10 steps to Success!
A PiXL 10-session Booster Resource for early entry Linear GCSE
Contents
1. Displaying Data / Sampling / Scatter Graphs
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•
•
•
•
•
•
•
•
Construct a stem-and-leaf diagram (ordered)
Bar Chart
Pie Chart
Frequency polygon
Classify and know the difference between various types of data
Design and use data collection sheets and questionnaires
Identify possible sources of bias
Draw a scatter graph by plotting points on a graph
Interpret the scatter graph (positive and negative correlation)
•
Draw a line of best fit on the scatter graph by inspection
2. Averages / Probability
•
•
•
•
•
•
Calculate the mean, mode and median for small data sets
Calculate the mean for a frequency distribution
Find the mean for grouped data
Find the modal class for grouped data
Understand that probabilities must be written as fractions, decimals or percentages
Use the fact that the probabilities of mutually exclusive events add up to 1
•
Use a two-way table to find a probability
3. Transformations / co-ordinates
•
•
•
•
•
Reflect simple shapes using a mirror line
Identify reflection symmetry in 3-D solids
Rotate shapes about any point
Translate a shape using a description such as 4 units right and 4 units down
Enlarge a shape by a positive scale factor from a given centre
•
•
Find the coordinates of the midpoint of the line segment AB, given the points A and B
Plot points in all 4 quadrants
4. 2D/3D Shapes
•
•
•
•
•
•
•
Jim King
Know the name of standard 3D shapes
Calculate volumes of triangular prisms, parallelogram-based prisms and cylinders
Calculate surface areas of prisms and cylinders
Find the area of a triangle ,parallelogram and trapezium
Find the area and perimeter of compound shapes
Construct and recognise the nets of 3-D solids such as pyramids and triangular prisms
Draw plans and elevations of 3-D solids
Page 1
5. Indices / Factors & Multiples / Bodmas
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•
•
•
•
•
•
Find the least common multiple (LCM) of two simple numbers
Find the highest common factor (HCF) of two simple numbers
Write a number as a product of prime factors
Use index notation and index laws for positive and negative powers
Square, positive and negative square root, cube and cube root
Using a calculator
BODMAS
6. Formulae / Equations
•
•
•
•
•
•
Substitute numbers into formulae and expressions
Rearrange linear formulae such as s = 4q - 7
Use formulae expressed in words
Solve linear equations with unknowns on each side such as 3x – 4 = 5 + x
Solve linear equations with brackets such as 2(5x + 1) = 28
Solve more complex linear equations such as 3x – 12 = 2(x – 5)
7. Fractions & Decimals / Sequences
•
•
•
•
•
•
•
•
•
•
Simple fractions involving multiplication and division
Simple fractions involving addition and subtraction
Order fractions
Find the reciprocal of a number
Understand the effects of multiplying and dividing by numbers between 0 and 1
Order decimals
Convert decimals to fractions and percentages and percentages & fractions to decimals
Write the terms of a sequence or a series of diagrams given the nth term
Generate terms of a sequence using term-to-term methods
Write the nth term of a sequence or a series of diagrams
8. Basic arithmetic / Simplify & Expand
•
•
•
Use of Basic Arithmetic in the context of a bill
Reading number lines and scales
Reading timetables
•
•
•
Multiply out brackets expressions with brackets such as 5(3x-2)
Collecting like terms
Factorise expressions
9. Angles / Travel Graphs
•
•
Alternate& corresponding angles
Angle properties of triangles and quadrilaterals
•
•
•
Distance / time graphs
Calculate complex average speeds from distance-time graphs
Travel graphs
10.Percentages / Ratio
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•
•
•
•
•
Work out a percentage of a quantity
Work out a percentage increase or decrease
Express one quantity as a percentage of another
Increase or decrease a quantity by a given percentage
Divide a quantity in a given ratio
Solve word problems involving ratio and proportion
Jim King
Page 2
Session 1
Displaying Data / Sampling / Scatter Graphs
Displaying Data
Content
•
•
•
•
Construct a stem-and-leaf diagram (ordered)
Bar Chart
Pie Chart
Frequency polygon
Question 1
Emma asks her friends what type of TV programme they like best.
