11 - 19 PROGRESSION
Edexcel GCSE (9-1)
Mathematics
Sample
material
Access to Foundation
Introduction
Introduction
Helpingyou
youprepare
preparefor
forEdexcel
Edexcel
GCSE
(9-1)
Mathematics
– Foundation,
workbook
a good
Helping
GCSE
(9-1)
Mathematics
– Foundation,
thesethis
workbooks
are isa good
wayto
torefresh
refreshyour
yourlearning
learning
Number
(and
a little
Algebra).
way
onon
Number
(and
a little
Algebra),
Statistics and Geometry (including
Measures).
Work your way through this book unit by unit:
Work your
through
theobjectives
books unithelp
by unit:
Theway
clear
learning
you focus
points give you reminders
•The The
clearkey
learning
objectives help you focus
The worked examples guide you through to the solution
•The All
key points give you reminders
the carefully stepped practice develops your confidence
•The Stretch
workedyourself
examples
guide
through
to the solution
a bit
withyou
extend
questions
•All the
stepped practice
your
confidence
Thecarefully
unit summaries
help youdevelops
recap and
revise
•Stretch
yourself
a
bit
with
extend
questions
Take the unit tests to check your fluency and build your confidence
•The Take
unit summaries
recap
and
the Numberhelp
Testyou
at the
end
ofrevise
the book to check your progress.
•Take
the unit
tests
to check your fluency
and
buildiv-v
your
And
there’s
a useful
self-assessment
chart on
pages
forconfidence
you to fill in as you go!
•Take the Practice Test at the end of the book to check your progress.
And there’s a useful self-assessment chart provided for you to fill in as you go!
Name
Class
Self-assessment chart
Need more practice
Almost there
Got it!
Unit 1 Integers (1)
1.1 Read, write, order and compare positive integers
1.2 Add and subtract positive integers
1.3 Multiply and divide by 10, 100 and 1000
1.4 Multiplication and division facts up to 10 × 10
1.5 Multiply and divide by a single digit
1.6 Round to the nearest 10, 100 and 1000
1.7 Find multiples and factors and identify prime numbers
1.8 Understand and use negative numbers
Unit 2 Order of operations
2.1 Order of operations
Unit 3 Decimals (1)
3.1 Read, write and order decimals
3.2 Add and subtract simple decimals
3.3 Multiply and divide decimal angles
3.4 Rounding decimals
Unit 4 Approximations (1)
4.1 Check solutions
Geometry and Statistics
Unit 5 Fractions (1)
5.1 Read, write and order fractions
5.2 Use equivalent fractions
5.3 Write fractions in their simplest form
As further preparation alongside
before you progress on to the Foundation GCSE course,
5.4 Convert between fractions Number,
and decimals
5.5 Add and subtract fractions
you could also refresh your
learning
in
geometry,
statistics and probability.
5.6 Find fractions of quantities
Contents
Unit 6 Percentages (1)
Samples from Number and Statistics and Geometry Workbooks
6.1 Decimals, fractions and percentages
6.2 Order and compare percentages
6.3 Find percentages of quantities
Unit 7 Money
Multiply and divide by 10, 100 and 1000
3
Rounding decimals 4
Convert between units of time Access 7to
Use Access
fractions
Foundation:
Accessto
toto compare quantities
Access8to
Foundation:
Find
percentages of quantities 9
Foundation:
Foundation:
Geometry10
and
Read and interpret data presented in tables
Number
Statistics
Number
Number
Constructing
Workbooktriangles13
7.1 Read and order amounts of money
7.2 Calculating with money
Unit 8 Time
8.1 Read, record and measure time
8.2 Use units of time
8.3 Convert between units of time
8.4 Use calendars
Unit 9 Integers (2)
+
9.1 Read, write, order and compare integers
9.2 Add and subtract integers
9.3 Multiply and divide integers
9.4 Multiply and divide using negative integers
9.5 Read, write and use squares, cubes and square roots
9.6 Use index notation
Workbook
Unit 10 Function machines
10.1 Function machines
Unit 11 Decimals (2)
11.1 Multiply and divide decimals
11.2 Round decimals
11.3 Add and subtract any decimals
iv
Draft, subject to endorsement
vi
Workbook
Workbook
AccessGCSE
to
Edexcel
Foundation:
(9-1) Mathematics
Number
– Foundation
Workbook
Need more practice
1.3
Almost there
Got it!
