sample edexcel gcse (9-1) ial mathematics you prepare for edexcel gcse (9-1) ... (1) 6.1 decimals,...

Edexcel GCSE (9-1)

MathematicsAccess to Foundation

11 - 19 PROGRESSION

Sample material

Introduction

vi

Introduction

Helping you prepare for Edexcel GCSE (9-1) Mathematics – Foundation, this workbook is a good way to refresh your learning on Number (and a little Algebra).

Work your way through this book unit by unit:

The clear learning objectives help you focus The key points give you reminders The worked examples guide you through to the solution All the carefully stepped practice develops your confidence Stretch yourself a bit with extend questions The unit summaries help you recap and revise Take the unit tests to check your fluency and build your confidence Take the Number Test at the end of the book to check your progress.

And there’s a useful self-assessment chart on pages iv-v for you to fill in as you go!

Access to Foundation:

Number Workbook


Number Workbook

+Access to

Foundation:

Number Workbook


Geometry and Statistics

Workbook


Number Workbook

Edexcel GCSE

(9-1) Mathematics – Foundation

Geometry and StatisticsAs further preparation alongside Number, before you progress on to the Foundation GCSE course, you could also refresh your learning in geometry, statistics and probability.

Draft, subject to endorsement

Helping you prepare for Edexcel GCSE (9-1) Mathematics – Foundation, these workbooks are a good way to refresh your learning on Number (and a little Algebra), Statistics and Geometry (including Measures).

Work your way through the books unit by unit:

• The clear learning objectives help you focus • The key points give you reminders • The worked examples guide you through to the solution • All the carefully stepped practice develops your confidence • Stretch yourself a bit with extend questions • The unit summaries help you recap and revise • Take the unit tests to check your fluency and build your confidence • 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!

iv

Self-assessment chart

Name Class

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

Unit 5 Fractions (1)

5.1 Read, write and order fractions

5.2 Use equivalent fractions

5.3 Write fractions in their simplest form

5.4 Convert between fractions and decimals

5.5 Add and subtract fractions

5.6 Find fractions of quantities

Unit 6 Percentages (1)

6.1 Decimals, fractions and percentages

6.2 Order and compare percentages

6.3 Find percentages of quantities

Unit 7 Money

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

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

Contents Samples from Number and Statistics and Geometry Workbooks

Multiply and divide by 10, 100 and 1000 3Rounding decimals 4Convert between units of time 7Use fractions to compare quantities 8Find percentages of quantities 9Read and interpret data presented in tables 10 Constructing triangles 13

5

1 Work out the answers to these multiplications.

a 34 � 10 � 340

b 123 � 10 �

c 560 � 100 �

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.

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.

a 45 � 10 � b 450 � 10 �

c 45 � 100 � d 4500 � 10 � e 4500 � 100 �

f 45 � 1000 � g 45 000 � 1000 � h 45 000 � 100 �

6 a Write a matching multiplication and division. 720 � � � �

b Fill in the missing number. 63 � � 6300

c Fill in the missing number. � 1000 � 32

Exam

ple Hint

10 times table facts and related divisions.

Hint

274 � 10 � 200 � 10 � 70 � 10 � 4 � 10 � 2000 � 700 � 40 � 2740

Prac

tice

Exam

ple Hint

270 � 10 � 200 �10 � 70 � 10� 20 � 7 � 27

Prac

tice

45 000450045045

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nd

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

Multiply and divide by 10, 100 and 1000

Multiplying a number by 10, 100 or 1000 means that each digit moves in place value to the left.

Dividing a number by 10, 100 or 1000 means that each digit moves in place value to the right.

Key points

Need more practice Almost there Got it!

1.3

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3

Unit 3 Decimals (1)

21

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

456 4 100 5 k 6789 4 100 5 l 5432 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

752 4 100 5 k 3764 4 100 5 l 4821 4 100 5

8 Use a calculator to find which answer belongs to which calculation.

a 17.08 3 6 5

b 567.25 4 5 5

c 443.1 4 4.2 5

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 3.2 3 6 5

Hint

Dividing by 10 moves each digit one place to the right; dividing by 100 moves each digit two places to the right.

