Cambridge IGCSE Biology Revision Guide SAMPLE
Cambridge IGCSE BiologyMaths Skills WorkbookGemma YoungCompletely Cambridge – Cambridgeresources for Cambridge qualificationsCambridge University Press works with Cambridge InternationalExaminations and experienced authors, to produce high-qualityendorsed textbooks and digital resources that support CambridgeTeachers and encourage Cambridge Learners worldwide.Other titles in the series:Coursebook – 978-1-107-61479-6Workbook – 978-1-107-61493-2Teacher’s Resource – 978-1-107-61496-3BiologyMaths Skills WorkbookGemma YoungGemma YoungTo find out more about our resources, visiteducation.cambridge.org/cieE Endorsed by Cambridge International Examinations. Straightforward writing style makes the revision guide idealfor international learners. Progress Check questions allow you to check your knowledgeand understanding as you work your way through the book. Important terms and equations are clearly defined in every chapter. Worked examples provide step-by-step guidance to help youanswer different kinds of questions. Tip boxes flag up key things to remember and help you to practiseyour revision technique and to avoid common mistakes. Chapter summaries review each chapter and allow you to track yourrevision. Exam-style Questions are included throughout to help you preparefor examinations.PLThe guidance sits alongside concise and straightforward coverageof the Cambridge IGCSE Biology syllabus (0610) for examinationfrom 2016.Cambridge IGCSE SAMThis Cambridge IGCSE Biology Revision Guide helps you to reachyour full potential through specially designed guidance, helping you toapply your knowledge and build the confidence you need during yourexam preparation.Cambridge IGCSE Biology Maths Skills WorkbookAre you looking for a Revision Guide to support you as you preparefor your Cambridge IGCSE Biology exams?Original material Cambridge University Press 2018
ContentsSkills navigation grid ivChapter 1: Representing values 2Maths focus 1: Using units EIntroduction 2Maths focus 2: Representing very large and very small values 6Maths focus 3: Using unit prefixes and converting units 9PLChapter 2: Working with data 1616Maths focus 2: Collecting data 20Maths focus 3: Recording and processing data 28Chapter 3: Drawing graphs and charts 34Maths focus 1: Drawing bar charts 34Maths focus 2: Drawing histograms 43Maths focus 3: Drawing line graphs 51Chapter 4: Interpreting data 62Maths focus 1: Interpreting bar charts, histograms and pie charts 62Maths focus 2: Interpreting relationships in graphs 65Maths focus 3: Reading values from a line graph 74Chapter 5: Doing calculations 82Maths focus 1: Calculating percentages 82Maths focus 2: Using scale drawings and magnification 87Maths focus 3: Understanding ratio and probability 92Chapter 6: Working with shape 98Maths focus 1: Calculating area 98SAMMaths focus 1: Naming types of data Additional questions involving several maths skills 106Glossary 108Original material Cambridge University Press 2018iii
Introduction representing values working with data drawing graphs and charts interpreting data doing calculations working with shape.EThis workbook has been written to help you to improve your skills in the mathematicalprocesses that you need in your Cambridge IGCSE Biology course. The exercises will guideyou and give you practice in:PLEach chapter focuses on several maths skills that you need to master to be successful inyour biology course. It explains why you need these skills. Then, for each skill, it presents astep-by-step worked example of a question that involves the skill. This is followed by practicequestions for you to try. These are not like exam questions. They are designed to develop yourskills and understanding; they get increasingly challenging. Tips are often given alongside toguide you. Spaces, lines or graph grids are provided for your answers.In biology, there are lots of contexts where maths is used. You will be calculatingmagnification and using scale when working with microscopes. Probability and ratio are usedto interpret the results from genetic crosses. An important skill is analysing data in the formof tables, graphs and charts. This could be data that you, or other scientists, have collectedduring an investigation.Some of the maths concepts and skills are only needed if you are following the Extendedsyllabus (Core plus Supplement). The headings of these sections are marked ‘Supplement’. Inother areas just one or two of the practice questions may be based on Supplement syllabuscontent, and these are also clearly marked.SAMivThere are further questions at the end of each chapter that you can try to give you moreconfidence in using the skills practised in the chapter. At the end of the book there areadditional questions that may require any of the maths skills from all of the chapters.Original material Cambridge University Press 2018