Multiply and divide by
10, 100 and 1000
By the end of this section you will know how to:
Multiply integers by 10, 100 and 1000
Divide multiples of 10, 100 and 1000 by 10, 100 and 1000
Key points
Multiplying a number by 10, 100 or 1000 means that each digit moves in place value to the left.
Example
Dividing a number by 10, 100 or 1000 means that each digit moves in place value to the right.
1
Work out the answers to these multiplications.
Hint
a 34 10 340
Hint
274 10
200 10 70 10 4 10
2000 700
40
2740
b 123 10 c 560 100 10 times table
facts and
related divisio
ns.
Practice
Example
Practice
d 37 1000 2 Work out the answers to these multiplications.
a 57 10 b 583 10 c 120 10 d 6 100 e 72 100 f
376 100 g 60 1000 h 752 1000 i
360 1000 3 Work out the answers to these divisions.
Hint
a 120 10 12
b 2650 10 c 4800 100 d 7000 1000 4 Work out the answers to these divisions.
a 50 10 b 290 10 c 5000 10 d 400 100 e 6000 100 f
2500 100 g 8300 100 h 3000 1000 i
12 000 1000 5 Use the numbers in the cloud to give the answers to the
following calculations.
Extend
270 10
200 10 70 10
20 7
27
45
4500
450
45 000
a 45 10 b 450 10 c 45 100 d 4500 10 e 4500 100 f
g 45 000 1000 h 45 000 100 45 1000 6 a Write a matching multiplication and division.
b Fill in the missing number.
c Fill in the missing number.
63 720 6300
1000 32
5
3
Unit 3 Decimals (1)
6 Use a calculator to check what happens when you divide whole numbers
and decimals by 10 or 100.
a 36 4 10 5
b 72 4 10 5
c 15.4 4 10 5
d 28.3 4 10 5
e 5.6 4 10 5
f
4.8 4 10 5
g 27 4 100 5
h 93 4 100 5
i
123 4 100 5
k 6789 4 100 5
l
5432 4 100 5
456 4 100 5
7 Look at the answers in question 6 to work out these calculations without a calculator.
a 49 4 10 5
b 84 4 10 5
c 17.6 4 10 5
d 37.4 4 10 5
e 4.8 4 10 5
f
8.9 4 10 5
g 36 4 100 5
h 72 4 100 5
i
468 4 100 5
k 3764 4 100 5
l
4821 4 100 5
752 4 100 5
Hint
Dividing by 10
moves each di
git
one place to th
e right; dividin
g
by 100 moves
each digit two
places to the rig
ht.
8 Use a calculator to find which answer belongs to which calculation.
a 17.08 3 6 5
113.45
b 567.25 4 5 5
111.3138
c 443.1 4 4.2 5
102.48
105.5
Extend
d 9.23 3 12.06 5
9 a Use the fact that 24 3 8 5 192 to work out 2.4 3 8 5
b Use the fact that 192 4 8 5 24 to work out 19.2 4 8 5
c Work out the answers.
1200 4 1000 5
1.234 3 1000 5
Needsmore
morepractice
practice
Need
3.4
3.2 3 6 5
Almost there
there
Almost
I’m proficient!
Got
it!
Rounding decimals
By the end of this section you will know how to:
Round decimals to the nearest whole number
Round decimals to one decimal place
Key points
The same rules of rounding apply to decimals and whole numbers.
Hint
und up,
5 and above ro
und down.
4 and below ro
Round to the nearest whole number: round 0.1, 0.2, 0.3 and 0.4 down; round 0.5, 0.6, 0.7, 0.8
and 0.9 up.
Round to the one decimal place: round down if the hundredths digit is 1, 2, 3 or 4;
round up if it is 5, 6, 7, 8 or 9.
4
21
Practice
Unit 3 Decimals (1)
1
Use the number line to help you to round these numbers to the nearest whole number.
round down
0
0.5
1.5
1
2.5
2
round up
3.5
3
4.5
4
5.5
5
6
3.7
2.2
a 5.2 rounds to
b 5.8 rounds to
c 2.7 rounds to
d 3.4 rounds to
e 1.3 rounds to
f
4.5 rounds to
2 a Join each decimal to the nearest one decimal place. Use the number line to help.