111.3138

102.48113.45

105.5

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Needs more practice Almost there I’m proficient!


Round decimals to the nearest whole number

Round decimals to one decimal place

Rounding decimals3.4

The same rules of rounding apply to decimals and whole numbers.

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.

Key points


Hint

5 and above round up,

4 and below round down.

4

Unit 3 Decimals (1)

22

1 Use the number line to help you to round these numbers to the nearest whole number.

0 0.5 1 1.5 2 2.5 3 3.5 4

round upround down

4.5 5 5.5 63.72.2

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 5.1 5.15 5.2 5.25 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

5.43 5.1 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 45.3456

c Write each number correct to one decimal place.

45.62 45.263 45.3456

3 a 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 3.672 4.835

f A number rounds up to 6, but down to 5.5. What number could it be?

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 to the

What is wrong with this? 3 4 . 5

� 2.5

5 9 . 5

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tice

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Hint

To round to the nearest whole number, look at the digit in the fi rst decimal place. To round to one decimal place, look at the digit in the second decimal place.

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Unit test

1 What is the value of the 6 in each of these numbers? 6

106

100 6 60

a 34.67 b 36.47 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 b 36.47 c 41.062

5 a Work out 56.4 � 31.78 b Work out 65.4 � 31.78

6 Work out

a 0.5 � 7 � b 5 � 0.7 � c 3.5 � 7 �

d 2.4 � 2 � e 4.2 � 7 � f 4.6 � 4 �

7 Use your calculator to work out

a 17.09 � 4.2 b 67.48 � 12.05

8 a Work out

24.05 � 10 � 2460 � 10 �

23 900 � 100 � 2.45 � 100 �

b Write your answers to part a in order. Start with the smallest number.

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5

Unit 3 Decimals (1)

23

Unit test

1 What is the value of the 6 in each of these numbers? 6

106

100 6 60

a 34.67 b 36.47 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 b 36.47 c 41.062

5 a Work out 56.4 1 31.78 b Work out 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

24.05 3 10 5 2460 4 10 5

23 900 4 100 5 2.45 3 100 5

b Write your answers to part a in order. Start with the smallest number.

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6

Unit 8 Time

54

1 Use the rhyme to fi ll in the number of days for each month.

January February March April

May June July August

September October November December

2 a Here is part of a calendar. Fill in the missing calendar dates.

June 2013

WedTuesMonSun Thurs Fri Sat

8

1514

27

19

5

11

4

25

10

1716

b What day of the week is 20 June 2013?

c What is the date of the next Tuesday after 15 June 2013?

d Juliana wants to have her birthday party on the Friday nearest to her birthday. Her birthday is on 12 June 2013. On which date should she have her party?

e What date is 2 weeks before 8 June 2013?

1 week before is June, so 2 weeks before is May

f What date is 4 weeks after 25 June 2013? 25 � 2 � , so

g What day of the week is 27 May 2013? 27 May is

Prac

tice Hint

30 days has September,April, June and November,all the rest have 31,except February,which has 28 days clearand 29 each leap year.

Exam

ple

Hint

The shaded dates show the last few days of the month before and the next few days after the month displayed.

Hint

Use 4 weeks � 28 days. Example: To work out 4 weeks after 21 January: January has 31 (or 28 � 3) days: 21 � 3 � 18. So 4 weeks after 21 January is 18 February

1 Use the numbers in the box to complete the statements about time.

1 2 12 30 52 60 240 366

a months � 1 year b hour � minutes c seconds � 4 minutes

d minutes � half an hour e weeks � 1 year 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 72 hours into days � � days

g 24 hours into seconds 24 � � � seconds

3 Use multiplication and division to convert these times.

a 4 days � hours b 56 days � weeks c 10 minutes � seconds

d months � 6 years e 420 minutes � hours f 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

b The TV programme lasts 2 1 __ 4 hours.

