![Diploma in Applied Science<br />(Forensic Science)<br />UNIT 6 USING MATHEMATICAL TOOLS FOR SCIENCE<br />Diploma in Applied Science (Forensic Science)<br />Unit 6 Mathematical tools for science<br />Aims and purpose<br />This unit enables learners to use mathematical tools which are essential for working in a science environment. Starting with basic numbers and simple algebraic manipulation, learners then move onto collecting and interpreting data on graphs and charts.<br />Unit introduction<br />Anyone who works in a science-related area needs to be confident in handling numbers in their day-to-day work. Their calculations may be used to design equipment or to predict how a new chemical is going to work. During experiments, data needs to be accurately collected and results displayed. Valid interpretation of the data is vital in order to make sense of what is going on in science experiments. Without the use of maths, science work would be paralysed.<br />This unit addresses the need for science workers to learn basic mathematical tools that are essential in the science industry. The intention is not maths for maths but maths for science and so there is an emphasis on integrating the maths to practical scientific work. By studying this unit learners will have the opportunity to consider a number of important concepts, including:<br />how to use the International System of Units (SI) correctly<br />how to leave an answer to the correct decimal place or significant figure<br />how to manipulate and use simple algebra correctly<br />how to measure and calculate experimental errors in experiments<br />how to display and interpret experimental data.<br />In the first learning outcome, the learner is introduced to the basics of maths; leaving answers to the correct decimal or significant figure is emphasised, including correct handling of scientific calculators. This outcome also focuses on how simple algebra helps solve scientific problems. Learning outcome 2 looks at the types of scientific data (primary and secondary) and how scientific data is collected and the errors that may occur during the collection process. The unit concludes by investigating how data can be displayed and how to correctly interpret graphs and charts. Throughout this unit learners will have plenty of opportunities to use graphical scientific calculators and ICT in the various activities available. This unit is vital for anyone intending to<br />follow a scientific pathway.<br />Learning outcomes<br />On completion of this unit a learner should:<br />Be able to use mathematical tools in science<br />Be able to collect and record scientific data<br />Be able to display and interpret scientific data.<br />Diploma in Applied Science (Forensic Science)<br />Be able to use mathematical tools in science<br />Mathematical tools: SI units (length, mass, time, area, volume, density, force); conversions, eg imperial to metric and vice versa; prefixes, eg giga, mega, kilo, deci, centi, milli, micro, nano, pico; accuracy of data (decimal places and significant figures); fractions; percentages; ratios; standard form; use of scientific calculators <br />Scientific problems involving algebra: transposition of formulae; substitution of equations; simple linear equations, eg involving force and mass (F = ma), speed and distance (v = s/t), mole calculations (n = m/Mr), voltage and current (V = IR), density and volume (ρ = m/V)<br />Mensuration: standard formulae to solve surface areas, eg total surface area of a cylinder = 2πrh + 2πr2, surface area of a sphere = 4πr2; volume of regular solids, eg volume of a cylinder = πr2h, volume of a sphere = 4/3πr3, volume of a cone = 1/3πr2h<br />Be able to collect and record scientific data<br />Data collection: methods, eg computer automation, manual collection (eg handling of instruments); primary data, eg data obtained from own experiment; secondary data, eg data taken from research papers, data taken from website<br />Errors and accuracy: precision of instrument, eg rule, measuring cylinder, micrometer, balance; systematic and random errors; maximum error of instrument, eg half the precision value; absolute error of measurement; maximum percentage error of measurement, eg maximum error of instrument divided by measurement<br />Recording data: data tables in a lab book, eg collecting data manually (borders and correct labelling and units of physical quantities); by data loggers, eg when taking data from an experiment over days<br />Be able to collect and record scientific data<br />Charts: data represented by statistical diagrams (bar charts, pie charts); histograms (continuous and discrete variants)<br />Type of graphs: linear graphs, eg distance time graphs, graphs obeying Ohm’s law (voltage against current); non-linear graphs, eg rate of catalytic reaction against temperature, hydrogen gas given off against time, radioactive decay, bacterial growth<br />Interpretation of data: random data, patterns in data; calculation of the arithmetic mean, mode and median; continuous data, eg rate of production over time, population count of invertebrates or plants; discrete data, eg fingerprint type, shoe size; raw and derived data, eg measure time and distance travelled by a car and calculate (derive) the speed<br />Interpretation of graphs: calculating the gradient of a straight line graph; calculating the area under a straight line graph; taking tangents of non-linear graphs in order to determine the gradient at a point; explaining trends in both linear and non-linear graphs<br />Task 1: Numbers for science<br />You are a trainee electronics physicist using mathematical tools.