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3.6 Additional practice

Here is a mixed bag of exercises, in case you feel that you need more practice. Do the exercises which you feel will help you.


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3.5.1 Try some yourself

1 Give the appropriate rounding for each of the values below:

  • (a) Carpet floor area = 26.456 sq metres

  • (b) Interest earned = £109.876 5439

  • (c) Bill for £84.90 shared by
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1.3.6 Weighted mean

The concise formula that you have just used is useful in itself for calculating a mean when you are given data in frequency form. But, even more useful, it can be extended, leading to the idea of a weighted mean, that has many applications, as you will see.

Example 5: Assignment scores


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1.2.3: A typical shopping basket

This subsection discusses using a typical basket of goods to analyse price changes over time. However, what is meant by ‘typical’?

Think back to the last time you went shopping. What did you buy? The electric light bulbs that you have just stocked up on are unlikely to be in your shopping basket next week, whereas milk may well be there every week. And there may be items—a new toothbrush for example—that you buy from time to time, but not this week.

To monitor price change
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Introduction

This Unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You will also look at the important statistical and mathematical ideas that contribute to the construction of a price index.

In order to complete this Unit you will need to have obta
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6.5.1 Another ‘making a lawn’ solution

Example 18 Making a lawn

Suppose you have some friends who are planning to put a new lawn in their garden. The lawn is to be 12 m by 14 m and they have a choice of either laying turf or sowing grass seed. You have been asked to help them decide between the two.

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6.3 Solving the riddle of St Ives

Write out your own solution to the following problem.

Example 17: St Ives

As I was going to St Ives

I met a man with seven wives.

Each wife had seven sacks.

Each sack had seven cats.

Each cat had seven kits.

Kits,
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4.2 A better solution

Here is an improved solution which shows working.

Example 13

Suppose you plan to redecorate your bathroom. The end wall has the following shape, with dimensions as shown on the diagram. The quality of the plasterwork is not good and you are considering tiling the wall.

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3.3.1 Try some yourself

1 If tomatoes cost 75 pence per kg, how much would 1.45 kg cost in pounds (£)?

Answer

The formula is

cost of tomatoes = (price per kilogram) × (number of k
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3.2 Using formulas

Formulas are important because they describe general relationships, rather than specific numerical ones. For example, the tins of paint formula applies to every wall. To use such a formula you need to substitute specific values for the general terms, as the following examples show.

Example 8

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2.6.1 Arithmetical symbols

You will have already met the symbols for the basic arithmetical operations, which are +, −, × and ÷, but you may not have met some of the alternative ways of writing × and ÷.

To recap, the main symbols for arithmetical operations are:

There are other alternati
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2.3.1 Try some yourself

1 In the following two pieces of mathematical writing, remove or replace any inappropriate equals signs, and add link words and punctuation to help somebody else understand the mathematics.

  • (a)


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1.8.9 A mathematician’s journey

Distance-time graphs can show more than one journey on the same graph. The journeys do not have to start from the same place, or start at the same time, but all times and distances must be measured from a common origin along a common route. In this subsection, you will see how drawing a distance-time graph can help in planning a journey.

Bob and Alice both work for the Open University. Bob lives in Edinburgh in Scotland and Alice lives in Milton Keynes in England about 510 kilometres to
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Acknowledgements

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

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.

The material acknowledged below is Proprietary and is made
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12 Dividing decimal numbers by moving the decimal point

Doing division when decimal numbers are involved is the same as doing divisions involving whole numbers, with a few extra steps to take care of the decimal point.

Either the number you are dividing into or the number you are dividing by, or both of them, may be a whole number or a decimal number. So, for example, you might want to do the following divisions:

  • Example 1: 49.26457 ÷ 8
  • Example 2: 2.601 ÷ 1.22
  • Example 3: 678 ÷ 27.3
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1.1.3: USA workforce

The data set in Table 2 comprises the figures published by the US Labor Department for the composition of its workforce in 1986. It shows the average numbers over the year of male and female workers in the various different employment categories and is typical of the kind of data publ
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3.5 Maths in archaeology

In several different parts of the world, footprints from prehistoric human civilisations have been found preserved in either sand or volcanic ash. From these tracks it is possible to measure the foot length and the length of the stride. These measurements can be used to estimate both the height of the person who made the footprint and also whether the person was walking or running by using the following three formulas:

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“Reconceptualizing the Question: Intervention Strategies” (video)
Myerson & Sahlins photoA presentation and discussion with University of Chicago Professors Roger Myerson, Department of Economics & Marshall Sahlins, Department of Anthropology. Roger Myerson: "A Field Manual for the Cradle of Civilization" Marshall Sahlins: "On the Anthropology of the Counterinsurgency Field Manual" Part of the April 2009 conference on "Reconsid
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Staff Service Awards Slideshow (March 20, 2012)
Slideshow of staff at the University of Richmond.
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1.5.3 Labelling

Official language about informal carers is at variance with the way we normally talk about family life. How many children or young people who care – for parents or other relatives – would spontaneously label themselves a ‘young carer’? How many parents would describe their son or daughter in this way? How many people who frame census questions would have thought of including a question to find out, until ‘young carer’ became a category like ‘disability’ or ‘age’ that censu
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