PLC Papers
Created For:
Frequency Trees 2
Objective:
Grade 3
Record, describe and analyse the frequency of outcomes of probability experiments
using tables and frequency trees (probabilities as fractions, decimals or percentages)
Question 1.
Year 9 has 250 students.
There are 2 bands in Year 9: X band and Z band.
There are 140 pupils in X band, of these 80 are female.
There are 65 males in Z band.
(a) Complete the frequency tree.
(2)
(b) A pupil is chosen at random.
What is the probability that the pupil is a female from Z band?
..............................................
(1)
(Total 3 marks)
PiXL PLC 2017 Certification
Question 2.
There are 100 members of a swimming club.
48 of the members are male.
17 of the male members are under 12, the rest are over 15.
26 of the female members are under 12, the rest are over 15
(a) Use this information to complete the frequency tree.
.
(2)
(b) A member is chosen at random.
What is the probability that they are aged under 12?
..............................................
(1)
(c) A girl is chosen at random.
What is the probability that she is aged over 15?
..............................................
(1)
(Total 4 marks)
PiXL PLC 2017 Certification
Question 3.
78 people sat their driving test.
43 are male, out of these 32 pass.
8 females fail their driving test
(a) Use this information to complete the frequency tree.
(2)
(b) Work out the probability of a pupil chosen at random being a male who fails the test.
..............................................
(1)
(Total 3 marks)
Total /10
PiXL PLC 2017 Certification
Probability of equally likely outcomes 2
Objective:
Grade 3
To calculate the probability using equally likely outcomes.
Question 1.
Sara buys cartons of different flavoured yoghurts.
She buys 5 peach yoghurts, 6 strawberry yoghurts, 8 banana yoghurts and 11 apple yoghurts.
Sara takes one of these 30 yoghurts at random.
(a) Find the probability that the flavour of the yoghurt she takes is apricot.
..............................................
(1)
(b) Find the probability that the flavour of the yoghurt she takes is
(i) peach,
..............................................
(2)
(ii) banana or apple.
..............................................
(2)
(Total: 5 marks)
PiXL PLC 2017 Certification
Question 2
In a pencil case there are 8 coloured pencils.
There are:
3 red pencils
4 blue pencils
1 green pencil.
Sonya takes a pencil at random from the pencil case.
(a) Write down the probability that the pencil will be a red pencil.
..............................................
(2)
(b) Write down the probability that the pencil will not be a green pencil.
..............................................
(2)
(c) Write down the probability that the pencil will be a yellow pencil.
..............................................
(1)
(Total 5 marks)
Total /10
PiXL PLC 2017 Certification
Charts & Diagrams 2
Objective:
Grade 3
Interpret and construct charts and diagrams (including bar charts, pictograms and
frequency diagrams) for categorical data
Question 1
The football matches for a league were played on Sunday.
The table shows the number of goals scored in each match.
Number of goals
Frequency
0
18
1
23
2
15
3
11
4
7
5
2
Use the grid below to draw a Bar Chart to display the information.
(4)
PiXL PLC 2017 Certification
Question 2
Brandon asked pupils in his year group to vote for their favourite author.
The votes for the top five are shown in the pictogram.
Author
Votes
Cabot
16
Horowitz
10
Pratchett
12
Pulman
Rowling
8
Key:
represents ……………………………. votes
(a) Complete the pictogram by filling in the key and the three spaces in the diagram
(4)
(b) How many people did Brandon ask?
(2)
Total
PiXL PLC 2017 Certification
/ 10
Pie charts 2
Objective:
Grade 3
To be able to construct and interpret pie charts
Question 1
There are 30 sweets in a tube.
Each sweet is red or green or yellow or orange.
The table gives information about the number of sweets of each colour in the tube.
Colour
Number of sweets
red
10
green
5
yellow
6
orange
9
Angle in pie chart
Complete the pie chart to show this information.
(4)
PiXL PLC 2017 Certification
Question 2
Gavin carried out a survey of 40 people to find out the type of film they like the best.
The table gives his results.
Type of film
Number of people
Comedy
10
Action
12
Horror
18
Complete the pie chart to show this information.
(3)
PiXL PLC 2017 Certification
Question 3
Harry asked each student in his class how they travelled to school that day.
He used the results to draw this pie chart.
(a) How did most of the students travel to school?
(1)
Harry asked a total of 24 students.
(b) Work out the number of students who cycled to school.
(2)
Total Mark /10
PiXL PLC 2017 Certification
Types of Data 2
Objective:
Grade 3
Be able to categorise different types of data, including primary, secondary, discrete,
continuous
Question 1.
What is meant by discrete data?
(1)
Question 2.
What is meant by primary and secondary data? Give an example of each.
.
(4)
Question 3.
For the following experiments/questions decide whether the data collected will be qualitative or quantitative.
