Foundation June 2023 Paper 2 Q26
26 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 |
|---|---|
| \(17 \times 11\) (= 187) or \(18.5 \times 12\) (=222) or \(18 \times 9\) (=162) or \(18.5 \times 10\) (= 185) | M1 |
\(18.5 \times 12 - 17 \times 11\) (\(\text{``}{222}\text{''} - \text{``}{187}\text{''}\))(= 35) or \(18.5 \times 10 - 18 \times 9\) (\(\text{``}{185}\text{''} - \text{``}{162}\text{''}\))(= 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 \(\text{``}{187}\text{''} - \text{``}{162}\text{''}\) (= 25) or Diff between A and B after further round \(\text{``}{222}\text{''} - \text{``}{185}\text{''}\) (= 37) [or \(2 \times 18.5\) (= 37) where 2 must come from correct working] | M1 |
| \(\text{``}{35}\text{''} - \text{``}{23}\text{''}\) or \(\text{``}{37}\text{''} - \text{``}{25}\text{''}\) or \(\text{``}{16.5}\text{''} - \text{``}{4.5}\text{''}\) | 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 \(1.5 \times 11 + 18.5\) (= 35) or \(9 \times 0.5 + 18.5\) (= 23)
OR
\(1.5 \times 11\) (= 16.5) or \(0.5 \times 9\) (= 4.5)
The 2 is 2 further rounds of 18.5 ie 37 comes from \(18.5 \times 12 - 18.5 \times 10\) so the \(2 \times 18.5\) is \((12 - 10) \times 18.5\)