Maths

Equations Part 1

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

Equations and formulae are simply mathematical statements in which letters stand for numbers. They are a fundamental part of Algebra, a branch of Mathematics whose roots can be traced back to the ancient Babylonians in around 2000BC. We use equations to help us describe real life problems or situations. By generalising problems in this way, they can be easier to solve. In this title, we look at setting up equations and formulae, as well as solving equations using simple rules. We then move onto substituting values into formulae and re-arranging formulae. We also consider trial and improvement, which we use when the equation doesn't have an exact answer. Finally, we define inequalities and describe how to solve them. Don't forget to test your understanding using the questions that follow Chapter Six.

Equations Part 2 - Higher Level Only

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, we'll look at how both direct and inverse proportion are used and how the relationship between quantities can be defined. We then move on to solving quadratic equations by factorising, completing the square and using the quadratic formula. Remember, a quadratic equation is an equation in which the highest power of x is x squared. In Chapter 3, we'll look at different methods of solving simultaneous equations, including by elimination and by substitution. Please note that before listening to this title, you should feel confident expanding brackets and factorising, as well as being able to re-arrange and solve equations. You could listen to the Algebra titles 'Equations Part 1' or 'The Use of Letter Symbols' if you need help on any of these areas.

Graphs and Functions

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, we'll look at basic graph skills, including plotting coordinates. We'll then move on to drawing straight line graphs by plotting a set of coordinates in a table. These graphs can be given an equation in the form of y = mx + c. We'll explain what each part of this equation means, and will learn how to draw graphs from equations. We'll then discuss recognising and drawing quadratic graphs. For those sitting the Higher level paper, we'll also consider function notation and look at how to work out the equation of a circle from a graph.

Please note - Chapter 7 'The Equation of a Circle - Higher Level only' is not relevant to WJEC.

Sequences

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this Algebra title, we'll be looking at sequences. You'll find out how to recognise some common sequences, how to continue a sequence and then do more clever things still. These include looking for patterns and rules to help us predict the future, or maybe using those rules to generate a list of numbers in a sequence. We'll also consider how to make a number sequence from a visual pattern. If you're taking the Higher level paper, we'll show you how to deal with more complex sequences based on squared terms. Don't forget to 'Test Yourself' in the questions that follow Chapter Six!

The Use of Letter Symbols

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

Welcome to the wonderful world of algebra! Algebra is a word that seems to scare people for some reason. With the help of this title, you'll feel more confident using algebra. We'll cover four main reasons for using algebra and consider what you're allowed to do when adding, subtracting, multiplying and dividing with algebra. We'll look at how to simplify algebra and explain substituting numbers in place of letters. This title also includes information on how we deal with one or two sets of brackets, and looks at how we can put brackets back into expressions. For those sitting the Higher level paper, we'll show you how to factorise quadratic expressions. So let's get started, bearing in mind that algebra is not to be feared.

Averages

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

We can collect results from different areas, such as experiments or questionnaires. To look for trends or patterns in results, we look for a result that represents the data. This is called an average. There are three different types of average - the mode, the median and the mean - and each gives you a different view of the data. The range is often grouped with these values. It is not really an average, but it does give you a view of the data. This title considers how to work out averages, both from lists of data and from frequency tables. Chapter Three looks at how we work out the averages of grouped data. For those sitting the Higher level paper, Chapter Four considers comparing averages of several sets of data. You can then test your understanding with some questions on averages.

Data

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

The word 'data' just means information. Everyone uses data, even if they don't realise it. Millions of pounds are spent every year trying to collect and make good use of data. In this title, we'll look at types of data and why it matters so much. We'll also consider sensible ways of collecting data, while thinking carefully about who to ask and what we should ask them. We'll then look at some of the most common reasons for collecting data and get to grips with the key words. In terms of collecting data, we'll consider the benefits of sampling and the most appropriate techniques for doing this. There will also be a focus on stratified sampling for Higher tier students.

Probability Part 1

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

Probability is around us all the time and this title will help you to�understand it. We'll look at common words used in probability and use numbers on a scale to describe how likely things are to happen. We'll consider events that are equally likely and discuss how we might find all of the possible events. Sometimes, events are not equally likely, so we'll also think about how we can get around this problem by using relative frequency. We'll take a look at the differences between the theory of probability, and what happens when you actually try some experiments. Finally, we'll consider the phrase 'mutually exclusive' and look at how this can help us. So, let's get started, as there's a high chance you'll find this title very useful.

Probability Part 2 - Higher Level Only

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, we'll look at whether you can get away with handing homework in late, how to win raffles and whether you should play fairground games. To do all of this, we'll use the power of probability. We're going to learn two useful tricks that reduce the amount of work we have to do. These are the 'and' rule and the 'or' rule. We'll also look at how to draw tree diagrams and use them to find different probabilities. Don't forget to test yourself in the questions that follow Chapter Two.
You may wish to listen to �Probability Part One' before listening to this Higher level title.