How many minutes are there in 2 1 __ 4 hours? minutes

c Susie cycles at a speed of 12 miles per hour. She cycles for 3 hours. How many miles does she cycle? miles

d Joe travelled 100 miles in 2 hours. How many miles per hour is that? miles per hour

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convert between different units of time

Convert between units of time8.3

1 day is 24 hours; 1 week is 7 days; 1 year is 12 months.

1 hour is 60 minutes; 1 minute is 60 seconds.

1 year is 365 days, 52 weeks or 12 months.

Key pointsHint

A leap year has an extra day � 29 February.

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7

Unit 13 Fractions (2)

79

1 Work out

a 3 __ 4 of 60 b 5 __

8 of 72

60 � 4 � 72 � �

� 3 � � �

2 Which is larger, 2 __ 3 of 45 or 5 __

6 of 42? You must show your working.

45 � � � � 42 � � � �

so is larger than

3 Work out 3 __ 7 of £56.

£

4 Work out 4 __ 5 of £85.

£

5 Work out 7 ___ 12

of £144.

£

6 A clothes shop gives a student discount of 1 __ 8 off the price.

A student buys a dress with a price of £128.

How much does she have to pay?

£

Exam

ple Hint

To fi nd 1 __ 4

of something divide by 4. To fi nd 3 __

4 of something divide by 4

and multiply by 3.

Prac

tice

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Hint

You need to subtract the discount from the price.

Use fractions to compare quantities


13.1

13 Fractions (2)


Find a fraction of a quantity

Solve fraction problems

You can fi nd a fraction of a quantity by using multiplication of fractions.

You can use fractions to solve problems.

Key points Hint

To fi nd a fraction of a quantity, divide by the bottom and multiply by the top.

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8

82

Unit 14 Percentages (2)

1 Find 70% of 120.

a using a calculator 70 ____ 100

� 120 �

b using the % key 120 � 70 % answer �

c without a calculator 10% of 120 � so 70% � 7 � �

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

a 2 __ 3 of 60 or 70% of 55

b 2 __ 5 of 50 or 45% of 60?

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ded

Exam

ple

Exam

ple Hint

Instead of 70 ___ 100 you could use 7 __ 10

or 0.7.

Prac

tice

Prac

tice


Find a percentage of a quantity

Find percentages of quantities


14.1

There are a number of different ways to work out a percentage of an amount:

• 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

• when not using a calculator, fi rst work out 10% and build up the percentage.

Key points

Hint

To change a percentage

to a fraction or a decimal,

divide by 100.

Hint

10% � 1 __ 10

so to fi nd 10% of

an amount, divide by 10.

14 Percentages (2)

1 Write

a 32 as a percentage of 50 32 ___ 50

� ____ 100 answer � %

b 11 as a percentage of 20 11 ___ 20

� ____ 100 answer � %

2 Work out

a 20 centimetres as a percentage of 4 metres b 15 minutes as a percentage of 2 hours

4 m � cm 20 _____ � 100 � % 2 hours � min 15 _____ � 100 � %

3 Write

a 18 as a percentage of 300 b 4 as a percentage of 25

% %

4 Work out

a 80 grams as a percentage of 2 kilograms b 400 metres as a percentage of 5 kilometres

% %

5 180 of the 600 people in a cinema are children. Work out 180 as a percentage of 600.

%

Exam

ple Hint

When working without a calculator try writing the fraction as an equivalent fraction with a denominator of 100, then the answer is the numerator.

Prac

tice

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9

1 The table shows the number of students in each year group in a secondary school.

Year group Number of students11 12410 116 9 137 8 128 7 112

a How many students are in Year 11?

b Which is the largest year group?

c The senior students are in Years 10 and 11. How many senior students are there?

2 Here is part of a train timetable. It shows the time that a train leaves each station.

Station TimeBempton 1253Hunmanby 1303Filey 1308Seamer 1320Scarborough 1325

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?

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ded

Exam

ple

Hint

Look for the largest number in the second column. Find the matching year group.

