plc papers - king's lynn...

PLC Papers

Created For:

PiXL PLC 2017 Certification

Frequency Trees 2 Grade 3

Objective: 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)


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)


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


Probability of equally likely outcomes 2 Grade 3

Objective: 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)


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


Charts & Diagrams 2 Grade 3

Objective: 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)


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 / 10


Pie charts 2 Grade 3

Objective: 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 Angle in pie chart

red 10

green 5

yellow 6

orange 9

Complete the pie chart to show this information.

(4)


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


(3)


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


Types of Data 2 Grade 3

Objective: 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.

(5) Total / 10

Qualitative or Quantitative Continuous or Discrete Name of favourite book. Shoe Size Heights of Girls in your maths class


Vertical Line Charts 2 Grade 3

Objective: 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)


Question 2.

The table below shows how many languages pupils in 9A can speak.

Number of Languages Frequency 1 21 2 8 3 1

Draw a vertical line chart to represent this data.

(4)

Total / 10

PLC Papers

Created For:


Frequency Trees 2 Grade 3 SOLUTIONS

Objective: 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.

All correct outcomes completed M2 Award M1 if at least 3 are correct.

(2)

(b) A pupil is chosen at random. What is the probability that the pupil is a female from Z band?

45250 =

950 A1

..............................................

(1)

(Total 3 marks)

250

140

110

80

60

65

45


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.

.

All correct outcomes completed M2

Award M1 if at least 3 are correct. (2)

(b) A member is chosen at random. What is the probability that they are aged under 12?

43100 A1

..............................................

(1)

(c) A girl is chosen at random. What is the probability that she is aged over 15?

2652 =

12 A1

..............................................

(1)

(Total 4 marks)

100

48

52

17

31

26

26


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.

.

All correct outcomes completed M2

Award M1 if at least 3 are correct. (2)

(b) Work out the probability of a pupil chosen at random being a male who fails the test.

1178 A1

..............................................

(1)

(Total 3 marks)

78

43

35

32

11

27

8


Total /10


Probability of equally likely outcomes 2 Grade 3 SOLUTIONS

Objective: 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 = 530 =

16 M1 for �30 where n < 30

A1 for 530 oe

..............................................

(2) (ii) banana or apple.

Probability of banana or apple = 1930 M1 for

(8+11)30

A1 for 1930

..............................................

(2) (Total: 5 marks)


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 = 38 M1 for

�8 or 3�

A1 for 38

..............................................

(2)

(b) Write down the probability that the pencil will not be a green pencil.

Probability of pencil not green = 78 M1 for

3+48 or 1 - 18

A1 for

78

.............................................

(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


Charts & Diagrams 2 Grade 3 SOLUTIONS

Objective: 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.

Axes labelled 1M

Suitable scales drawn 1M

Bars correctly drawn 2M

(1M if at least 3 bars drawn correctly)

(4)

10

0

20

f

0 2 1 3 Number of goals 5 4


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 / 10


Pie charts 2 Grade 3 SOLUTIONS

Objective: 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 Angle in pie chart

red 10 1030 x 360° = 120°

green 5 530 x 360° = 60°

yellow 6 630 x 360° = 72°

orange 9 930 x 360° = 108°


(4)

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


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 �� x 360° = 90°

Action 12 �� x 360° = 108°

Horror 18 �� x 360° = 162°


(3)

M1 for pie chart with at least 1

correct angle drawn or

calculated

A1 for correct pie chart

A1 for correct labels


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


Types of Data 2 Grade 3 SOLUTIONS

Objective: 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.

(5) Total / 10

Qualitative or Quantitative Continuous or Discrete Name of favourite book. Qualitative B1 Shoe Size Quantitative B1 Discrete B1 Heights of Girls in your maths class Quantitative B1 Continuous B1


Vertical Line Charts 2 Grade 3 SOLUTIONS

Objective: 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)143 =

352143 2M

= 2.46 1M

(3)


Question 2.

The table below shows how many languages pupils in 9A can speak.

Number of Languages Frequency 1 21 2 8 3 1

Draw a vertical line chart to represent this data.

Graph will depend on pupils scale. Axis labelled correctly 1M Vertical Lines drawn 1M

Lines all correct height 1M Appropriate Title given to chart 1M

(4)

Total / 10

0

5

10

15

20

25

1 2 3

Fre

qu

en

cy

Number of Pieces of Languages Spoken

Number of Languages spoken by pupils in 9A.

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