Ways of Presenting Data Part 1

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In today's world, we take in overwhelming amounts of data, from the nutritional information on our breakfast cereal to the national debt. In order to make sense of this data, it is presented in a huge variety of ways. In this title, we'll cover the key methods for presenting data and look at what different graphs and diagrams tell us about the data they contain. Each type of diagram or graph is given an individual chapter, as we work our way through from basic bar charts to scatter graphs and correlation. You can then test your understanding in the questions that follow Chapter Eight.

Ways of Presenting Data Part 2 - Higher Level Only

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, we'll look at ways of presenting data using diagrams. We'll also look at measures of average and measures of spread. We use histograms when data is presented in groups that are not of equal size, so that the diagram in not misleading. We'll then explain cumulative frequency and look at how to draw cumulative frequency diagrams. We can use these diagrams to estimate the median value, as well as the lower and upper quartile values. The title then goes on to consider box plots. We'll look at how to draw this type of diagram, which highlights the minimum value, the lower quartile value, the median value, the upper quartile value and the maximum value in a sample. Finally, we'll discuss using moving averages, which allow us to analyse trends in data that has seasonal fluctuations.

Decimals

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title is dedicated to all things decimal. It progresses past the use of integer, or whole number, values to show you the infinite amount of numbers that lie between the 'counting' numbers. Recognizing the size of decimal numbers is considered first, combating the most common misconceptions and allowing you to order decimal numbers. Next comes the appreciation of number rationality - we ask, how can a number be considered rational or irrational? Once you understand what decimal numbers are, we can then consider their use in calculations, beginning with addition and subtraction, and then moving on to multiplication and division. Finally, some interesting facts about the use of numbers between 0 and 1 in calculations will be considered. Throughout this title, common exam-style questions will be explained to ensure your understanding, with a 'Test Yourself' section following Chapter Six.

Fraction, Decimal and Percentage Conversions

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

It is important to understand the links between fractions, decimals and percentages, and the methods for converting between them. The title begins by looking at converting percentages and decimals to fractions, then moves onto converting from percentages and fractions to decimals. In Chapter Three, we consider converting from decimals and fractions to percentages. The next chapter details conversions that you'll be expected to know from memory in the exam. It then considers using our conversion knowledge in the context of ordering a variety of numbers, which may be shown as fractions, decimals or percentages. For those sitting the Higher Level paper, the title then looks at how recurring decimals can be converted into fractions. Finally, don't forget to try the 'Test Yourself' questions, so that you can test your understanding and be ready for your exams.

Fractions

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

Fractions are an important part of Maths and are often thought of as being difficult. However, you just need to remember a few tricks for the different types of fraction questions that you will be asked and they become a lot more straightforward. The chapters in this title are broken down into the different types of fraction question, taking you through step-by-step all that you need to know for the exam. Make sure you understand each chapter before moving on, as they build upon each other to progress to the more difficult fraction questions. For example, you will be unable to understand the addition and subtraction of fractions without first understanding equivalent fractions. You will also need to be confident with cancelling down, or simplifying, fractions throughout the title.�Don't forget to �Test Yourself' at the end of the title.

Integers

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title looks at numbers and the number system. We start by considering place value, before moving on to ordering whole numbers, including negative numbers. The title then explains factors, multiples and prime numbers. It is essential that you fully understand the difference between these 'grade D' topics, as they then progress onto the 'grade C' topics. These are finding the Highest Common Factor, or the HCF, and the Lowest Common Multiple, or the LCM, as well as using Prime Factor Trees to find the product of prime factors. If you are sitting the Higher level paper, you also need to know how to find the HCF and the LCM using Prime Factor Trees, which is covered at the end of Chapter Five. Finally, we have generated some typical exam questions for you to practise in the 'Test Yourself' chapter.

Number Operations Part 1

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title you'll learn about addition and subtraction, which are fundamental operations in Maths. Subtracting, or taking away, is simply finding the difference between two numbers. We'll examine techniques and strategies for whole numbers, decimals and simple fractions. We'll also consider multiplying and dividing by 10, 100 and 1,000. There are some simple rules to follow for this. Once you understand these, it then becomes easy to multiply or divide by any multiple of 10. The title then looks further at multiplication and division, which are essential skills that have been used in countless areas of Maths for thousands of years. You'll learn about methods to carry out a range of multiplication and division calculations involving whole numbers, decimals and simple fractions. Reciprocals are then explained - showing what they are and how they are used in Maths.

Number Operations Part 2

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title you'll learn about one of the most important areas of number work - the order of operations. You'll learn that the order in which we carry out any calculation is very important. Chapter 1 describes a simple set of rules that make sure that anyone doing a calculation does so in the same way. You'll see that these rules can be remembered really easily using the acronym BIDMAS, or BODMAS as it is also known. The GCSE�Maths exam is made up of a calculator paper and a non-calculator paper. It is important you understand how your calculator works in order to get the best from it. So we've dedicated a whole chapter to helping you use your calculator in complex calculations in number work.