Hint

Add the number of students in Year 10 to the number of students in Year 11.

Hint

1253 is the same as 12:53 or 53 minutes past 12.

Hint

Work out the time that is 3 minutes earlier than the time shown for Seamer.


Find and understand information given in tables

Read and interpret data presented in tables4.1

Use the labels on the rows and columns to fi nd information.

You may need to add values in a row or column to fi nd a total.

You may need to subtract one value from another in the table to fi nd a difference.

Key points

4 Interpreting data 5 The table shows the midday temperatures in fi ve towns.

Location TemperatureCardiff 23°CLancaster 21°CPoole 2°CStone 1°CWhitby 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 TimeThirsk 0610Northallerton 0618Darlington 0636Thornaby 0653Middlesbrough 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 fi ve sales people over a four-week period.

Week 1 Week 2 Week 3 Week 4Graham 3 4 3 4Jinty 4 3 4 6Matt 4 2 4 4Sally 3 3 4 5Mike 2 3 4 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?

Prac

tice

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tice


44

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10

Unit 4 Interpreting data

5 The table shows the midday temperatures in five towns.

Location TemperatureCardiff 23°CLancaster 21°CPoole 2°CStone 1°CWhitby 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 TimeThirsk 0610Northallerton 0618Darlington 0636Thornaby 0653Middlesbrough 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.

Week 1 Week 2 Week 3 Week 4Graham 3 4 3 4Jinty 4 3 4 6Matt 4 2 4 4Sally 3 3 4 5Mike 2 3 4 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?

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tice


46


11


8 The table shows the distances in miles between some English cities.

Shef

fieldMan

ches

ter

HullEx

eterDove

r

242

249

275

234

190

284

234

232

95

64 39

Worce

ster

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?

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 Rainfall (mm)1954 13092000 13372002 12842008 12952012 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?

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47


12



Draw triangles accurately when at least one angle is given.

Draw triangles accurately when given all three sides.

Constructing triangles11.2

A metric ruler shows centimetres and millimetres; it is used to measure lines accurately.

A protractor is used to measure angles accurately.

A pair of compasses is used to locate the point of intersection of two sides of a triangle.

Key points

11 Accurate drawings

80

1 Make an accurate drawing of this triangle.

Measure the length of BC : BC = cm


Measure the length of EF : EF = cm

Need more practice Almost there Got it! Pr

actic

eEx

ampl

ePr

actic

ePr

actic

e

Hint

Step 2Measure 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.

Hint

Step 3Measure 4 cm from A along the 60° line ... label this point C.Join BC.

Hint

This is just a sketch, you need to draw it full size.

Hint

Step 1Draw a line AB, 8 cm long.

Hint

Always fully label your accurate drawing.

Hint

The line DE has been drawn for you.

8 cm

60°

4 cm

8 cm

60°

60

0A B

7 cm

70°

3 cm

D

F

E

7 cmD E


13

Unit 11 Accurate drawings

81


Measure the length of PR : PR = cm


Measure the lengths of JL and KL : JL = cm

KL = cm

Hint

Always fully label your accurate drawing.

Hint

Step 1Draw a line JK, 7.3 cm long.

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Exam

ple

Hint

Step 2Measure 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

Step 3Measure an angle of 60° at K.

Hint

Step 4Draw the lines JL and KL long enough so that they intersect.

10 cm50°

6 cm

P

R

Q

7.5 cm60°40°

J

L

K

7.5 cm

40°

40

0J K


14

Unit 11 Accurate drawings

82


Measure the lengths of MP and NP : MP = cm

NP = cm

6 Make an accurate drawing of this diagram.

Measure the lengths of VY, XZ and XY :

VY = cm XZ = cm XY = cm

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tice

Exam

ple

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Hint

Start by drawing the line VWZ and measure a right-angle at W.

6 cm70°50°

M

P

N

4.5 cm 7.5 cm

30°55°V W

YX

Z


15

T972a

Pearson Ltd is committed to reducing its impact on the environment by using responsibly sourced and recycled paper.U089

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.

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