1. [4]
the sum of the numbers you throw. It is your turn, you need to score exactly 4 to
dice your score is the number you throw. If you throw two dice your score is
In a game you can choose to throw one dice or two dice. If you throw one
win. Should you choose to throw one dice or two dice?
A spinner has 3 unequal sectors, each to be painted a different colour: red, green or yellow. The probability that the spinner lands on green is 1/10. The probability that the spinner lands on yellow is twice the probability that the spinner lands on red. Calculate the angle of the yellow sector.
A group of men were asked what colour car they own. The pie chart shows the results. If 60 own a silver car, work out the number
of men who own a blue or red car.
120 women were also asked what colour car they own. The results are shown in the table. Draw and label a pie chart showing this information.
10 boys and 10 girls are each given 20 mental arithmetic questions. Here are the number of correct
answers for each boy          18         12         19         9          20        11        9        18       12
    For the girls’ scores, the range is 12 and the mean is Investigate the hypothesis,
‘Boys are better at mental arithmetic than girls’
A tutor records the number of times her students were late during a term. She shows the data for those who were late in a stem and leaf diagram. 17 students were never late. Calculate the mean number of
times students were late for the whole form.
Each of the numbers 1, 2, 3, and 4 must occur at least once on the spinner.
Write one of the numbers in each of the six sections so that on each spin the;
-probability of getting a 1 is equal to the probability of getting a 2.
-probability of getting a 3 is greater than the probability of getting a 1.
-probability of getting a 4 is less than the probability of getting a 3.
A bag contains only red, blue, white, and black counters. The number of white is the same as the number of black. The table shows the probability of a red or blue counter being
chosen at random. The bag contains 240 counters. Work out how many white counters
there are in the bag.
The second set of four discs are labelled 2, 4, 6, 8.  Players turn over one disc, at random, from each set and
Ronan designs a game. He has two sets of discs. The first set of 5 discs are labelled 1, 3, 5, 7, 9.
add the numbers. Ronan uses the game to raise money for charity. Each player pays 20 p to play the
game. They win a chocolate bar if they score exactly13. It costs Ronan 50 p for each bar of chocolate.
If 100 people play the game, show that Ronan should expect to raise £12.50 for charity. (5 marks)
Data and Probability – Drawing & interpreting pie charts, Drawing bar charts, Estimating mean from grouped data, Averages, Probability - Sum to 1, Listing outcomes…
The pie chart shows the ways that 30 pupils travel to school. On the grid below, draw and label a bar chart to represent the same information.
Seb investigates whether members of an athletics club perform better than
non-members in a 10 km race. The table summarises the finishing times of the
members. Calculate an estimate of the mean finishing time of the members.
The pie charts show the age distribution in two villages A and B. There are 1320 people under 65 in village A. There is a third more people in village B than village A. Which village has the most over 65?
Bus
Car
Walk
Bike
96o
120o
72o
Village A                  Village B

