11-19 PROGRESSION. Sample material. Edexcel GCSE (9-1) Mathematics. Access to Foundation

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1 11-19 PROGRESSION Edexcel GCSE (9-1) Mathematics Access to Foundation Sample material

2 Introduction Introduction Helping you prepare for for Edexcel GCSE GCSE (9-1) (9-1) Mathematics Foundation, Foundation, these this workbooks are is a good a good way to to refresh your learning on on Number (and (and a little a little Algebra), Algebra). Statistics and Geometry (including Measures). Work your way through this book unit by unit: Work your The way clear through learning the objectives books unit help by unit: you focus The key points give you reminders The clear learning objectives help you focus The worked examples guide you through to the solution The key points give you reminders All the carefully stepped practice develops your confidence The Stretch worked yourself examples a bit guide with you extend through questions to the solution All the The carefully unit summaries stepped practice help you develops recap and your revise confidence Stretch Take yourself the unit a bit tests with to extend check your questions fluency and build your confidence The Take unit summaries the Number help Test you at the recap end and of revise the book to check your progress. And Take there s the unit a useful tests self-assessment to check your fluency chart on and pages build iv-v your for confidence 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 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 Multiplication and division facts up to Multiply and divide by a single digit 1.6 Round to the nearest 10, 100 and 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 R write and order deci Need more practice Almost there Got it! Geometry and Statistics Contents As further preparation alongside Number, before you progress on to the Foundation GCSE course, you could also refresh your learning in geometry, statistics and probability. Samples from Number and Statistics and Geometry Workbooks Multiply and divide by 10, 100 and Rounding decimals 4 Convert between units of time Access 7to Use Access fractions to to to compare quantities Foundation: Access 8to Find Foundation: percentages of quantities Foundation: 9 Read and interpret data presented + in tables Geometry 10 and Number Statistics Constructing Number Workbook triangles 13 Workbook Workbook Edexcel Access GCSE to Foundation: (9-1) Mathematics Foundation Number Workbook Draft, subject to endorsement vi

3 1.3 Key points Need more practice 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 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. Example 1 Work out the answers to these multiplications. a b c times table facts and related divisions. d Practice 2 Work out the answers to these multiplications. a b c d e f g h i Example Practice 3 Work out the answers to these divisions. a c Work out the answers to these divisions. b d a b c d e f g h i Use the numbers in the cloud to give the answers to the following calculations a b c d e f g h Extend 6 a Write a matching multiplication and division. 720 b Fill in the missing number c Fill in the missing number

4 6 Use a calculator to check what happens when you divide whole numbers and decimals by 10 or 100. Unit 3 Decimals (1) a b c d e f g h i k l Look at the answers in question 6 to work out these calculations without a calculator. a b c d e f g h i Dividing by 10 moves each digit one place to the right; dividing by 100 moves each digit two places to the right k l Use a calculator to find which answer belongs to which calculation. a b c d Extend 9 a Use the fact that to work out b Use the fact that to work out c Work out the answers Key points Needs more practice Almost there Got I m proficient! 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 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. 5 and above round up, 4 and below round down. 21

5 Unit 3 Decimals (1) Practice 1 Use the number line to help you to round these numbers to the nearest whole number. round down round up 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 b Write each number correct to the nearest whole number c Write each number correct to one decimal place 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. Extend 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 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 22 What is wrong with this?

6 Unit test 1 What is the value of the 6 in each of these numbers? 6 10 Unit 3 Decimals (1) a b c Write these numbers in order of size. Start with the smallest number Round these numbers to the nearest whole number. a b c Round these numbers correct to one decimal place. a b c a Work out b Work out Work out a b c d e f Use your calculator to work out a b a Work out b Write your answers to part a in order. Start with the smallest number. 6 23

7 8.3 Need more practice Almost there Got it! Convert between units of time By the end of this section you will know how to: convert between different units of time Unit 8 Time Key points 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. A leap year has an extra day 29 February. Practice 1 Use the numbers in the box to complete the statements about time 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 Guided Example 2 Convert these units of time. a 5 hours into minutes b 36 months into years minutes 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 Practice Extend 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? b The TV programme lasts hours. How many minutes are there in 2 1 hours? minutes 4 c Susie cycles at a speed of 12 miles per hour. She cycles for 3 hours. How many miles does she cycle? miles days 54 d Joe travelled 100 miles in 2 hours. How many miles per hour is that? miles per hour 7

