Foundation November 2021 Unit 1 Q15
15. Some letters are made using only straight lines e.g. T.
Some letters are made using straight lines and curved lines e.g. P.
Some letters are made using only curved lines e.g. S.
Six cards spell out the name BANGOR.
| B | A | N | G | O | R |
In a game, the six cards are placed in a bag.
One card is chosen at random.
The letter on the card is noted and the card is returned to the bag.
If the card has a letter on it that is made using only straight lines, the player gains 10 points.
A card with any other type of letter gains no points.
Leah plays the game 24 times.
Do you expect Leah to score a total of 100 points?
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| Indicates 2 (letters out of 6 gain points) | B1 | Any unambiguous indication. |
| (Expected number of wins =) \(\dfrac{2}{6} \times 24\) or equivalent | M1 | FT ‘their stated number of ’10 point’ letters’. |
| = 8 | A1 | Award M1A1 for 8/24 suggesting ‘8 wins out of 24’ |
| (Points gained =) 8 × 10 | M1 | FT ‘their derived 8’ × 10 only if ‘their derived 8’ < 24. |
| = 80 (points) AND ‘No’ (Leah is not expected to score 100 points) | A1 | FT their derived number of points |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| Indicates 2 (letters out of 6 gain points) | B1 | Any unambiguous indication. |
| (Each letter expected to be drawn) \(\dfrac{24}{6}\) (times) | M1 | |
| = 4 (times) | A1 | |
| (Points gained = ) 4 × 2 × 10 | M1 | FT ‘their derived 4’ and ‘their stated 2’. |
| = 80 (points) AND ‘No’ (Leah is not expected to score 100 points) | A1 | FT their derived number of points. |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| Indicates 2 (letters out of 6 gain points) | B1 | Any unambiguous indication. |
| (Expected number of wins =) \(\dfrac{2}{6} \times 24\) or equivalent | M1 | FT ‘their stated number of ’10 point’ letters’. |
| = 8 | A1 | Award M1A1 for 8/24 suggesting ‘8 wins out of 24’ |
| (Number of wins required =) \(\dfrac{100}{10}\) | M1 | |
| = 10 (wins) AND ‘No’ (Leah is not expected to score 100 points) | A1 | FT their derived number of expected wins. Note for Alternative method 2 If ‘number of wins required’ is calculated before calculating ‘number of expected wins’ then the conclusion (‘AND’) will be attached to the 8 rather than the 10. |
Corrected by Westie's Workshop
- The board's mark scheme printed “‘No’ (Leah is not expected score 100 points)”. Changed to “‘No’ (Leah is not expected to score 100 points)” because the word “to” is missing (this appears in the main method and both alternative methods).
Original: see the board's mark scheme PDF (link above).