \div\) their (0).45 and \(5.5 \div\) their (0).49 | M1dep | \(5 \div\) their 45 and \(5.5 \div\) their 49 |
| 11.1(…) (hours) and 11.2(…) (hours) | A1 | (0).111(…) (hours) and (0).112(…) (hours) |
| brand B | A1ft | ft correct decision for their values with M3 scored |
| Alternative method 4 of 6 – common number of batteries | ||
| Scaling towards a cost for a common number of batteries (eg 24 batteries) eg \(8 \times 3 \times 5\) or 120 and \(6 \times 4 \times 5.5\) or 132 | M1 | |
| eg \(3 \times 3.60\) or 10.8(0) and \(4 \times 2.94\) or 11.76 | M1 | eg \(3 \times 360\) or 1080 and \(4 \times 294\) or 1176 |
| eg their 10.8(0) \(\div\) their 120 or (0).09 and their 11.76 \(\div\) their 132 or (0).08(9…) | M1dep | eg their 1080 \(\div\) their 120 or 9 and their 1176 \(\div\) their 132 or 8.(9…) dependent on M1M1 |
| (£)0.09 and (£)0.08(9…) | A1 | 9(p) and 8.(9…) (p) |
| brand B | A1ft | ft correct decision for their values with M3 scored |
| Alternative method 5 of 6 – number of hours per unit cost from batteries per unit cost | ||
| \(8 \div 3.6(0)\) or 2.2(…) or \(6 \div 2.94\) or 2.04(…) | M1 | \(8 \div 360\) or 0.022(…) or \(6 \div 294\) or 0.0204(…) |
| their 2.2(…) \(\times\) 5 or 11.1(…) or their 2.04(…) \(\times\) 5.5 or 11.2(…) | M1dep | their 0.022(…) \(\times\) 5 or 0.111(…) or their 0.0204(…) \(\times\) 5.5 or 0.112(…) |
| their 2.2(…) \(\times\) 5 and their 2.04(…) \(\times\) 5.5 | M1dep | their 0.022(…) \(\times\) 5 and their 0.0204(…) \(\times\) 5.5 |
| 11.1(…) (hours) and 11.2(…) (hours) | A1 | (0).111(…) (hours) and (0).112(…) (hours) |
| brand B | A1ft | ft correct decision for their values with M3 scored |
| Alternative method 6 of 6 – cost for common number of battery hours | ||
| \(3.6(0) \div 8\) or (0).45 or \(2.94 \div 6\) or (0).49 | M1 | \(360 \div 8\) or 45 or \(294 \div 6\) or 49 |
| Scaling towards a common number of battery hours (eg 55 hours) eg their (0).45 \(\times\) 11 or their (0).49 \(\times\) 10 | M1dep | eg their 45 \(\times\) 11 or their 49 \(\times\) 10 |
| eg their (0).45 \(\times\) 11 and their (0).49 \(\times\) 10 | M1dep | eg their 45 \(\times\) 11 and their 49 \(\times\) 10 |
| eg (£)4.95 and (£)4.9(0) | A1 | eg 495(p) and 490(p) |
| brand B | A1ft | ft correct decision for their values with M3 scored |
Additional guidance
| For the first A mark the values must not be rounded to the same value | |
| A1ft can be awarded after A0 for the same value for the correct decision eg 0.09 and 0.09 with decision ‘both the same’ | M3A0A1ft |
| \(8 \times 5 = 40\) and \(40 \div 3.6(0)\) and \(6 \times 5.5 = 33\) and \(33 \div 2.94\) is equivalent to \(8 \div 3.6(0) \times 5\) and \(6 \div 2.94 \times 5.5\) on Alt 5 | M3 |
| \(8 \times 5 = 40\) and \(40 \div 3.6(0)\) is equivalent to \(8 \div 3.6(0) \times 5\) on Alt method 5 | M2 |
| \(6 \times 5.5 = 33\) and \(33 \div 2.94\) is equivalent to \(6 \div 2.94 \times 5.5\) on Alt method 5 | M2 |
| (0).45 \(\div\) 5 | M1M1 |
| (0).45 \(\div\) 5 and (0).49 \(\div\) 5.5 | M1M1M1 |
| (0).45 \(\div\) 5 and (0).415 \(\div\) 5.5 \(\qquad\) 0.415 is not from a correct method | M1M1M0 |
| In Alt method 4 M1M1 can be awarded in either order | |
| In Alt method 5 their 2.2(…) must be correct or from correct method their 2.04(…) must be correct or from correct method | |
| Accept misread of 4 batteries (A) or 3 batteries (B) for up to M3A0A1ft | |
| Accept working with minutes eg in Alt method 3 for 2nd M1dep accept \(\quad 300 \div 45 = 6.6(\ldots)\) or 6.7 or \(\;330 \div 49 = 6.7(\ldots)\) for 3rd M1dep accept \(\quad 300 \div 45\) and \(330 \div 49\) for first A mark must see 6.6(…) or 6.67 and 6.7(…) or 6.7 and 6.73(…) |