8 13 Fractions (2) 13.1 Need more practice Almost there Got Unit it! 13 Fractions (2) Use fractions to compare quantities By the end of this section you will know how to: Find a fraction of a quantity Solve fraction problems Key points You can find a fraction of a quantity by using multiplication of fractions. You can use fractions to solve problems. To fi nd a fraction of a quantity, divide by the bottom and multiply by the top. Example 1 Work out a 3 4 of 60 b 5 of To fi nd To fi nd and multiply by 3. of something divide by 4. of something divide by 4 2 Which is larger, 2 3 of 45 or 5 of 42? You must show your working so is larger than Practice 3 Work out 3 of Work out 4 of Work out 7 of Extend 6 A clothes shop gives a student discount of 1 off the price. 8 A student buys a dress with a price of 128. How much does she have to pay? You need to subtract the discount from the price. 8 79

9 14 Percentages (2) 14.1 Need more practice Almost there Unit Got 14 it! Percentages (2) 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: 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, first work out 10% and build up the percentage. To change a percentage to a fraction or a decimal, divide by % so to fi nd 10% of an amount, divide by 10. Example Guided 1 Find 70% of 120. a using a calculator b using the % key % answer c without a calculator 10% of 120 so 70% 7 Instead of or you could use 7 10 Practice 2 Work out a 45% of 400 b 55% of 60 3 Work out a 15% of 80 b 35% of Which is larger a 2 of 60 or 70% of 55 3 b 2 of 50 or 45% of 60?

10 4 Interpreting data 4.1 Need more practice Almost there 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. You may need to subtract one value from another in the table to find a difference. Guided Example 1 The table shows the number of students in each year group in a secondary school. Year group Number of students 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? Look for the largest number in the second column. Find the matching year group. Add the number of students in Year 10 to the number of students in Year Here is part of a train timetable. It shows the time that a train leaves each station. Station Time Bempton 1253 Hunmanby 1303 Filey 1308 Seamer 1320 Scarborough 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? Work out the time that is 3 minutes earlier than the time shown for Seamer.

11 Practice 5 The table shows the midday temperatures in five towns. Location Temperature Cardiff 23 C Lancaster 21 C Poole 2 C Stone 1 C Whitby 22 C Unit 4 Interpreting data 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 Time Thirsk 0610 Northallerton 0618 Darlington 0636 Thornaby 0653 Middlesbrough 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 4 Graham Jinty Matt Sally Mike 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? 46 11

12 8 The table shows the distances in miles between some English cities. Unit 4 Interpreting data Dover Exeter Hull Manchester Sheffield Worcester 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 Extend 9 Records of rainfall in the UK go back to The table shows the amounts of rainfall for the wettest five years in that time. Year Rainfall (mm) 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? 47 12

13 11 Accurate drawings 11.2 Need more practice Almost there 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. A pair of compasses is used to locate the point of intersection of two sides of a triangle. Example Practice 1 Make an accurate drawing of this triangle. 4 cm This is just a sketch, you need to draw it full size cm Step 1 Draw a line AB, 8 cm long. 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 A 0 8 cm Measure the length of BC : BC = cm B Step 3 Measure 4 cm from A along the 60 line... label this point C. Join BC. Always fully label your accurate drawing. Practice 2 Make an accurate drawing of this triangle. 3 cm F 70 D 7 cm E The line DE has been drawn for you. D 7 cm E Measure the length of EF : EF = cm 80 13

14 3 Make an accurate drawing of this triangle. P R 6 cm cm Q Unit 11 Accurate drawings Always fully label your accurate drawing. Measure the length of PR : PR = cm Guided Example 4 Make an accurate drawing of this triangle. J L cm K Step 1 Draw a line JK, 7.3 cm long. 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. 40 J cm K Measure the lengths of JL and KL : JL = cm Step 3 Measure an angle of 60 at K. Step 4 Draw the lines JL and KL long enough so that they intersect. KL = cm 14 81

15 Unit 11 Accurate drawings Example Practice 5 Make an accurate drawing of this triangle. M P cm N Measure the lengths of MP and NP : MP = cm NP = cm Practice Extend 6 Make an accurate drawing of this diagram. V Y X cm W 7.5 cm Z 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 82 15

16 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 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