(a)
Type of TV programme
Frequency
Cartoons
4
Drama
2
Quizzes
1
Soaps
6
Draw a bar chart to show Emma’s results.
7
6
5
Frequency
4
3
2
1
0
Cartoons
Drama
Quizzes
Soaps
(2)
(b)
Emma chooses one of her friends at random. What is the probability that this friend
chose cartoons?
Answer .............................................
(3)
(Total 5 marks)
Jim King
Page 3
Question 2
The stem and leaf diagram shows the ages, in years, of 15 members of a badminton club.
Key:
(a)
7
2
2
7
8
3
0
2
4
8
4
1
2
3
3
5
3
6
6
2
means an age of 27 years
4
6
How many members are aged over 40?
Answer ...........................................................
(1)
(b)
What is the median age of the members?
Answer ................................................... years
(1)
(Total 2 marks)
Question 3
A school entered 144 pupils for GCSE Mathematics as shown in the table.
Tier
Number of pupils
Foundation
46
Intermediate
70
Higher
28
Complete the pie chart for the school GCSE Mathematics entry.
Label each sector clearly.
(Total 3 marks)
Total Mark / 10
Jim King
Page 4
Sampling
Content
•
•
•
Classify and know the difference between various types of data
Design and use data collection sheets and questionnaires
Identify possible sources of bias in the design and use of data collection sheets & questionnaires
Question 1
A survey is to be carried out to investigate the shopping habits of the population of a town.
(a)
Give two reasons why the survey should not be carried out between 9am and 5pm on a
Wednesday.
Reason 1 .....................................................................................................................
.....................................................................................................................................
Reason 2 .....................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
Write two suitable questions that could be asked in the survey.
Question 1 ..................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Question 2 ..................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 4 marks)
Jim King
Page 5
Question 2
Chandni wants to survey pupils in her school about their reading habits.
(a)
Write a question that would help Chandni to investigate how often pupils in her school read for
pleasure.
Include a response section.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(2)
(b)
There are 1000 pupils in Chandni’s school.
Chandni samples 50 pupils at random and asks them to complete her survey.
She finds that 16 of the pupils in the sample read comics.
Estimate the number of pupils in the school who read comics.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer ............................................................
(2)
(Total 4 marks)
Jim King
Page 6
Question 3
Mandip is doing a survey on “Healthy Eating” in the town where he lives.
(a)
One of the questions he asks is
“Do you eat fruit or sweets?”
Explain why this is a poorly worded question.
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
There are 2000 people in the town where Mandip lives.
He interviews 15 people for his survey.
Explain why his survey may not be representative of the people in the town.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 2 marks)
Total Mark / 10
Jim King
Page 7
Scatter Graphs 1
Content
•
•
•
Draw a scatter graph by plotting points on a graph
Interpret the scatter graph (positive and negative correlation)
Draw a line of best fit on the scatter graph by inspection
Question 1
The scatter graph shows the number of ice creams sold plotted against the midday temperature.
200
180
160
140
Number of
ice creams 120
sold
100
80
60
40
20
0
50
(a)
52
54
56
58
60
62
64
Midday temperature (ºF)
66
68
70
Draw a line of best fit on the scatter graph.
(1)
(b)
Describe the relationship between the number of ice creams sold and the midday temperature.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 2 marks)
Jim King
Page 8
Question 2
Mrs Millington gives her class two mock GCSE examination papers. The scatter graph shows the results.
100
80
60
Paper 2 mark
40
20
0
0
(a)
20
40
60
Paper 1 mark
80
100
Write down the highest mark scored on Paper 2.
Answer ...................................................... marks
(1)
(b)
Describe the relationship shown on the scatter graph.
.......................................................................................................................................
.......................................................................................................................................