Then where appropriate decide if the data is continuous or discrete.
Qualitative or Quantitative
Continuous or Discrete
Name of favourite book.
Shoe Size
Heights of Girls in your maths class
Total
PiXL PLC 2017 Certification
(5)
/ 10
Vertical Line Charts 2
Objective:
Grade 3
Interpret and construct vertical line charts for ungrouped discrete data.
Question 1.
The vertical line chart shows the number of pieces of homework pupils in Year 11 got set on Monday.
(a) How many students are there in Year 11?
(2)
(b) What is the range of this data?
(1)
(c) What is the mean number of pieces of homework set for Year 11?
(3)
PiXL PLC 2017 Certification
Question 2.
The table below shows how many languages pupils in 9A can speak.
Number of Languages
1
2
3
Frequency
21
8
1
Draw a vertical line chart to represent this data.
(4)
Total
PiXL PLC 2017 Certification
/ 10
PLC Papers
Created For:
Frequency Trees 2
Objective:
Grade 3
SOLUTIONS
Record, describe and analyse the frequency of outcomes of probability experiments
using tables and frequency trees (probabilities as fractions, decimals or percentages)
Question 1.
Year 9 has 250 students.
There are 2 bands in Year 9: X band and Z band.
There are 140 pupils in X band, of these 80 are female.
There are 65 males in Z band.
(a) Complete the frequency tree.
60
140
80
250
65
110
45
All correct outcomes completed
Award M1 if at least 3 are correct.
M2
(2)
(b) A pupil is chosen at random.
What is the probability that the pupil is a female from Z band?
45
250
=
9
50
A1
..............................................
(1)
(Total 3 marks)
PiXL PLC 2017 Certification
Question 2.
There are 100 members of a swimming club.
48 of the members are male.
17 of the male members are under 12, the rest are over 15.
26 of the female members are under 12, the rest are over 15
(a) Use this information to complete the frequency tree.
.
17
48
31
100
26
52
26
All correct outcomes completed
Award M1 if at least 3 are correct.
M2
(2)
(b) A member is chosen at random.
What is the probability that they are aged under 12?
43
A1
100
..............................................
(1)
(c) A girl is chosen at random.
What is the probability that she is aged over 15?
26
1
=
52
2
A1
..............................................
(1)
(Total 4 marks)
PiXL PLC 2017 Certification
Question 3.
78 people sat their driving test.
43 are male, out of these 32 pass.
8 females fail their driving test
(a) Use this information to complete the frequency tree.
.
32
43
11
78
27
35
8
All correct outcomes completed
Award M1 if at least 3 are correct.
M2
(2)
(b) Work out the probability of a pupil chosen at random being a male who fails the test.
11
78
A1
..............................................
(1)
(Total 3 marks)
PiXL PLC 2017 Certification
Total /10
PiXL PLC 2017 Certification
Probability of equally likely outcomes 2
Objective:
Grade 3
SOLUTIONS
To calculate the probability using equally likely outcomes.
Question 1.
Sara buys cartons of different flavoured yoghurts.
She buys 5 peach yoghurts, 6 strawberry yoghurts, 8 banana yoghurts and 11 apple yoghurts.
Sara takes one of these 30 yoghurts at random.
(a) Find the probability that the flavour of the yoghurt she takes is apricot.
Probability of apricot = 0 A1
..............................................
(1)
(b) Find the probability that the flavour of the yoghurt she takes is
(i) peach,
Probability of peach =
5
30
=
1
M1 for
6
A1 for
�
where n < 30
5
oe
30
30
..............................................
(2)
(ii) banana or apple.
Probability of banana or apple =
19
30
M1 for
A1 for
(8+11)
19
30
30
..............................................
(2)
(Total: 5 marks)
PiXL PLC 2017 Certification
Question 2
In a pencil case there are 8 coloured pencils.
There are:
3 red pencils
4 blue pencils
1 green pencil.
Sonya takes a pencil at random from the pencil case.
(a) Write down the probability that the pencil will be a red pencil.
Probability of red pencil =
3
�
M1 for or
8
8
A1 for
3
�
3
8
..............................................
(2)
(b) Write down the probability that the pencil will not be a green pencil.
Probability of pencil not green =
7
8
M1 for
3+4
A1 for
7
8
or 1 -
1
8
8
.............................................
(2)
(c) Write down the probability that the pencil will be a yellow pencil.
Probability of yellow pencil = 0 A1
..............................................
(1)
(Total 5 marks)
Total /10
PiXL PLC 2017 Certification
Charts & Diagrams 2
Objective:
Grade 3
SOLUTIONS
Interpret and construct charts and diagrams (including bar charts, pictograms and
frequency diagrams) for categorical data
Question 1
The football matches for a league were played on Sunday.