Chapter 3:Drawing graphs and chartsOur understanding of chemistry has been developed through the observation of the world around us.Two types of data may be collected. In chemistry: Bt Why do you need to be able to draw graphs and charts in biology? Biologists use graphs and charts to display data that they have collected. This makes it easier to compare data andsee patterns.There are different types of graph and chart used in biology; these include bar charts, pie charts, histograms, line graphsand scatter graphs.The type of graph or chart chosen depends on the type of data.E PLMaths Focus 1: Drawing bar chartsBar chartsA bar chart can be used to compare the amount of fat in different foods, see Figure 3.1.The height of eachbar shows the valuefor each category90The y-axis (verticalaxis) shows the rangeof values80SAM70On the y-axis there aretick marks (linesextending outwards)Fat per 100 g605040302010Each axis has a labelincluding units if neededdsaladavocmonorchocbi olasc teuitboiledegg0te34See Chapter 2,Maths focus 1‘Naming typesof data’, for moreinformation onthese types ofdata.Bar charts are used to show data that can be sorted into different categories. This might becategorical or discrete data.butLINKFoodThe x-axis (horizontalaxis) shows the categoriesFigure 3.1 A bar chart to show the amount of fat per 100 g of different foodsOriginal material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsWhat maths skills do you need to draw a bar chart?1 Choosing a suitable scale for the y-axis Aim to use as much of the graph paper as you can Avoid scales that make the values hard to read Show each category by one bar Make all the bars the same width and separate them with a gap Draw the bars as accurately as you can to the correct heightMaths skill practiceE2 Drawing the barsChoose the scale so all the data can be includedHow does drawing bar charts relate to discontinuous variation?PLIn biology you might collect data on variation in a group of people, animals or plants. Someof this data will be discontinuous, which means it can be sorted into categories. For example,a person’s blood group is either A, B, AB or O. This is shown in Table 3.1.Blood groupNumber of peopleA24B6AB2O28Table 3.1 Number of people with the different blood groupsSAMDrawing a chart will show more clearly how many people have each blood group so you cancompare them. The data is categorical so can be displayed using a bar chart.Maths skill 1: Choosing a suitable scale for the y-axisIn the bar chart showing blood groups, the y-axis is going to display the number of people.WATCH OUTThe lowest number of people is 2 and the highest is 28.In some countriesgraph paper is alsocalled millimetrepaper, becauseeach little square is1 mm 1 mm.It is always best to start the y-axis at 0 (unless all the numbers are very large). So, for this barchart the y-axis will start at 0 and go up to at least 28.Graph paper is normally divided up into large squares, see Figure 3.2. Each square containsmany smaller squares, normally: 10 10 100The side of each large square on the graph paper should have a value of 1, 2 or 5 multipliedby a power of 10.For example, you could choose:0.1110100, etc.TIPor0.2220200, etc.The scale youchoose dependson how big thenumbers are thatyou need to show.or0.5550500, etc.Figure 3.2 One large square on this graph paperOriginal material Cambridge University Press 201835
Cambridge IGCSE Maths Skills for ScienceWORKED EXAMPLE 1For the data on blood groups in Table 3.1, which of the scales shown in Figure 3.3would you choose? Explain your choice.ab12E6105836Number of people3624120030SAMcPLNumber of people4d60WATCH OUTMake sure you leaveenough space towrite the title of they-axis next to it.2550204015Number of peopleThe axis with thescale you havechosen should takeup over half of thespace you havegiven, whether thisis a whole sheet ofgraph paper or thegraph paper drawnon an exam paper.Number of peopleTIP30102051000Figure 3.3 Different scales for drawing the y-axisThe scale in C would be the best choice.This is because in A and B the scales mean that the bar for 28 people will not fit onthe paper.The scale in D results in the bar for two people being too small to read easily.Original material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsPractice question 1Some people can roll their tongue and others cannot.The number of students who can or can’t roll their tongue in a class was counted.The data are shown in Table 3.2.Tongue rollerNumber of students18Eyesno12Table 3.2 Results for a survey on tongue rollingWhich y-axis scale (A–C) is the best choice to display this data?Draw a circle around the correct b840201530410202510000SAM6Practice question 2A student collected data on the colour of flowers on different pea plants.His data are shown Table 3.3.Colour of flowersNumber of plantswhite82yellow26red14Table 3.3 Results for a survey on the colour of flowersOriginal material Cambridge University Press 201837