.......................................................................................................................................
(1)
(c)
Draw a line of best fit on the scatter graph.
(1)
(d)
Kay was absent for Paper 2, but scored a mark of 56 on Paper 1.
Use your line of best fit to estimate Kay’s mark on Paper 2.
.......................................................................................................................................
Answer ...................................................... marks
(1)
(Total 4 marks)
Jim King
Page 9
Question 3
The scatter graph shows the number of petrol pumps and the number of cars queuing at midday at six
garages.
6
×
5
× ×
4
×
Number
of cars 3
queuing
×
×
2
1
0
0
(a)
1
2
5
3
4
6
Number of petrol pumps
7
8
9
State the type of correlation shown.
Answer ............................................
(1)
(b)
Use the scatter graph to estimate the number of cars queuing at a garage with
8 petrol pumps.
Answer ............................................
(1)
Jim King
Page 10
Question 4
Eight teenagers took part in a general knowledge quiz and a pop-music quiz.
The scatter graph shows their scores.
14
12
10
Score in
pop-music 8
quiz
6
4
2
0
0
(a)
2
4
6
8
10
12
14
Score in general knowledge quiz
16
18
20
Draw a line of best fit on the scatter graph.
(1)
(b)
Describe the relationship shown in the scatter graph.
Total Mark / 10
Jim King
Page 11
Session 2
Averages / Probability
Mean, mode, median 1
Content
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•
•
•
Calculate the mean, mode and median and range for small data sets
Calculate the mean from a frequency distribution.
Find the mean for grouped data
Find the modal class for grouped data
Question 1
The sizes of the first eleven pairs of shoes sold in a shop one morning are
8
(a)
5
4
5
7
10
9
5
11
5
6
What is the mode of the data?
......................................................................................................................................
Answer ..........................................................
(1)
(b)
What is the median shoe size?
......................................................................................................................................
Answer ..........................................................
(2)
(c)
Which of the mode or median would be more useful to the shopkeeper when he is ordering
more shoes?
Explain your answer.
......................................................................................................................................
......................................................................................................................................
(1)
(Total 4 marks)
Jim King
Page 12
Question 2
Sethina recorded the times, in minutes, taken to repair 80 car tyres.
Information about these times is shown in the table.
Time(tminutes)
Frequency
0<t≤6
15
6<t≤2
25
12 < t ≤ 18
20
18 < t ≤ 24
12
24 < t ≤ 30
8
Calculate an estimate for the mean time taken to repair each car tyre.
........................ minutes
(Total 4 marks)
Question 2
The following people work for the AQA Motor Company
Job
Wage per week (£)
(b)
Apprentice
200
Cleaner
200
Foreman
350
Manager
800
Mechanic
250
Parts Manager
520
Sales Manager
620
What is the median wage?
Answer £ .............................................................
(2)
Total Mark / 10
Jim King
Page 13
Simple Probability 1
Content
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•
•
•
•
•
Understand that probabilities must be written as fractions, decimals or percentages
Understand mutually exclusive events
Use the fact that the probabilities of mutually exclusive events add up to 1
Use a two-way table to find a probability
Understand relative frequency as an estimate of probability
Use relative frequency to compare outcomes of experiments
Question 1
In a raffle 200 tickets are sold.
There is only one prize.
Mr Key buys 10 tickets.
Mrs Key buys 6 tickets.
Their children, Robert and Rachel, buy 2 tickets each.
(a)
Which member of the family has the best chance of winning the prize?
Give a reason for your answer.
......................................................................................................................................
......................................................................................................................................
(1)
(b)
What is the probability that Mrs Key wins the prize?
......................................................................................................................................
Answer ...........................................................
(1)
(Total 2 marks)
Question 2
The probabilities of the following events have been marked on the probability scale below.
A: The next person to pass you will be less than 80 years old.
B: Tomorrow will be Sunday.
C: A fair three-sided spinner, coloured red, blue and green, will land on red.
0
1
Label each arrow with a letter to show which event it represents.