The table shows the number of goals scored in each match.
Number of goals
Frequency
0
18
1
23
2
15
3
11
4
7
5
2
Use the grid below to draw a Bar Chart to display the information.
f
20
10
0
0
Axes labelled
Suitable scales drawn
Bars correctly drawn
(1M if at least 3 bars drawn correctly)
1
2
3
4
5
Number of goals
1M
1M
2M
(4)
PiXL PLC 2017 Certification
Question 2
Brandon asked pupils in his year group to vote for their favourite author.
The votes for the top five are shown in the pictogram.
Author
Votes
Cabot
16
Horowitz
10
Pratchett
12
Pulman
9
Rowling
8
Key
represents ……………5………………. votes
(a) Complete the pictogram by filling in the key and the three spaces in the diagram.
See above
(4)
(b) How many people did Brandon ask?
55
(2)
Total
PiXL PLC 2017 Certification
/ 10
Pie charts 2
Objective:
Grade 3
SOLUTIONS
Interpret and construct pie charts for categorical data
Question 1
There are 30 sweets in a tube.
Each sweet is red or green or yellow or orange.
The table gives information about the number of sweets of each colour in the tube.
Colour
Number of sweets
red
10
green
5
yellow
6
orange
9
Complete the pie chart to show this information.
Angle in pie chart
10
30
x 360° = 120°
5
x 360° = 60°
6
x 360° = 72°
30
30
9
30
x 360° = 108°
M1 for at least 2 correct angles
(may be implied from pie chart)
M1 for at least 3 correct angles
A1 for correct pie chart
B1 for correct labels
(4)
PiXL PLC 2017 Certification
Question 2
Gavin carried out a survey of 40 people to find out the type of film they like the best.
The table gives his results.
Type of film
Number of people
Comedy
10
Action
12
��
x 360° = 108°
Horror
18
��
x 360° = 162°
��
��
��
��
x 360° = 90°
Complete the pie chart to show this information.
M1 for pie chart with at least 1
correct angle drawn or
calculated
A1 for correct pie chart
A1 for correct labels
(3)
PiXL PLC 2017 Certification
Question 3
Harry asked each student in his class how they travelled to school that day.
He used the results to draw this pie chart.
(a) How did most of the students travel to school?
Walk
B1
(1)
Harry asked a total of 24 students.
(b) Work out the number of students who cycled to school.
¼ of 24 = 6 students
M1 for 24 ÷ 4 oe A1 for 6
(2)
Total Mark /10
PiXL PLC 2017 Certification
Types of Data 2
Objective:
Grade 3
SOLUTIONS
Be able to categorise different types of data, including primary, secondary, discrete,
continuous
Question 1.
What is meant by discrete data?
Discrete data is data that falls in to categories/set values. E.g. Shoe Size.
(1)
Question 2.
What is meant by primary and secondary data? Give an example of each.
Primary data is data you collect yourself – e.g. asking people in your class their favourite colour B1B1
Secondary data is data that you have used from someone else – e.g. getting the internet usage of the UK
from an internet provider.
B1B1
.
(4)
Question 3.
For the following experiments/questions decide whether the data collected will be qualitative or quantitative.
Then where appropriate decide if the data is continuous or discrete.
Name of favourite book.
Shoe Size
Heights of Girls in your maths class
Qualitative or Quantitative
Qualitative B1
Quantitative B1
Quantitative B1
Continuous or Discrete
Discrete B1
Continuous B1
Total
PiXL PLC 2017 Certification
(5)
/ 10
Vertical Line Charts 2
Objective:
Grade 3
SOLUTIONS
Interpret and construct vertical line charts for ungrouped discrete data.
Question 1.
The vertical line chart shows the number of pieces of homework pupils in Year 11 got set on Monday.
(a) How many students are there in Year 11?
6 + 29 + 36 + 42 + 25 + 5 = 143
2M
(1M for at least three numbers correct in the sum)
(2)
(b) What is the range of this data?
5–0=5
1M
(1)
(c) What is the mean number of pieces of homework set for Year 11 (to 2 decimal places)?
(0×6)+(1×29)+(2×36)+(3×42)+(4×25)+(5×5)
= 2.46
143
=
352
143
2M
1M
(3)
PiXL PLC 2017 Certification
Question 2.
The table below shows how many languages pupils in 9A can speak.
Number of Languages
1
2
3
Frequency
21
8
1
Draw a vertical line chart to represent this data.
Number of Languages spoken by pupils in 9A.
25
Frequency
20
15
10
5
0
1
2
3
Number of Pieces of Languages Spoken
Graph will depend on pupils scale.
Axis labelled correctly
Vertical Lines drawn
Lines all correct height
Appropriate Title given to chart
1M
1M
1M
1M
(4)
Total
PiXL PLC 2017 Certification
/ 10