5
5.05
5.43
5.1
5.15
5.2
5.25
5.1
5.3
5.35
5.4
5.45
5.5
5.55
5.6
5.65
5.7
5.75
5.8
5.85
5.9
5.95
6
5.06
5.2
5.3
5.17
5.4
5.55
5.5
5.6
5.73
5.7
5.92
5.8
5.24
5.9
5.64
b Write each number correct to the nearest whole number.
45.62
45.263
Hint
To round to the
nearest whole
number, look at
the digit in the
first
decimal place.
To round to on
e
decimal place,
look at the digi
t in
the second de
cimal place.
45.3456
c Write each number correct to one decimal place.
45.62
Extend
3 a
45.263
45.3456
Write two decimal numbers that round up to 8.
b
Write two decimal numbers that round down to 8.
c
Write two decimal numbers that round up to 3.4
d
Write two decimal numbers that round down to 3.4
e
Write these decimals correct to one decimal place. 2.916
f
A number rounds up to 6, but down to 5.5. What number could it be?
3.672
4.835
Don’t forget!
When you multiply a number by 10, each digit moves one place to the
When you divide a number by 100, each digit moves
What is wrong with this?
to the
3 4.5
2.5
5 9.5
22
5
Unit 3 Decimals (1)
Unit test
1
6
10
What is the value of the 6 in each of these numbers?
a 34.67
b 36.47
6
100
6
60
c 34.76
2 Write these numbers in order of size. Start with the smallest number.
34.7
34.67
36.47
34.76
36.04
3 Round these numbers to the nearest whole number.
a 24.67
b 16.48
c 29.706
4 Round these numbers correct to one decimal place.
a 15.33
5 a Work out
b 36.47
c 41.062
b Work out
56.4 1 31.78
65.4 2 31.78
6 Work out
a 0.5 3 7 5
b 5 3 0.7 5
c 3.5 4 7 5
d 2.4 3 2 5
e 4.2 4 7 5
f
4.6 3 4 5
7 Use your calculator to work out
a 17.09 3 4.2
b 67.48 4 12.05
8 a Work out
b
6
24.05 3 10 5
2460 4 10 5
23 900 4 100 5
2.45 3 100 5
Write your answers to part a in order. Start with the smallest number.
23
Need more practice
Almost there
Got it!
Unit 8 Time
Convert between units of time
8.3
By the end of this section you will know how to:
convert between different units of time
Key points
Hint
1 day is 24 hours; 1 week is 7 days; 1 year is 12 months.
A leap year ha
s an extra day
29 February.
1 hour is 60 minutes; 1 minute is 60 seconds.
Example
Guided
Practice
1 year is 365 days, 52 weeks or 12 months.
1
Use the numbers in the box to complete the statements about time.
1
2
12
30
Practice
60
a
months 1 year
b
hour d
minutes half an hour
e
weeks 1 year
240
minutes
366
c
seconds 4 minutes
f
days in a leap year
2 Convert these units of time.
a 5 hours into minutes
5 60 300 minutes
b 36 months into years
36 12 3 years
c 60 minutes into seconds
60 seconds
d 416 weeks into years
years
e 315 days into weeks
weeks
f
days
72 hours into days
24 g 24 hours into seconds
Extend
52
seconds
3 Use multiplication and division to convert these times.
a 4 days d
hours
months 6 years
b 56 days e 420 minutes weeks
hours
c 10 minutes f
seconds
years 48 months
4 Work out the answers.
a Eryk is at college 5 days a week for 32 weeks. How many days is that?
days
1 hours.
b The TV programme lasts 2 __
4
1 hours?
How many minutes are there in 2 __
4
c Susie cycles at a speed of 12 miles per hour. She cycles for 3 hours.
How many miles does she cycle?
54
d Joe travelled 100 miles in 2 hours. How many miles per hour is that?
minutes
miles
miles per hour
7
13
Need more practice
Fractions (2)
Almost there
GotUnit
it! 13 Fractions (2)
Use fractions to compare
quantities
13.1
By the end of this section you will know how to:
Find a fraction of a quantity
Solve fraction problems
Key points
Hint
You can find a fraction of a quantity by using multiplication of fractions.
Example
You can use fractions to solve problems.
1
Work out
3
a __
of 60
Hint
5
b __
of 72
4
To find __1 of so
8
60 4 72 3
To find a fractio
n of a quantity,
divide by the bo
ttom and
multiply by the
top.