2. [4]
1/10 x 360o (= 36o) B1
2 parts, one twice the other M1
2/3 x 324o oe way to split into
360o - 36o (= 324o) B1
216o A1
3o = 1 car M1
45 ÷ 3 (= 15) blue M1
30 ÷ 3 (= 10) red M1 A1
P(4 with one dice) 1/6 B1
List of combinations that score 4 on 2 dice (1,3), (2,2), (3,1) M1
P(4 with two dice) 3/36 or 1/12 A1
One dice, as 1/6 > 1/12 A1 ft
One correct sector eg 360 ÷ 120 x 42o oe M1
4 or 5 correct 126o , 105o , 75o , 30o , 24o A1
All 5 angles drawn correctly ±2o A1
All 5 sectors correctly labelled B1
the sum of the numbers you throw. It is your turn, you need to score exactly 4 to
dice your score is the number you throw. If you throw two dice your score is
In a game you can choose to throw one dice or two dice. If you throw one
win. Should you choose to throw one dice or two dice?
A spinner has 3 unequal sectors, each to be painted a different colour: red, green or yellow. The probability that the spinner lands on green is 1/10. The probability that the spinner lands on yellow is twice the probability that the spinner lands on red. Calculate the angle of the yellow sector.
The pie chart shows the results. If 60 own a silver car, work
A group of men were asked what colour car they own.
out the number of men who own a blue or red car.
120 women were also asked what colour car they own. The results are shown in the table. Draw and label a pie chart showing this information.
10 boys and 10 girls are each given 20 mental arithmetic questions. Here are the number of correct
answers for each boy          18         12         19         9          20        11        9        18       12
    For the girls’ scores, the range is 12 and the mean is Investigate the hypothesis ,‘
Boys are better at mental arithmetic than girls’
A tutor records the number of times her students were late during a term. She shows the data for those who were late in a stem and leaf diagram. 17 students were never late.
Calculate the mean number of times students were late for the whole form.
Boys range = 11 B1
Σboys scores = 140 (Mean =) 14 A1
Conclusion using data comparing mean and range
eg, girls are better as mean higher and range about same
There is no difference as means and ranges about the same
Q1 partial conclusion or lack of clarity Q2
Attempt to add at least 12 correct
values from Stem and Leaf M1
270    A1
‘their 270’ ÷ 30 Must divide by M1 dep
9        A1
Each of the numbers 1, 2, 3, and 4 must occur at least once on the spinner.
Write one of the numbers in each of the six sections so that on each spin the;
-probability of getting a 1 is equal to the probability of getting a 2.
-probability of getting a 3 is greater than the probability of getting a 1.
-probability of getting a 4 is less than the probability of getting a 3.
A bag contains only red, blue, white, and black counters. The number of white is the same as the number of black. The table shows the probability of a red or blue counter being chosen at random. The bag contains 240 counters. Work out how many white counters
there are in the bag.
1,2,3,3,3,4
One each of 1 and 2 B1
Three 3s B2
One 4 B1
2 blank sections B0
1 – 0.2 – 0.5 (= 0.3) M1
0.3 ÷ 2 (=0.15) M1
0.15 x 240    M1 A1
The second set of four discs are labelled 2, 4, 6, 8.  Players turn over one disc, at random, from each set and
Ronan designs a game. He has two sets of discs. The first set of 5 discs are labelled 1, 3, 5, 7, 9.
add the numbers. Ronan uses the game to raise money for charity. Each player pays 20 p to play the
game. They win a chocolate bar if they score exactly13. It costs Ronan 50 p for each bar of chocolate.
If 100 people play the game, show that Ronan should expect to raise £12.50 for charity. (5 marks)
Data and Probability – Drawing & interpreting pie charts, Drawing bar charts, Estimating mean from grouped data, Averages, Probability - Sum to 1, Listing outcomes…
The pie chart shows the ways that 30 pupils travel to school. On the grid below, draw and label a bar chart to represent the same information.
Bus
Car
Walk
Bike
96o
120o
72o
Fully correct bar chart B4
Walk (10), Bus (8), Car (6) and Bike (6)
Labelled frequency axis Scale on frequency axis
Equal width bars correctly labelled
Condone no gaps between bars Condone lines
Seb investigates whether members of an athletics club perform better than
non-members in a 10 km race. The table summarises the finishing times of the
members. Calculate an estimate of the mean finishing time of the members.
The pie charts show the age distribution in two villages A and B. There are 1320 people under 65 in village A. There is a third more people in village B than village A. Which village has the most over 65?
P(13) = 3/20 so 15 winners in 100 plays B2
(Chocolate costs) 15 x 0.50 = £7.50 B1
(Takings) 100 × 0.20 (= £20) B1
(Profit) £20 – £7.50 (= £12.50) B1
10 × their 35 (=350) 12 × their 45 ( = 540)
6 × their 55 (= 330) 2 × their 65 (= 130) M1
Their 1350 ÷ 30 (30 must be correct) M1dep
Sight of midpoint B1
One correct product eg,
45 A1
Over 65 village B (their) 2640 ÷ 4 (= 660) M1
Overall village B 660 x 4 (= 2640) M1
Over 65 village A ÷ 2 (= 660) M1
Both the same A1
Village A                  Village B

3. 1 o’clock 3o = 1 car M1 45 ÷ 3 (= 15) blue M1 30 ÷ 3 (= 10) red M1
A group of men were asked what colour car they own.
The pie chart shows the results. If 60 own a silver car, work out the number of men who own a blue or red car.
3o = 1 car M1
45 ÷ 3 (= 15) blue M1
30 ÷ 3 (= 10) red M1 A1

4. 2 o’clock
120 women were also asked what colour car they own. The results are shown in the table. Draw and label a pie chart showing this information.
Angle
126o
105o
75o
30o
24o
One correct sector eg 360 ÷ 120 x 42o oe M1
4 or 5 correct 126o , 105o , 75o , 30o , 24o A1
All 5 angles drawn correctly ±2o A1
All 5 sectors correctly labelled B1

5. 3 o’clock
A tutor records the number of times her students were late during a term. She shows the data for those who were late in a stem and leaf diagram. 17 students were never late. Calculate the mean number of times students were late for the whole form.
Attempt to add at least 12 values from Stem and Leaf M1
270    A1
‘their 270’ ÷ 30 Must divide by M1 dep
9        A1

6. 4 o’clock 1 – 0.2 – 0.5 (= 0.3) M1 0.3 ÷ 2 (=0.15) M1 0.15 x 240 M1
A bag contains only red, blue, white, and black counters. The number of white is the same as the number of black. The table shows the probability of a red or blue counter being chosen at random. The bag contains 240 counters. Work out how many white counters there are in the bag.
0.15
1 – 0.2 – 0.5 (= 0.3) M1
0.3 ÷ 2 (=0.15) M1
0.15 x 240    M1 A1