<br />-63212-3822-63212155563P1 Carry out mathematical calculations using suitable mathematical tools<br />P2 Carry out mathematical calculations using algebra<br />-64482-647M1 Use standard form to solve science problems<br />-64482-3187M2 Use mensuration to solve scientific problems<br />-644824433D1 Use ratios to solve scientific problems<br />-6321213323D2 Use algebra to solve scientific problems<br />You need to complete the following task<br />A small mirror designed for a European telescope has dimensions of 7 inches x 8 inches. Convert into SI units P1<br />It is estimated that light takes 100 000 years to travel the full distance across our galaxy, the Milky Way. If light travels 3.0 x 108 m in 1 second, how long is the Milky Way in metres? Give your answer in standard form M1<br />A block cut from asteroid rock was measured to have dimensions: 13.3 mm x 12.4 mm x 15.2 mm. <br />Convert the dimensions into SI units. P1<br />Find the volume of the block. Give your answer in standard form and to the appropriate significant figures. P1 M1<br />You are working as a clinical chemist in charge of the testing of blood samples. You are required to mix a sodium chloride solution with water in the ratio of 2:5<br />Starting with 780 ml of the sodium chloride, how much water needs to be added? D1<br />Give your answer in standard form to an appropriate number of significant figures. M1<br />,[object Object],Calculate the radius of the Earth and then the volume of the Earth P2 M2 D2<br />Use your answer to part a to determine the density of the Earth. Give your answer in standard form to the appropriate number of significant figures D2<br />,[object Object],Grading tips<br />To achieve P1 in question 1, remember that in science most quantities have a unit, without a unit you will not know what quantity it is. To achieve M1 in question 2, remember to use standard form. HINT: before you start change the years into seconds. When attempting P1 in question 3a the number of significant figures in the final answer should not be any more than those given in the question. When working towards M1 in question 3b, don’t get confused with the notation on your calculator; this will not be in standard form. Learners often make the mistake of trying to solve ratios in one step. To achieve D1 in question 4a, make sure you first find the total volume of the solution required and then subtract the solution of sodium chloride to get the volume of water required. For P2 in question 5a, remember if you divide by a number on one side of an equation you will need to do the same on the other side. For D2 in question 5, be careful when you transpose the equations. The key to answering problems like question 6 is first to identify the shape M2, write out the equation and then use the basic rules of algebra to rearrange the equation to get the subject P2. Make sure that you have converted all dimensions to SI units. Substituting the value correctly and leaving your answer to the appropriate number of significant figures with the correct unit will go towards meeting P1 M1 D2<br />Deadline:_______________<br />Task 2: Data collection methods<br />As a trainee engineer, you are working to develop a state of the art greenhouse. You have been assigned to investigate how the temperature varies in a greenhouse between 11 am and 3 pm during spring and summer. So far, you have collected the data for Monday as shown in the table. You used a watch to note the time and a digital thermometer to measure the temperature.<br />Temperature / C at time:11:0012:0013:0014:00DayMonday18:0319:6724:4526:45TuesdayWednesdayThursdayFriday<br />-98161-5715P3 Collect and record scientific data<br />P4 Identify errors associated with collecting data in an experiment<br />M3 Describe the process involved in accurately collecting and recording scientific data<br />M4 Calculate any errors associated with scientific data collected in an experiment<br />D3 Compare methods of data collected<br />D4 Explain how errors can be minimized in data collected in the experiment<br />You need to complete the following task:<br />,[object Object]](https://image.slidesharecdn.com/unit6usingmathematicaltoolsforsciencewrongtable-110123072201-phpapp01/85/Unit-6-using-mathematical-tools-for-science-wrong-table-1-320.jpg)
![Write down some of the errors that could occur in the experiment P4. Calculate the maximum percentage error in the average temperature M4. Explain how the errors you have listed can be minimised? D4Grading tips<br />To achieve P3 in question 1, don’t forget to include both random and systematic errors. For M4, show your working. A common mistake when attempting D4 is to generalise and not refer to the experiment.<br />Deadline _________________<br />Task 3: Displaying data<br />You are working as a microbiologist investigating yeast cells. You have collected the data shown below.<br />Time / hoursNumber of cells0215215340411053006800<br />-556161701800-565155979P5 Select the appropriate formats for displaying the scientific data that have been collected<br />P6 interpret scientific data<br />M5 interpret the trend in the scientific data collected in an experiment<br />D5 Calculate scientific quantities from linear and non-linear graphs<br />You need to complete the following task<br />,[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Unit 6 using mathematical tools for science wrong table
- 3. Explain the trend in the graph you have plotted M5
- 4. Estimate the rate of growth by taking tangents at three different points on the curve D5
- 5. Explain what is happening to the rate of growth of the yeast cells P6Grading tips<br />When displaying data make sure that you label your graphs or charts, otherwise you will not meet P5. To achieve M5 you will need to cover the full timescale of your experiment, not just the start or the end, and explain possible reasons for the trend in your graph. For D5 make sure that you include the units and give your answer to the correct significant figures. For P6 make sure you use appropriate mathematical terminology.<br />Deadline _________________<br />Outline of evidence requirements<br />Assessment criteriaAssessment DescriptionEvidence needsAssignmentP1Carry out mathematical calculations using suitable mathematical tools6.1P2Carry out mathematical calculations using algebra6.1M1Use standard form to solve science problems6.1M2Use mensuration to solve scientific problems6.1D1Use ratios to solve scientific problems6.1D2Use algebra to solve scientific problems6.1P3Collect and record scientific data6.2P4Identify errors associated with collecting data in an experiment6.2M3Describe the process involved in accurately collecting and recording scientific data6.2M4Calculate any errors associated with scientific data collected in an experiment6.2D3Compare methods of data collected6.2D4Explain how errors can be minimized in data collected in the experiment6.2P5Select the appropriate formats for displaying the scientific data that have been collected6.3P6Interpret scientific data6.3M5Interpret the trend in the scientific data collected in an experiment6.3D5Calculate scientific quantities from linear and non-linear graphs6.3<br />