Higher June 2023 Paper 2 Q10
10 Team A and Team B take part in a quiz league.
After 11 rounds, Team A has a mean score per round of 17
After 9 rounds, Team B has a mean score per round of 18
Both teams take part in a further round.
After this round, both teams have a mean score per round of 18.5
In the further round, Team A scored more points than Team B.
How many more?
(4)
| Scheme | Marks |
|---|---|
| 17 × 11 (= 187) or 18.5 × 12 ( =222) or 18 × 9 (=162) or 18.5 × 10 (= 185) | M1 |
18.5 × 12 − 17 × 11 (“222” – “187”)(= 35) or 18.5 × 10 − 18 × 9 (“185” – “162” )(= 23) or \(\dfrac{\text{``}{187}\text{''} + x}{12} = 18.5\) (\(x = 35\)) or \(\dfrac{\text{``}{162}\text{''} + y}{10} = 18.5\) (\(y = 23\)) or Diff between A and B in first rounds “187” – “162” (= 25) or Diff between A and B after further round “222” – “185” (= 37) [or 2 × 18.5 (= 37) (2 must come from correct working)] | M1 |
| “35” – “23” or “37” – “25” or “16.5” – “4.5” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 12 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Expression for total of A or B either including or excluding last round
M1: expression for number of points gained by A or B in the last round
or
for an equation that could lead to the number of points gained by A or B in the last round
M1: calculation for difference between number of points scored in last round
M2 for
1.5 × 11 + 18.5 (= 35) or
9 × 0.5 + 18.5 (= 23)
OR
1.5 × 11 (= 16.5) or
0.5 × 9 (= 4.5)
The 2 is 2 further rounds of 18.5 ie 37 comes from 18.5 × 12 – 18.5 × 10 so the 2 × 18.5 is (12 – 10) × 18.5