(Total 2 marks)
Jim King
Page 14
Question 3
The two-way table gives some information about how 100 children travelled to school one day.
Walk
Boy
15
8
Girl
Total
Car
37
Other
Total
14
54
16
100
100
(a) Complete the two-way table.
(3)
One of the children is picked at random.
(b) Write down the probability that this child walked to school that day.
.....................................
(1)
One of the girls is picked at random.
(c) Work out the probability that this girl did not walk to school that day.
.....................................
(2)
(Total 6 marks)
Total Mark / 10
Jim King
Page 15
Session 3
Transformations / Co-ordinates
Transformations 1
Content:
•
•
•
•
•
Reflect simple shapes using a mirror line
Identify reflection symmetry in 3-D solids
Rotate shapes about any point
Translate a shape using a description such as 4 units right and 4 units down
Enlarge a shape by a positive (inc fractional0 scale factor from a given centre
Question 1:
Jim King
Page 16
Question 2:
Jim King
Page 17
Question 3
On the grid, draw an enlargement, scale factor 2, of the shaded shape.
(2)
Jim King
Page 18
Question 4
(a)
Shade one more square to make a pattern with 1 line of symmetry.
(1)
(b) Shade one more square to make a pattern with rotational symmetry of order 2
(1)
(Total 2 marks)
Jim King
Page 19
Coordinates 1
Content
•
•
•
Find the coordinates of the midpoint of the line segment AB, given the points A and B
Plot points in all 4 quadrants
Understand coordinates in three dimensions
Question 1
The square PQRS is drawn on a centimetre square grid.
y
5
P
Q
4
3
2
1
S
R
0
0
1
2
3
5 x
4
The coordinates of P are (1, 5).
Write down the coordinates of Q, R and S.
Answer
Q ( ………… , ………… )
R ( ………… , ………… )
S ( ………… , ………… )
(3)
Question 2
Points A, B and C are three corners of a square ABCD. Write down the coordinates of A, B and C.
y
7
×C
6
5
4
×B
3
2
×
1
0
A (............... , .................)
A
0
1
2
3
4
5
B (............... , .................)
6
7 x
C (............... , .................)
(3)
Jim King
Page 20
Question 3
(a) Write down the coordinates of the point P.
(.......... , ..........)
(1)
(b) Write down the coordinates of the point Q.
(.......... , ..........)
(1)
M is the midpoint of the line from Q to P.
(c) Find the coordinates of M.
(.......... , ..........)
(2)
(Total 4 marks)
Total Mark / 10
Jim King
Page 21
Session 4
2D/3D Shapes
3D Shapes
Content:
•
•
•
•
•
Know the name of standard 3D shapes
Calculate volumes of triangular prisms, parallelogram-based prisms and cylinders
Calculate surface areas of prisms and cylinders
Construct and recognise the nets of 3-D solids such as pyramids and triangular prisms
Draw plans and elevations of 3-D solids
Q1:
Q2:
Here is a solid prism made of centimetre cubes.
Find the volume of the solid prism.
........................................ cm3
(3)
Jim King
Page 22
Question 3
This box has the shape of a cuboid.
It has no lid.
2 cm
4 cm
3 cm
(a)
Draw an accurate net of the box.
(Total 3 marks)
Jim King
Page 23
Question 4
The diagram shows a prism with an L-shaped cross section.
On the grid below, draw the elevation of this solid, from the direction shown by the arrow.
(Total 2 marks)
Total Mark / 10
Jim King
Page 24
2 D shapes
Content:
•
•
Find the area of a triangle ,parallelogram and trapezium
Find the area and perimeter of compound shapes
Q1:
The diagram shows a shaded shape drawn on a centimetre grid.
(a) Work out the perimeter of the shaded shape.
................................ cm
(1)
(b) Work out the area of the shaded shape.
State the units of your answer.
......................................
(2)
Q2:
Here is a shape drawn on a centimetre grid.