4
mething divide
4
mething divide
3
To find __
of so
and multiply by
by 4.
by 4
3.
5 of 42? You must show your working.
2 of 45 or __
2 Which is larger, __
3
45 Practice
so
6
42 is larger than
3 of £56.
3 Work out __
7
£
4 of £85.
4 Work out __
5
£
7 of £144.
5 Work out ___
12
Extend
£
1 off the price.
6 A clothes shop gives a student discount of __
8
A student buys a dress with a price of £128.
How much does she have to pay?
Hint
You need to su
btract the
discount from
the price.
£
8
79
14
Need more practice
Percentages (2)
14.1
Almost there
Got 14
it! Percentages (2)
Unit
Find percentages of quantities
By the end of this section you will know how to:
Find a percentage of a quantity
Key points
There are a number of different ways to work out a percentage of an
amount:
Hint
• when using a calculator, change the percentage to a fraction or decimal
then multiply by the amount
• or, when using a calculator, you can multiply the amount by the
percentage then press the percentage key on your calculator
Hint
1
__
find 10% of
10% 10 so to
vide by 10.
an amount, di
Practice
Example
Guided
• when not using a calculator, first work out 10% and build up the
percentage.
1
rcentage
To change a pe
a decimal,
to a fraction or
divide by 100.
Find 70% of 120.
Hint
70_
Instead of __
yo
7
100 u could use __
or 0.7.
10
a using a calculator
70 ____
b using the % key
120 70 %
answer c without a calculator
10% of 120 so 70% 7 100
120 2 Work out
a 45% of 400
b 55% of 60
3 Work out
a 15% of £80
b 35% of £120
£
£
4 Which is larger
2
a __
of 60 or 70% of 55
3
2
b __
of 50 or 45% of 60?
5
82
9
4
Interpreting
data
4.1
Almost there
Need more practice
Got it!
Read and interpret data
presented in tables
By the end of this section you will know how to:
Find and understand information given in tables
Key points
Use the labels on the rows and columns to find information.
You may need to add values in a row or column to find a total.
Example
Guided
You may need to subtract one value from another in the table to find a difference.
1
The table shows the number of students in each year group in a secondary school.
Year group
11
10
9
8
7
Number of students
124
116
137
128
112
a How many students are in Year 11?
Hint
b Which is the largest year group?
Look for the largest number in the second
column. Find the matching year group.
c The senior students are in Years 10 and 11.
How many senior students are there?
Hint
Add the number of students in Year 10
to the number of students in Year 11.
2 Here is part of a train timetable. It shows the time that a train leaves each station.
Station
Bempton
Hunmanby
Filey
Seamer
Scarborough
Time
1253
1303
1308
1320
1325
Hint
1253 is the same as 12:53
or 53 minutes past 12.
a What time does the train leave Hunmanby?
b The train is in Seamer station for 3 minutes. What time did the train arrive at Seamer?
Hint
10
44
Work out the time that is 3 minutes earlier
than the time shown for Seamer.
Practice
Practice
Unit 4 Interpreting data
5 The table shows the midday temperatures in five towns.
Location
Cardiff
Lancaster
Poole
Stone
Whitby
Temperature
23°C
21°C
2°C
1°C
22°C
a What is the temperature in Whitby?
b Which is the coldest location?
c How much warmer is Poole than Whitby?
6 Here is part of a train timetable. It shows the time that the train leaves each station.
Station
Thirsk
Northallerton
Darlington
Thornaby
Middlesbrough
Time
0610
0618
0636
0653
0703
a What time does the train leave Thornaby?
b The train stops at Middlesbrough for 5 minutes. How long does it take to get from
Darlington to Middlesbrough?
minutes
7 The table shows the numbers of cars sold by five sales people over a four-week period.
Graham
Jinty
Matt
Sally
Mike
Week 1
3
4
4
3
2
Week 2
4
3
2
3
3
Week 3
3
4
4
4
4
Week 4
4
6
4
5
4
a How many cars did Mike sell in Week 2?
b How many cars were sold altogether in Week 1?
c Who sold the most cars?
d How many more cars were sold in Week 4 than in Week 3?