7. 5 o’clock
The pie chart shows the ways that 30 pupils travel to school. On the grid below, draw and label a bar chart to represent the same information. 10 8 6 4 2
Walk
Bus
Car
Bus
Car
Walk
Bike
96o
120o
72o
Fully correct bar chart B4
Walk (10), Bus (8), Car (6) and Bike (6)
Labelled frequency axis Scale on frequency axis
Equal width bars correctly labelled
Condone no gaps between bars Condone lines

8. 6 o’clock Over 65 village A 1320 ÷ 2 (= 660) M1
The pie charts show the age distribution in two villages A and B. There are 1320 people under 65 in village A. There is a third more people in village B than village A. Which village has the most over 65?
Over 65 village A ÷ 2 (= 660) M1
Overall village B 660 x 4 (= 2640) M1
Over 65 village B (their) 2640 ÷ 4 (= 660) M1
Both the same A1

9. 7 o’clock Sight of midpoint B1 One correct product eg,
Seb investigates whether members of an athletics club perform better than non-members in a 10 km race. The table summarises the finishing times of the members. Calculate an estimate of the mean finishing time of the members.
Mid 35 45 55 65
Fxm
350
540
330
130
1350
Sight of midpoint B1
One correct product eg,
10 × their 35 (=350) 12 × their 45 ( = 540)
6 × their 55 (= 330) 2 × their 65 (= 130) M1
Their 1350 ÷ 30 (30 must be correct) M1dep
45 A1 30

10. 8 o’clock P(13) = 3/20 so 15 winners in 100 plays B2
Ronan designs a game. He has two sets of discs. The first set of 5 discs are labelled 1, 3, 5, 7, 9. The second set of four discs are labelled 2, 4, 6, 8.  Players turn over one disc, at random, from each set and add the numbers. Ronan uses the game to raise money for charity. Each player pays 20 p to play the game. They win a chocolate bar if they score exactly13. It costs Ronan 50 p for each bar of chocolate. If 100 people play the game, show that Ronan should expect to raise £12.50 for charity. (5 marks)
P(13) = 3/20 so 15 winners in 100 plays B2
(Chocolate costs) 15 x 0.50 = £ B1
(Takings) 100 × 0.20 (= £20) B1
(Profit) £20 – £7.50 (= £12.50) B1

11. 9 o’clock 1 One each of 1 and 2 B1 4 2 Three 3s B2 One 4 B1
Each of the numbers 1, 2, 3, and 4 must occur at least once on the spinner.
Write one of the numbers in each of the six sections so that on each spin the;
-probability of getting a 1 is equal to the probability of getting a 2.
-probability of getting a 3 is greater than the probability of getting a 1.
-probability of getting a 4 is less than the probability of getting a 3. 1
One each of 1 and 2 B1
Three 3s B2
One 4 B1
2 blank sections B0 4 2 3 3 3

12. 10 o’clock Boys range = 11 B1 Σboys scores = 140 (Mean =) 14 A1
10 boys and 10 girls are each given 20 mental arithmetic questions. Here are the number of correct answers for each boy.
12     18     12     19     9     20    11    9    18   12
For the girls’ scores, the range is 12 and the mean is Investigate the hypothesis ,
‘Boys are better at mental arithmetic than girls’
Boys range = 11 B1
Σboys scores = 140 (Mean =) 14 A1
Conclusion using data comparing mean and range
eg, girls are better as mean higher and range about same
There is no difference as means and ranges about the same. Q1 partial conclusion or lack of clarity Q2

13. 11 o’clock P(4 with one dice) 1/6 B1
In a game you can choose to throw one dice or two dice. If you throw one dice your score is the number you throw. If you throw two dice your score is the sum of the numbers you throw. It is your turn, you need to score exactly 4 to win. Should you choose to throw one dice or two dice?
P(4 with one dice) 1/6 B1
List of combinations that score 4 on 2 dice (1,3), (2,2), (3,1) M1
P(4 with two dice) 3/36 or 1/12 A1
One dice, as 1/6 > 1/ A1 ft

14. 12 o’clock 1/10 x 360o (= 36o) B1 360o - 36o (= 324o) B1
A spinner has 3 unequal sectors, each
to be painted a different colour:
red, green or yellow. The probability
that the spinner lands on green is 1/10.
The probability that the spinner lands on yellow is twice the probability that the spinner lands on red. Calculate the angle of the yellow sector.
1/10 x 360o (= 36o) B1
360o - 36o (= 324o) B1
2/3 x 324o oe way to split into
2 parts, one twice the other M1
216o A1