Second-order differential equations
This free course is concerned with second-order differential equations. Section 1 introduces some basic principles and terminology. Sections 2 and 3 give methods for finding the general solutions to one broad class of differential equations, that is, linear constant-coefficient second-order differential equations. Section 2 covers homogeneous equations and Section 3 covers inhomogeneous equations. Section 4 explains how extra information can be used to help to select particular solutions that ar
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Introduction to algebra
This free course is an introduction to algebra which builds on the idea of using letters to represent numbers. Section 1 looks at finding, simplifying and using formulas and includes useful tips on learning algebra. Section 2 introduces some of the terminology used in algebra and techniques such as evaluating and checking equivalence of expressions, identifying terms in an expression and collecting like terms. Section 3 looks at how to simplify terms and introduces index notation and multiplying
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This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.

Author(s): The Open University

Lastly consider division. Dividing 8 by 2 means â€˜How many times does 2 go into 8?â€™ or â€˜What must you multiply 2 by to get 8?â€™. The answer is 4.

So to find 8 Ã· âˆ’2, you need to ask â€˜What do I have to multiply âˆ’2 by to get 8?â€™. The answer is âˆ’4, since âˆ’2 Ã— âˆ’4 = 8.

So 8 Ã· âˆ’2 = âˆ’4.

Similarly, to find âˆ’8 Ã· âˆ’2 you need to ask â€˜what do I have to mul
Author(s): The Open University

## Activity 55

Author(s): The Open University

## Activity 52

Evaluate each of the following.

• Author(s): The Open University

## Activity 28

Look at the rules in the boxes above.

Write in your own words the rules for multiplying and dividing, adding and subtracting two numbers, giving an example of each.

Author(s): The Open University

## Activity 11

For each of the following shapes, indicate the fraction of the whole shape represented by the shaded parts:

Author(s): The Open University

## Activity 9

The diagram below shows an oatmeal cake marked into 12 equal portions. I want to give my sister a third of the cake. Where could I cut the cake, and what would be left over?

Author(s): The Open University

Itâ€™s important to remember that subtraction has different rules from addition.

For example, when you add up numbers, it doesnâ€™t matter what order you add them up in. So 6 + 4 is exactly the same as 4 + 6. The result is 10 in both cases.

But in subtraction, order matters. So 6 â€“ 4 is different from 4 â€“ 6.

With the first, you start with 6, subtract 4, and are left with 2.

But with the second you start with 4 and if you subtract 6, which is a bigger number, you a
Author(s): The Open University

Another way to say â€˜subtract one number from anotherâ€™ is to say â€˜one number minus anotherâ€™. And the standard sign to show this is a minus sign, which looks like this â€˜â€“â€™. The expressions â€˜take awayâ€™ or â€˜take fromâ€™ are also used to mean subtract or minus.

So the following expressions all mean the same thing:

• What do I get if I subtract 2 from 3?
• What do I get if I take 2 from 3?
• What is 3 take away 2?

• Author(s): The Open University

1. Data in the form of counts of individual entities (for example, people, animals, power stations) in a small set of discrete categories can be presented in bar charts or pie charts. For most purposes, bar charts are preferable. Pie charts draw particular attention to the proportions in which the entities are split between the different categories. However, they do so by representing the proportions by angles, and even when the main interest lies in the propor
Author(s): The Open University

## Activity 7 Health care personnel in Thailand: calculating percentages

Would it be helpful, in considering possible changes in the way health care personnel are divided into the five categories listed, to recalculate th
Author(s): The Open University

For the 23 infants who survived SIRDS, the lower quartile is qL =1.720 kg, and the upper quartile is qU =2.830 kg. Thus the interquartile range (in kg) is

qU â€“ qL = 2.830 â€“ 1.720 = 1.110.

For the 23 infants who survived SIRDS, the ordered birth weights are given in Table 9. The first quartile is

qL = x (Â¼(23+1)) = x (6) = 1.720kg.

The third quartile is

qU = x (Â¾
Author(s): The Open University

Figure 20 shows a histogram of waiting times, varying from about 40 minutes to about 110 minutes.

Author(s): The Open University

The second measure of location defined in this course for a collection of data is the mean. Again, to be precise, we are discussing the sample mean, as opposed to the population mean. This is what most individuals would understand by the word â€˜averageâ€™. All the items in the data set are added together, giving the sample total. This total is divided by the number of items (the sample size).

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## Activity 22

A friend has been quoted a price of Â£25.50 per square yard for tarmac surfacing of his yard. The yard measures 6 yards by 10 feet. Here is his calculation of the total cost. What is wrong with it?

cost =
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## Activity 21

Without using your calculator solve the following calculations.

• (a) 3 + 5 Ã— 2 = ?

• (b) 12 âˆ’ 6 + 6 = ?

• (c) 6 + (5 +
Author(s): The Open University

Author(s): The Open University