11
46
Unit 4 Interpreting data
et
er
st
er
Sh
234 232 64 39
ef
fie
an
M
275 234 95
W
ld
or
ce
st
er
ch
e
ul
l
249 284
H
242
Ex
D
ov
er
8 The table shows the distances in miles between some English cities.
190 133 159 112 102
a How far is it from Hull to Sheffield?
miles
b Which city is less than 200 miles from Dover?
c Which city is closest to Hull?
d Kari drives from Dover to Sheffield and then from Sheffield to Hull.
How far does she drive altogether?
miles
e Kari returns to Dover without going to Sheffield. How much shorter is this route?
Extend
miles
9 Records of rainfall in the UK go back to 1910.
The table shows the amounts of rainfall for the wettest five years in that time.
Year
1954
2000
2002
2008
2012
Rainfall (mm)
1309
1337
1284
1295
1331
a How many of the five wettest years have occurred from 2000 onwards?
b Which year was the wettest?
c How many years are there between the two most recent entries in the table?
d How many years are there between the two oldest entries in the table?
12
47
11
Accurate
drawings
Almost there
Need more practice
11.2
Unit 4 Interpreting
Got it! data
Constructing triangles
By the end of this section you will know how to:
Draw triangles accurately when at least one angle is given.
Draw triangles accurately when given all three sides.
Key points
A metric ruler shows centimetres and millimetres; it is used to measure lines accurately.
A protractor is used to measure angles accurately.
Example
Practice
A pair of compasses is used to locate the point of intersection of two sides of a triangle.
1
Make an accurate drawing
of this triangle.
Hint
This is just a sketch, you
need to draw it full size.
4 cm
60°
Hint
Step 1
Draw a line AB, 8 cm long.
8 cm
Hint
Step 2
Measure an angle of 60° at A.
Position the centre of the protractor at
A, with the zero line along AB.
Use the scale that starts at zero.
60
A
Hint
Step 3
Measure 4 cm from A along the 60°
line ... label this point C.
Join BC.
60°
0
Practice
Practice
Measure the length of BC :
B
8 cm
BC =
Hint
cm
2 Make an accurate drawing of this triangle.
Always fully label your
accurate drawing.
F
3 cm
70°
D
E
7 cm
Hint
The line DE has been drawn for you.
D
E
7 cm
Measure the length of EF :
EF =
cm
13
80
Unit 11 Accurate drawings
3 Make an accurate drawing of this triangle.
R
6 cm
P
50°
10 cm
Q
Hint
Always fully label your
accurate drawing.
Example
Guided
Measure the length of PR :
PR =
cm
4 Make an accurate drawing of this triangle.
J
L
40°
60°
K
7.5 cm
Hint
Step 1
Draw a line JK, 7.3 cm long.
Hint
Step 2
Measure an angle of 40° at J.
Position the centre of the protractor at
J, with the zero line along JK.
Use the scale that starts at zero.
Hint
40
Step 3
Measure an angle of 60° at K.
J
40°
0
Measure the lengths of JL and KL :
14
81
K
7.5 cm
Hint
JL =
cm
KL =
cm
Step 4
Draw the lines JL and KL long enough
so that they intersect.
Example
Practice
Unit 11 Accurate drawings
5 Make an accurate drawing of this triangle.
P
M
Extend
Practice
Measure the lengths of MP and NP :
50°
70°
6 cm
MP =
cm
NP =
cm
6 Make an accurate drawing of this diagram.
Y
X
30°
55°
V
N
4.5 cm
W
7.5 cm
Z
Hint
Start by drawing the line VWZ and
measure a right-angle at W.
Measure the lengths of VY, XZ and XY :
VY =
cm
XZ =
cm
XY =
cm
15
82
T972a
Which students are the Access to Foundation Workbooks designed to support?
For students who need a ‘refresher course’ to increase their fluency and confidence before
starting Edexcel GCSE (9-1) Mathematics Foundation course.
Two Access to Foundation Workbooks – Number;
Statistics and Geometry will enable students to
start the Foundation course with confidence.
They deliver a ‘two-term’ structured course
that provides additional support for the
Edexcel Access to Foundation Scheme of Work
and baseline tests.
For more information visit
www.edexcel.com/accesstofoundation
The write-on format encourages ownership
leading to fluency and mastery of the basics,
leading to increased confidence.
We are seeking endorsement for use with the
Edexcel GCSE (9-1) Mathematics specification.
U089
S14MAT02284
Pearson Ltd is committed to reducing its impact on the
environment by using responsibly sourced and recycled paper.
Temari balls © Fusako
Photograph by NanaAkua