Foundation November 2021 Paper 2 Q12

AQACurrent spec6 marksTree Diagrams

12 A sports team played 40 games.

Half were home games and half were away games.

Each game was a win, a draw or a loss.

Of the home games, \(\dfrac{2}{5}\) were losses.

Of the away games, \(\dfrac{1}{10}\) were wins.

(a) Complete the frequency tree. [4 marks]

(b) The team gets

6 points for a win
3 points for a draw
0 points for a loss.

Work out the total number of points that the team got. [2 marks]

Mark scheme (a)

Answer	Mark	Comments
20 home and 20 away	B1
8 home losses	B1ft	ft their \(20 \times \dfrac{2}{5}\) rounded to the nearest whole number
2 away wins	B1ft	ft their \(20 \times \dfrac{1}{10}\) rounded to the nearest whole number
5 home draws and 6 away draws	B1ft	ft their 8 and their 2 condone their 8 and their 2 as zero or non-integers award if total of home games is their 20 and total of away games is their 20 and total number of games is 40

Mark the cells in the frequency tree

Mark scheme (b)

Answer	Mark	Comments
Any two of (home wins =) \(7 \times 6\) or 42 or (home draws =) their \(5 \times 3\) or 15 or (away wins =) their \(2 \times 6\) or 12 or (away draws =) their \(6 \times 3\) or 18	M1	may be implied by one of (total points for their wins) 54 or (total points for their draws) 33 or (total points for their home) 57 or (total points for their away) 30
87	A1ft	ft their frequency tree with positive integers in all relevant sections

Using non-integers

M0A0