Foundation June 2019 Paper 2 Q9
9 56 customers pay for satellite television.
They all have the Basic package for £24.50 per month.
Some also have
the Sports package for £27.50 extra per month
the Movie package for £18 extra per month.
The frequency tree shows the number of customers with each package.
In total, how much per month do the 56 customers pay? [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(56 \times 24.5\) or 1372 or \(21 \times 27.5\) or 577.5 or \((14 + 8) \times 18\) or \(22 \times 18\) or \(14 \times 18 + 8 \times 18\) or \(252 + 144\) or 396 | M1 | amount for basic or amount for sports or amount for movies oe |
| Any two of \(56 \times 24.5\) or 1372 or \(21 \times 27.5\) or 577.5 or \((14 + 8) \times 18\) or \(22 \times 18\) or \(14 \times 18 + 8 \times 18\) or \(252 + 144\) or 396 | M1dep | any two of the above implies M2 |
| \(56 \times 24.5\) \(+\) \(21 \times 27.5\) \(+\) \((14 + 8) \times 18\) or \(22 \times 18\) or \(14 \times 18 + 8 \times 18\) or \(252 + 144\) or \(1372 + 577.5 + 396\) or 2345.5 | M1dep | full method that would lead to 2345.5 if evaluated correctly implies M3 |
| 2345.50 | A1 | |
| Alternative method 2 | ||
| \(14 \times (24.5 + 27.5 + 18)\) or \(14 \times 70\) or 980 or \(7 \times (24.5 + 27.5)\) or \(7 \times 52\) or 364 or \(8 \times (24.5 + 18)\) or \(8 \times 42.5\) or 340 or \(27 \times 24.5\) or 661.5 | M1 | amount for all 3 packages or amount for basic + sports or amount for basic + movies or amount for basic only |
| Any two of \(14 \times (24.5 + 27.5 + 18)\) or \(14 \times 70\) or 980 or \(7 \times (24.5 + 27.5)\) or \(7 \times 52\) or 364 or \(8 \times (24.5 + 18)\) or \(8 \times 42.5\) or 340 or \(27 \times 24.5\) or 661.5 | M1dep | any two of the above implies M2 |
| \(14 \times (24.5 + 27.5 + 18)\) or \(14 \times 70\) \(+\) \(7 \times (24.5 + 27.5)\) or \(7 \times 52\) \(+\) \(8 \times (24.5 + 18)\) or \(8 \times 42.5\) \(+\) \(27 \times 24.5\) or \(980 + 364 + 340 + 661.5\) or 2345.5 | M1dep | full method that would lead to 2345.5 if evaluated correctly implies M3 |
| 2345.50 | A1 | |
| Alternative method 3 | ||
| \(56 \times (24.5 + 27.5 + 18)\) or \(56 \times 70\) or 3920 or \(35 \times 27.5\) or 962.5 or \((27 + 7) \times 18\) or \(34 \times 18\) or \(27 \times 18 + 7 \times 18\) or \(486 + 126\) or 612 | M1 | amount if everyone has all 3 packages or amount for not having sports or amount for not having movies |
| Any two of \(56 \times (24.5 + 27.5 + 18)\) or \(56 \times 70\) or 3920 or \(35 \times 27.5\) or 962.5 or \((27 + 7) \times 18\) or \(34 \times 18\) or \(27 \times 18 + 7 \times 18\) or \(486 + 126\) or 612 | M1dep | any two of the above implies M2 |
| \(56 \times (24.5 + 27.5 + 18)\) or \(56 \times 70\) or 3920 \(-\) \(35 \times 27.5\) or 962.5 \(-\) \((27 + 7) \times 18\) or \(34 \times 18\) or \(27 \times 18 + 7 \times 18\) or \(486 + 126\) or 612 or \(3920 - 962.5 - 612\) or 2345.5 | M1dep | full method that would lead to 2345.5 if evaluated correctly implies M3 |
| 2345.50 | A1 | |
Additional guidance
| 2345.50(p) | M1M1M1A1 |
| 2345.5 | M1M1M1A0 |
| Working may be seen on the diagram | |
| Allow all decimal values to be seen as equivalent fractions eg \(\dfrac{1155}{2}\) for 577.5 for the M marks | |
| A ‘correct’ calculation does not have to be evaluated correctly | |
| Division or multiplication by 12 or division by 56 at the end will only lose the A mark eg \(2345.50 \div 56 = 41.88\) per person | M1M1M1A0 |
| For the first two marks use the scheme that awards the most credit and do not apply the rules of choice | |
| Addition may be implied by a column of figures |