Cambridge IGCSE Maths Skills for ScienceHe starts to write the scale on the y-axis on the graph paper as shown below.50E3020PLNumber of plants40100a Explain what he is doing wrong and why.SAM38b Suggest how he should draw the scale.Practice question 3Shoes come in different sizes. You can only be one shoe size.A student collected data on the shoe size of the girls in her class.Table 3.4 shows the data she collected.Shoe sizeNumber of girls3503633710386396404411420Table 3.4 Results for a survey on shoe sizeOriginal material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsOn the following graph paper, draw a suitable y-axis which can be used to show thisdata as a bar chart.TIPEThe categories canbe numbers. This iscalled discrete data.TIPPLThe y-axis is drawnvertically using aruler.SAMMaths skill 2: Drawing the barsDraw bars to extend from the x-axis.Each bar represents one category.The height of the bar shows the value for each category.WORKED EXAMPLE 2If we return to the blood group data from Table 3.1, we can see the steps needed todraw the bars.Blood groupNumber of peopleA24B6AB2O28Original material Cambridge University Press 201839
Cambridge IGCSE Maths Skills for Science3020ENumber of people251510PL50ABABOBlood groupFigure 3.4 A bar chart to show the number of people with different blood groupsStep 1: Draw a line for the x-axis.KEY QUESTIONS TO ASK YOURSELF:1 How many bars will you need to draw?TIPMake sure all thebars will fit onto thegraph paper.There are four blood groups, so there will be four bars.2 How wide will each bar be?SAM40The bars all need tobe the same width.Work out how you will fit the four bars on your grid.3 How much space will you leave between each bar?Allow the same amount of space between each.Step 2: Draw the bars in order of the rows in the table. So, for this chart the first barwill show the number of people with blood group A. Use a ruler to draw thefirst bar next to the y-axis.Use the scale to work out where the top of the bar should be. Using this scale,two small squares represent 1 person. There is no need to colour the bars in.Step 3: Underneath the bar, write the name of the category.Step 4: Leave a gap and draw the next bar. The size of the gap is not important, as longas the bars are not touching.Step 5: Underneath the x-axis, write the label (copy this from the table). For this chart,it is ‘Blood group’.Original material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsPractice question 4A student collected data on the number of boys in each year in his school.His data are shown in the table.Number of boys71208899101101171195He draws a bar chart.PLa State the title of the x-axis.EYearb State the name of the first bar he will draw.Practice question 5The student then collected data on how many boys in the school were left or right handed.His data are shown in the table.HandednessNumber of boys354Left168SAMRightComplete the bar chart to show the data.400Number of boys3002001000Original material Cambridge University Press 201841
Cambridge IGCSE Maths Skills for SciencePractice question 6The student collected data on how many brothers or sisters (siblings) the students in hisclass had.His data is shown in the table.Number of siblingsNumber of students2112211344 E0112108SAMNumber of students42PLDraw a bar chart to show the data below.6420Original material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsMaths focus 2: Drawing histogramsA histogram is used to display the distribution, or spread, of continuous data.The data in Table 3.5 shows the masses of some bananas.You could draw a bar chart to show the mass of each banana but that would contain a lot ofbars. Because mass is a continuous variable, you can group them together into groups calledclasses. This is displayed in a frequency table, as in Table 3.5.The second column showsthe frequency.The size of the class is called theclass interval. In this case it is 10.This is how many bananas are ineach class.FrequencyPLMass/gEThe fi rst column showsthe ble 3.5 Frequency table of masses of bananasThis data can be used to draw a histogram, which shows the spread of the data as in Figure 3.5.WATCH OUTFrequency is put onthe y-axis. It is thenumber of bananas ineach category.6SAMThere aredifferencesbetween themeaning of‘histogram’ inmathematicsand science. Inmathematicsthe widths ofeach column aredifferent to eachother, becausetheir area is equalto the value. Inscience the barsare the sameheight, so the areais not equal to thevalue.The histogram showsthat most of thebananas are between120 and 140 g.5Unlike a bar chart, thebars on a histogramare touching. Thisshows that the datais continuous.Frequency43210Mass of bananas isput on the x-axis.110120130Mass / g140150Figure 3.5 A histogram to show the distribution in mass of some bananasOriginal material Cambridge University Press 2018The divisions on thex-axis show the lowervalue of each class.43
