Foundation November 2022 Paper 2 Q18
18 A football team plays two matches.
(a) For the first match, 40 000 tickets are sold.
Assume that each ticket costs £38.50
Work out the total amount of money from ticket sales for this match. [2 marks]
(b) In fact, for the first match,
some of the tickets cost less than £38.50
and
some of the tickets cost more than £38.50
What does this mean about the total amount of money from ticket sales for this match?
Tick one box. [1 mark]
- It will be more than the answer to part (a)
- It will be the same as the answer to part (a)
- It will be less than the answer to part (a)
- It is not possible to tell
(c) For the second match, the number of tickets sold increases from 40 000 to 55 000
Is the increase in tickets sold more than 35% ?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(38.5(0) \times 40\,000\) | M1 | oe implied by digits 154 |
| 1 540 000 | A1 | oe eg \(1.54 \times 10^6\) or 1.54 million or 1.54 m SC1 3 080 000 or 770 000 |
Additional guidance
| Allow any commas or spaces eg 154,00,00 | M1A1 |
| Using decimal points is A0, even if 1 540 000 seen in working eg 15 400.00 | M1A0 |
| 1 540 000 seen in working but loses or gains one zero on answer line is acceptable as a transcription error eg 1 540 000 seen and answer 1 5040 000 or answer 1 540 00 | M1A1 |
| Do not allow the A1 for further work (but may gain M1 eg for digits 154 seen or SC1) |
| Answer | Mark | Comments |
|---|---|---|
| It is not possible to tell | B1 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 Working out the increase using 35% | ||
| \(55\,000 - 40\,000\) or 15 000 | M1 | oe |
| \(0.35 \times 40\,000\) or 14 000 | M1 | oe |
| 15 000 and 14 000 and Yes | A1 | oe |
| Alternative method 2 Working out the tickets for the second or first match using 35% | ||
| \(0.35 \times 40\,000\) or 14 000 | M1 | oe |
| \(40\,000 + 0.35 \times 40\,000\) or 54 000 or \(55\,000 - 0.35 \times 40\,000\) or 41 000 | M1dep | oe \(1.35 \times 40\,000\) scores M2 |
| 54 000 and Yes or 41 000 and Yes | A1 | oe |
| Alternative method 3 Working out the percentage increase | ||
| \(55\,000 - 40\,000\) or 15 000 or \(\dfrac{55\,000}{40\,000}\) or 1.375 | M1 | oe |
| \(\dfrac{55\,000 - 40\,000}{40\,000}\) or \(\dfrac{15\,000}{40\,000}\) or \(\dfrac{55\,000}{40\,000} - 1\) or \(1.375 - 1\) or 0.375 or 37.5 or 1.375 and 1.35 | M1dep | oe eg \(\dfrac{55 - 40}{40}\) |
| 37.5 and Yes or 0.375 and 0.35 and Yes or 1.375 and 1.35 and Yes | A1 | oe |
Additional guidance
| Up to M2 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts | |
| May use sales of tickets but must use 1 540 000 Alt 1 \(55\,000 \times 38.5 - 40\,000 \times 38.5\) or \(2\,117\,500 - 1\,540\,000\) or 577 500 \(0.35 \times 1\,540\,000\) or 539 000 577 500 and 539 000 and Yes Alt 2 \(0.35 \times 1\,540\,000\) or 539 000 \(1\,540\,000 + 539\,000\) or 2 079 000 or \(2\,117\,500 - 539\,000\) or 1 578 500 2 079 000 and 2 117 500 and Yes or 1 578 500 and 1 540 000 and Yes Alt 3 \(55\,000 \times 38.5 - 40\,000 \times 38.5\) or \(2\,117\,500 - 1\,540\,000\) or 577 500 or \(\dfrac{2\,117\,500}{1\,540\,000}\) \(\dfrac{2\,117\,500 - 1\,540\,000}{1\,540\,000}\) 37.5 and Yes | M1 M1 A1 M1 M1dep A1 M1 M1dep A1 |
| Only \(40\,000 - 55\,000\) (may be recovered) | M0 |
| In Alt 1 the 2nd mark is not dependent | |
| Build-up to 35% must be correct or full method must be shown | |
| Accept \(35\% \times 40\,000\) for 2nd mark of Alt 1 or 1st mark of Alt 2 | M1 |