Course image: JÃ¶rg 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
Author(s): The Open University

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.

Author(s): The Open University

## Activity 2

Here is a poor example of mathematical writing, although the final answer is correct. Rewrite it, correcting the layout and the mathematical punctuation.

Author(s): The Open University

## Activity 33

The population of a village is 5481. Round this:

• (a) to the nearest thousand people;

• (b) to the nearest hundred people.

Author(s): The Open University

## Activity 24

For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result.

• (a) 22.12 Ã· 4.12

Author(s): The Open University

## 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

## Activity 14

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).

Author(s): The Open University

Sometimes it doesnâ€™t make sense to round to a specific number of decimal places. If, say, you were calculating the cost of fencing at Â£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 Ã— 185 Ã— 0.3048. (Conversion of feet to metres was given in Author(s): The Open University

Numbers are often approximated to make them easier to handle, but sometimes it doesnâ€™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 Â£24Â 695Â 481. Rounded to the nearest 10, it's Â£24Â 695Â 480; and to the nearest 100, it's Â£24Â 695Â 500. But Â£24Â 695Â 500 is still a complicated number to deal with in your head. That's why it was rounded to Â£25 000 000 in the newspaper
Author(s): The Open University

In this section, we revisit the construction of surfaces by identifying edges of polygons, as described in Section 2. Recall that, if we take any polygon in the plane and identify some of its edges in pairs, then we obtain a surface. When specifying how a given pair of edges is to be identified, we choose one of the two possible re
Author(s): The Open University

In Section 2 we start by introducing surfaces informally, considering several familiar examples such as the sphere, cube and MÃ¶bius band. We also illustrate how surfaces can be constructed from a polygon by identifying edges. A more formal approach to surfaces is presented at the end of the section.

Figure 3 shows
Author(s): The Open University

The main teaching text of this course is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click the link below to open the workbook (PDF, 0.4 MB).

workbook

Click the link below to open the answerbook (PDF, 0.2 MB).<
Author(s): The Open University

The main teaching text of this course is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click the link below to open the workbook (PDF, 0.2 MB).

workbook

Click the link below to open the answerbook (PDF, 0.1 MB).<
Author(s): The Open University

After studying this course, you should be able to:

• create simple models, given a clear statement of the problem

• identify the simplifying assumptions that underpin a model

• identify the key variables and the parameters of a model

• apply the inputâ€“output principle to obtain a mathematical model, where appropriate.

Author(s): The Open University

1 Calculate the area of a carpet in a model house if the real carpet has an area of 22 m2. On the scale used, 1 cm represents 0.25 m.

(a) Since 1
Author(s): The Open University

What is a volume? The word usually refers to the amount of three-dimensional space that an object occupies. It is commonly measured in cubic centimetres (cm3) or cubic metres (m3).

A closely related idea is capacity; this is used to specify the volume of liquid or gas that a container can actually hold. You might refer to the volume of a brick and the capacity of a jug â€“ but not vice versa. Note that a container with a particular volume will not nec
Author(s): The Open University

1 Find the area of a circle of (a) radius 8 cm, and (b) radius 15 m.

• (a)

Author(s): The Open University

1 Find the area of each of these shapes.

Author(s): The Open University

Drawing circles freehand often produces very uncircle-like shapes! If you need a reasonable circle, you could draw round a circular object, but if you need to draw an accurate circle with a particular radius, you will need a pair of compasses and a ruler. Using the ruler, set the distance between the point of the compasses and the tip of the pencil at the desired radius; place the point on the paper at the position where you want the centre of the circle to be and carefully rotate the compass
Author(s): The Open University

## Question 1

Find the area of a circle of (a) radius 8 cm, and (b) radius 15 m.