Jim King
Page 25
(a) Find the perimeter of the shaded shape.
………………. cm
(1)
(b) Find the area of the shaded shape.
State the units of your answer.
………………………….
(2)
(Total 3 marks)
Question 3
Total Mark ……/ 10
Jim King
Page 26
Session 5
Indices / Factors & Multiples / Bodmas
Factors & Multiples
Content
•
•
•
Find the least common multiple (LCM) of two simple numbers
Find the highest common factor (HCF) of two simple numbers
Write a number as a product of prime factors
Question 1
(a)
Find the highest common factor (HCF) of 30 and 45
(b)
Find the lowest common multiple (LCM) of 30 and 45
(2)
(2)
Question 2
(3)
(3)
Total Mark / 10
Jim King
Page 27
Indices & BODMAS
Content
•
•
•
•
Use index notation and index laws for positive and negative powers
Square, positive and negative square root, cube and cube root
Using a calculator
BODMAS
Question 1
Question 2
(1)
Question 3
(1)
Question 4
(a) Work out
4.6 + 3.85
3.2 2 − 6.51
Write down all the numbers on your calculator display.
Jim King
Page 28
.........................................................
(2)
(b) Give your answer to part (a) correct to 1 significant figure.
.................................
(1)
(Total 3 marks)
Question 5
(a)
Work out 4 × 5 – 8
.....................................
(1)
(b) Work out 18 + 2 × 3
.....................................
(1)
(c) Work out (4 + 3) × 7
.....................................
(1)
(Total 3 marks)
Total Mark / 10
Jim King
Page 29
Session 6
Formulae / Equations
Formulae
Content
•
•
•
Substitute numbers into formulae
Rearrange linear formulae such as s = 4q - 7
Use formulae expressed in words
Question 1
Jim King
Page 30
Question 2
Question 3
Total Mark / 10
Jim King
Page 31
Simple linear equations
Content
•
•
•
Solve linear equations with unknowns on each side such as 3x – 4 = 5 + x
Solve linear equations with brackets such as 2(5x + 1) = 28
Solve more complex linear equations such as 3x – 12 = 2(x – 5)
Question 1
Question 2
Jim King
Page 32
Question 3
Question 4
Total Mark / 10
Jim King
Page 33
Session 7
Fractions & Decimals / Sequences
Fractions 1
Content
•
•
•
•
Simple fractions involving multiplication and division
Simple fractions involving addition and subtraction
Order fractions
Find the reciprocal of a number
Question 1
(1)
(1)
Question 2
5
8
1
2
3
4
Write these fractions in order of size.
Start with the smallest fraction.
(1)
Question 3
(1)
Jim King
Page 34
(1)
Question 4
Question 5
(2)
Total Mark / 10
Jim King
Page 35
Decimals
Content
•
•
•
Understand the effects of multiplying by numbers between 0 and 1
Convert decimals to fractions and percentages and percentages & fractions to decimals
Order decimals
Question 1
Question 2
Question 3
Question 4
Jim King
Page 36
Question 5
Question 6
(a)
Calculate
1 ÷ 0.2
(b)
Calculate
2.4 ÷ 0.6
(c)
Calculate
3.7 x 0.4
Total Mark / 10
Jim King
Page 37
Sequences
Content:
•
•
•
Write the terms of a sequence or a series of diagrams given the nth term
Generate terms of a sequence using term-to-term methods
Write the nth term of a sequence or a series of diagrams
Question 1.
Write down the next two terms in the number pattern
3, 7, 11, 19, …, …
a) Write down, in words, the rule for finding the next number in the pattern from
the one before.
b) Write down the rule for finding the nth term for the pattern
(4 marks)
Question 2
Copy and complete the table
Shape number
Number of dots
1
5
2
8
3
11
4
…
5
…
(2 mark)
Jim King
Page 38
Question 3
Total Mark / 10
Jim King
Page 39
Session 8
Basic arithmetic / Simplify & Expand
Simplify & Expand
Content:
•
•
•
Multiply out brackets expressions with brackets such as 5(3x-2)
Collecting like terms
Factorise expressions
Question 1
Question 2
(a) Simplify m + m + m + m
.........................
