Acknowledgements The content acknowledged below is Proprietary (see terms and conditions) and is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence Grateful acknowledgement is made to the following sources for permission to reproduce material in this course:<
Acknowledgements
Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence. The material acknowledged below is Proprietary and used under licence (not
1.9.1 Introduction The main aim of this section is to show an application of distance-time graphs in the operation of a railway service. You will need graph paper for this section. This section uses the video ‘Single track minders’ to illustrate how distance-time graphs are drawn and interpreted by the timetable planners of a small railway company, and shows the role of this graphical technique in planning a flexible service. Graphical representations of journeys have been used for over a centur
1.6.3 Don’t jump to conclusions Time-series graphs are popular with newspapers for suggesting and comparing trends. But showing how a single quantity varies with time is not the same as showing how two quantities vary, and then suggesting a link between them. 1.5.1 Mathematical graphs: special terms Mathematicians use some special terms to talk about graphs. Understanding and feeling confident with this graphical language is as much a part of mathematics as doing calculations, or working with formulas. By convention, the horizontal axis of a graph – the one running across the page from left to right – is often called the ‘x-axis’, and the vertical axis – the one running up the page – is called the ‘y-axis’, as in Author(s): 3.3 Time-series graphs: summing up So time-series graphs must be read with care. Adopt a questioning attitude when you are faced with a graph. Look carefully at the vertical axis to see just what the range of variation is, and at the horizontal axis to see what time intervals have been chosen. Ask yourself about the significance of this choice – what might be going on between each plotted point? You might question whether the plotted variation is significant or whether it is the result of expected fluctuations. What ab Acknowledgements Grateful acknowledgement is made to the following sources for permission to reproduce material in this course: The content is taken from an activity written by Marion Hall for students taking courses in Health and Social Care, in particular those studying K101 An Introduction to Health and Social Care. The original activity is one of a set of skills activities made available to all HSC students via the HSC Resource Bank. Except for third party materials and otherwise stated (see 7 Subtracting decimals by lining them up Subtracting whole numbers such as 52 from 375 is fairly straightforward. Subtracting decimal numbers such as 6.892 from 223.6 uses the same process but with one extra step – you have to line the decimal points up first. Rather than arranging your two numbers so that they line up on the right-hand side, you need to line up the decimal points, regardless of how many numbers there are after the decimal point. In the example below, the top number has one number after the decimal point. It 11 Example of long division The example of 25546 divided by 53 is suitable for long division. First write the calculation down on paper in the same way you did before. 7 Dividing when you have to carry If the number you are dividing by does not go exactly (with no remainder) into the digit you are dividing into, you need to do something called carrying. Say you want to divide 952 by 7. The process is basically the same as in the previous section. First write it down on paper. Then, to do the calculation, you take each digit from the number being divided in turn, starting with the one on the far left, and see how many times the dividing number, 7 in this case, goes into it. The calcula 4.5: The mode The USA workforce data in Table 2 were usefully summarised in Figure 6, w Acknowledgements Course image: Jörg Reuter in Flickr made available under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence. Grateful acknowledgement is made to the following sources for permission to reproduce material in this course: The content acknowled 5 Approaches to problem solving You should not expect always to be able to read a problem and then just write down the answer. When you are faced with a written mathematical question or problem to solve, read it carefully. It is important that you get to grips with the question in two ways: first, that you absorb the information given; and second, that you find out what the question is really asking. Your solution will link the two. This method can be summarised by the following questions. 2.2.1 Try some yourself Here is a poor example of mathematical writing, although the final answer is correct. Rewrite it, correcting the layout and the mathematical punctuation. 3.6.1 Try some yourself The population of a village is 5481. Round this: (a) to the nearest thousand people; (b) to the nearest hundred people. 3.4.1 Try some yourself For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result. (a) 22.12 ÷ 4.12 Try some yourself Without using your calculator solve the following calculations. (a) 3 + 5 × 2 = ? (b) 12 − 6 + 6 = ? (c) 6 + (5 + 2.1.1 Try some yourself Measurement of a ceiling gives a length of 6.28 m and a width of 3.91 m. (a) Make a rough estimate of the area of the ceiling (the length times the width). 1.5 Significant figures Sometimes it doesn’t make sense to round to a specific number of decimal places. If, say, you were calculating the cost of fencing at £10.65 per metre, for a garden boundary, the length of which had been given to you as 185 feet, then you would want to multiply 10.65 × 185 × 0.3048. (Conversion of feet to metres was given in Author(s): 1.3 Rounding in general Numbers are often approximated to make them easier to handle, but sometimes it doesn’t help very much to round to the nearest 10 or the nearest 100 if the number is very large. For example, suppose the monthly balance of payments deficit was actually £24 695 481. Rounded to the nearest 10, it's £24 695 480; and to the nearest 100, it's £24 695 500. But £24 695 500 is still a complicated number to deal with in your head. That's why it was rounded to £25 000 000 in the newspaper
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