Cambridge IGCSE Maths Skills for ScienceWhat maths skills do you need to draw a histogram?1 Putting the data into classesChoose the class interval so there areneither too few nor too many classes The frequency of each class is worked out The classes are put on the x-axis The bars are drawn to show the frequencyof each classE2 Drawing the histogram Maths skill practiceThe bars must be touchingPLHow does drawing histograms relate to continuous variation?When you study variation, some of the data you collect will be continuous. Examples includethe height of plants, the hand-span of people or the mass of fruit.Maths skill 1: Putting the data into classesWORKED EXAMPLE 3TIPYour classesshould not overlap.For example,you cannotchoose classes of140–150 cm andthen 150–160 cm,because then it isnot clear in whichclass a height of150 cm would beplaced.The data below shows the height of a group of 15–16 year olds.Height/cm154, 156, 164, 151, 142, 168, 165, 170, 156, 151, 145, 142, 158, 171, 149, 165,169, 157SAM44Drawing a histogram will show more clearly the distribution of height in the class.This will show if more people are shorter or taller, and the most common height. Thispattern can then be compared to another class, or even the whole country.Step 1: Write the data out in order:Height/cm142, 142, 145, 149, 151, 151, 154, 156, 156, 157, 158, 164, 165, 165, 168, 169,170, 171Step 2: Now you can choose your class intervals. You should choose a size that givesyou not too few or too many classes. A total of 4–6 classes is a good number.Height/cm142, 142, 145,149,151, 151, 154, 156,156, 157, 158,164, 165, 165,168, 169,170, 171Classes140–149 cm150–159 cm160–169 cm170–179 cmFreq.4752Step 3: Finally, you can work out the frequency in each class. This is how many heightsfall into each class. For example, there are 4 in the 140–149 cm class.Original material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsPractice question 7The data shows the length of the middle finger of a group of women.Lengthof 07.57.98.2Complete this frequency table.FrequencyELength of middle finger/cm6.0–6.4PL6.5–6.97.0–7.47.5–7.98.0 – 8.545Practice question 8SAMThe data shows the mass of a collection of tortoises living in a zoo.The zoo keeper wants to display the data as a histogram.Mass oftortoise/g125101123130142100155a The zoo keeper starts to draw a frequency table.Complete the classes in the first column.Mass of tortoise/gFrequency100–114b Suggest why the zoo keeper chose this class interval.Original material Cambridge University Press 2018158154146132129
Cambridge IGCSE Maths Skills for SciencePractice question 9A student measured the length of the leaves on a bamboo shoot.The table shows her data, in order of length.Length ofleaf/mm50515357596363646668707172727373PLEChoose suitable class intervals and draw a frequency table to display the data.Maths skill 2: Drawing the histogram46SAMWORKED EXAMPLE 4Let’s return to the data we looked at in Maths skill 1, Worked example 3 about theheight of a group of 15–16 year olds.WATCH OUTYou should startthe y-axis at 0.Here is the frequency table for the ��1695The bars don’t haveto be one largesquare wide; youcan make themnarrower or wider.Try to fill the graphpaper you havebeen given.170–1792Step 1: Draw the y-axis.Frequency is plotted on the y-axis, so look at the highest and lowest frequencyin the table.In this example, the highest frequency is 7. Each large square has the value of one.Make sure you label the y-axis ‘frequency’.Original material Cambridge University Press 2018
Chapter 3: Drawing graphs and chartsStep 2: Draw the x-axis.The divisions on the x-axis show the class intervals.The first number will be the smallest value of your first class.In this example it is 140 cm. You do not have to start this axis at 0.E The lowest value of the next class is 150, so this is the value you write in the nextlarge square. Each large square in this histogram has the value of 10.Label the x-axis with the variable and unit.Step 3: Draw the bars.The height of each bar represents the frequency of that class, see Figure 3.6.Unlike a bar chart, the bars need to be touching.PL764SAMFrequency53210140150160Height / cm170180Figure 3.6 A completed histogram to show the heights of a class of studentsOriginal material Cambridge University Press 201847
Cambridge IGCSE Maths Skills for SciencePractice question 10WATCH OUTA student collected data on the students in her class.The data in thetable uses decimalnumbers, but themethod used isexactly the sameas with wholenumbers.She started with hand span. The data she collected is shown in the frequency 821. 0–22.9523.0–24.93EHand span/cm8765SAMFrequency48PLComplete the histogram on the axes below.4321015.017.019.0Hand span / cm21.023.0Original material Cambridge University Press 201825.0 page
of the Cambridge IGCSE Biology syllabus (0610) for examination from 2016. Endorsed by Cambridge International Examinations. Straightforward writing style makes the revision guide ideal for international learners. Progress Check questions allow you to check your knowledge and understanding as you work your way through the book.
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