Learning outcomes By the end of this unit you should be able to: evaluate the squares, cubes and other powers of positive and negative numbers with or without your calculator; estimate square roots and calculate them using your calculator; describe the power notation for expressing numbers; use your calculator to find powers of numbers; multiply and divide powers of the same number; understand and apply negative powers, t
3.3.1 Try some yourself 1 Look at the diagram below and answer the following questions: (a) Write down the coordinates of the points P, Q, R, S and T. (b) On this diagram, 3.1.1 Try some yourself 1 Write down the coordinates of A and B. 2.3.1 Try some yourself 1 This table categorises Tom's activities for the day. 2.3 Pie charts Pie charts are representations that make it easy to compare proportions: in particular, they allow quick identification of very large proportions and very small proportions. They are generally based on large sets of data. The pie chart below summarises the average weekly expenditure by a sample of families on food and drink. The whole circle represents 100% of the expenditure. The circle is then divided into ‘segments’, and the area of each segment represents a fraction or pe 2.2.1 Try some yourself 1 Consider the table about household sizes. 2.2 Tables and percentages Tables often give information in percentages. The table below indicates how the size of households in Great Britain changed over a period of nearly 30 years. 2.1.1 Try some yourself 1 The table below indicates the cooling rate of tea in a teapot. 2.1 Tables Experiments or surveys usually generate a lot of information from which it is possible to draw conclusions. Such information is called data. Data are often presented in newspapers or books. One convenient way to present data is in a table. For instance, the nutrition panel on the back of a food packet: 1.1.1 Try some yourself 1 On the plan of the bathroom in Example 1, what is the width of the window and 1.1 Understanding scale diagrams Plans of houses and instructions for assembling shelves, etc., often come in the form of scale diagrams. Each length on the diagram represents a length relating to the real house, the real shelves, etc. Often a scale is given on the diagram so that you can see which length on the diagram represents a standard length, such as a metre, on the real object. This length always represents the same standard length, wherever it is on the diagram and in whatever direction. 1 Modelling with first order differential equations The main teaching text of this unit 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. When prompted after exercise 2.2 to watch the video for this unit, return to this page and watch the four clips below. After you've watched the clips, return to the workbook. Click 'View document' to open the workbook (PDF, 1.0 MB). Learning outcomes After studying this unit you should be able to: understand and use the basic terms for the description of the motion of particles: position, velocity and acceleration; understand, use and differentiate vector functions; understand the fundamental laws of Newtonian mechanics; solve mechanics problems in one dimension by drawing a sketch, choosing a suitable x-axis and origin, drawing a force diagram, applying Newton’s second law, tak Introduction This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers. This unit is an adapted extract from the course Author(s): 1 Modelling with Fourier series The main teaching text of this unit 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 'View document' to open the workbook (PDF, 0.6 MB). 1.5 Exercises A vector a has magnitude
|a| = 7 and direction
θ = −70°.
Calculate the component form of a, giving the components
correct to two decimal places. 1.4.2 Displacements and bearings The displacement from a point P to a point
Q is the change of position between the two points, as
described by the displacement vector
If P and Q represent places on the
ground, then it is natural to use a bearing to describe the
direct 1.1: Converting to component form In some applications of vectors there is a need to move
backwards and forwards between geometric form and component form; we
deal here with how to achieve this. To start with, we recall definitions of cosine and sine. If
P is a point on the unit circle, and the line segment
OP makes an angle θ measured anticlockwise
from the positive x-axis, then
cos θ is the x-coordinate of
P and sin θ is the
y-coordinate of P ( Bibliography Ahmed, A. (1987) Better Mathematics, London, HMSO. DfEE (2001) Key Stage 3 National Strategy: Framework for Teaching Mathematics: Years 7, 8 and 9, London, DfEE. NCTM (1989) Curriculum and Evaluation Standards for School Mathematics Reston VA, National Council of Teachers of Mathematics. 1.1 Workbook contents The main teaching text of this unit 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. Section 4.2 of the unit requires you to listen to some audio files. You'll find these on the next page of this unit. Click on 'View document' to open the workbook (PDF, 4 MB).
Activity Time/hours
Number of people in household 1961 (%) 1971 (%) 1981 (%) 1991 (%) 1<
Time/mins
Nutrition Information
Exercise 1