(1)
(b) Simplify p×q×4
.........................
(1)
(c) Expand 5(3x – 2)
....................................
(1)
(d) Expand 3y( y + 4)
...................................
(2)
(Total 5 marks)
Jim King
Page 40
Question 3
(a) Simplify 8x – 4x
.....................................
(1)
(b) Simplify y × y × y
.....................................
(1)
(c) Simplify 4x + 3y – 2x + 5y
.....................................
(1)
(Total 3 marks)
Total Mark / 10
Jim King
Page 41
Basic Arithmetic & Reading Tables
•
•
•
Use of Basic Arithmetic in the context of a bill
Reading number lines and scales
Reading timetables
Question 1
Cinema tickets
Adult ticket: £8.65
Child ticket: £4.90
Senior ticket: £5.85
Tony buys one child ticket and one senior ticket.
(a) Work out the total cost.
£ ..................................
(1)
Stephanie buys adult tickets only.
The total cost is £60.55
(b) How many adult tickets does she buy?
.........................
(1)
Kamala buys one adult ticket and two child tickets.
She pays with a £20 note.
(c) How much change should she get?
£ ..................................
(2)
(Total 4marks)
Jim King
Page 42
Question 2
(a)
Write down the number marked by the arrow.
..............................
(1)
(b)
Find the number 110 on the number line.
Mark it with an arrow ( ↑ ).
(1)
(c)
Find the number 0.27 on the number line.
Mark it with an arrow ( ↑ ).
(1)
(Total 3 marks)
Jim King
Page 43
Question 3
The chart below shows the distances, in miles, between pairs of cities by the fastest route. For example,
the distance between Cardiff and Edinburgh is 400 miles by the fastest route.
London
(a)
155
Cardiff
212
245
York
413
400
193
Edinburgh
Write down the distance between London and Edinburgh by the fastest route.
..…………….. miles
(1)
Beccy drove from London to Cardiff by the fastest route and then she drove from Cardiff to York
by the fastest route. She then drove from York to London by the fastest route.
(b)
Work out the total distance that Beccy drove.
..……………….. miles
(2)
(Total 3 marks)
Total Mark / 10
Jim King
Page 44
Session 9
Angles / Travel Graphs
Angles 1
Content:
•
•
Alternate& corresponding angles
Angle properties of triangles and quadrilaterals
Question 1
Jim King
Page 45
Question 2:
Question
Question 3
Jim King
Page 46
Question 4
Total Mark / 10
Jim King
Page 47
Practical Graphs 2
•
•
•
Distance / time graphs
Calculate complex average speeds from distance-time graphs
Travel graphs
Question 1
Jim King
Page 48
Question 2
Total Mark / 10
Jim King
Page 49
Session 10
Percentages / Ratio
Percentages
Content
•
•
•
•
Work out a percentage of a quantity
Work out a percentage increase or decrease
Express one quantity as a percentage of another
Increase or decrease a quantity by a given percentage
Question 1
Question 2
Jim King
Page 50
Question 3
(3)
Question 4
(2)
Total Mark / 10
Jim King
Page 51
Ratio 1
Content
•
•
Divide a quantity in a given ratio
Solve word problems involving ratio and proportion
Question 1
Jack and Jill share £18 in the ratio 1:5
Work out how much each person gets.
Jack £ ……………..
Jill £ ……………....
(Total 2 marks)
Question 2
Tania went to Italy.
She changed £325 into euros (€).
The exchange rate was £1 = €1.68
(a) Change £325 into euros (€).
€ ..................................
(2)
When she came home she changed €117 into pounds.
The new exchange rate was £1 = €1.50
(b) Change €117 into pounds.
£ .................................
(2)
(Total 4 marks)
Jim King
Page 52
Total Mark / 10
Jim King
Page 53