Percentages

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title you'll learn about percentages. However, you probably know more about them already than you realize. We are surrounded by percentages in everyday life, whether it's in the news, in television adverts, in banks, shop sales or even the voting in television talent shows. But what does percentage actually mean? Well, quite literally it means out of 100, or parts per 100. So if you were to read that 75% of people in the UK own a computer, this means that 75 people out of every 100 own one. This also helps to demonstrate the relationship between percentages and fractions. 75% is simply the fraction 75 over 100. We can simplify this to three quarters by dividing the numerator and denominator, or the top and bottom, of the fraction by 25.

Powers and Roots

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title looks at powers, indices and roots, and this is a topic that can be tested on both the non calculator paper and the calculator paper. Chapter One looks at standard square and cube numbers, along with their corresponding roots. Indices, or powers, can be used to do calculations very quickly. Without a calculator, we follow the index laws and work out the highest common factors and lowest common multiples of different numbers. Standard Index Form, covered in Chapter Three, is a way of writing big and small numbers. This is one area that can occur on both papers. Chapter Four is for higher level only. Here, we consider how reciprocals can be written using negative indices. Finally, we have generated some typical exam questions for you to practise in the �Test Yourself' chapter.

Ratio and Proportion

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, we'll cover what ratios are used for, how to write them and how to simplify them. We'll explain how to share in a given ratio, as well as considering the unitary method of direct proportion. For those sitting the Higher level paper, we'll look at what inverse proportion means, how we can work out the constant of proportionality and we'll consider writing formulae that connects different variables. To help us explain all this, we'll be looking at wine gums, charities, boys, recipes, girls, toilet roll and starting up your own business, so there should be something for everyone! Don't forget to �Test Yourself' using the questions after Chapter Four.

Rounding and Estimating

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

Rounding numbers and quantities can be done in different ways. Firstly, to the nearest whole number, which is covered in Chapter One. Secondly, to decimal place value, which is considered in Chapter Two. Finally, numbers can be rounded to significant figures, which we'll look at in Chapter Three. All of these ways rely on the '5 rule' for rounding up or leaving numbers as they are. On the non calculator paper, you will be asked to estimate an answer. This is explained in Chapter Four and has very specific rules attached to it. In the Higher level paper, we are required to find upper and lower bounds, or simply to put a number back to its �un-rounded' state. Chapter Five details how we do this. Always remember to look carefully for the level of accuracy the question is asking for.

Surds (Higher Level Only)

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title is for those sitting the Higher Level paper. It considers surds - defining what they are, how they are used and how we manipulate them within expressions or equations. A surd is the square root of a number that cannot be expressed as a whole number. We'll learn the basic rules for adding, subtracting, multiplying and dividing surds. We then move on to simplifying surds by finding the largest 'perfect' square factor. Finally, we'll consider rationalising the denominator when a calculation involves surds. This means we'll learn how to get rid of any surds that are on the bottom line of any fraction, including when the denominator has more than one term in it. You can then �Test Yourself' on what you have learnt!

3D Objects

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title looks at 3D shapes and their properties. We consider whether certain shapes are prisms and how many vertices, edges and faces they have. You'll learn different ways of drawing 3D shapes and we'll look at how they can be built from a flat sheet of paper. We'll also discuss working out the surface area and the volume of certain 3D shapes. For those sitting the Higher Level paper, there are chapters on finding the surface area and volume of more difficult shapes, such as spheres, cones and frustums.

Angles

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title looks at the basics of angles, classifying them according to size, estimating their size, measuring them and drawing them. It goes on to explain how they are used in bearings and considers finding missing angles in various situations. It also looks at the angles in different polygons. As well as looking at angles in various contexts, there is also an explanation of using co-ordinates. Finally, you can �Test Yourself' on angles in the questions following Chapter Six, or try the additional tasks in the accompanying worksheet.

Circle Theorems - Higher Level Only

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title begins by revising circle definitions, including the terms radius, chord and segment. It then looks at various theorems. These are facts about the angles created in circles when certain lines meet. For example, did you know that when a tangent and a radius meet, they do so at an angle of 90 degrees? We also look at proving certain theorems. Once you've listened to the proof of a theorem, have a go at proving it yourself. It will help you to remember the theorem if you practice doing this.

It would be useful if you revised circles, angles and Pythagoras' theorem before listening. Please note that it is essential for you to view the supporting images in this title, due to the difficult concepts they explain.

Circles

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, you'll learn the meanings of various names we give to parts of circles. For instance, segment and major arc. You'll also find out how you can draw any regular polygon accurately inside a circle. The 'Test Yourself' section following Chapter Two gives you a chance to practice what you've learned. Make sure that you have a pair of compasses, a protractor and a sharp pencil to hand while you listen.

Constructions and Loci

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title is about drawing things accurately. We start by looking at scales and how we can use them. For example, we consider how to find out what a distance on a map represents in real life. We also look at how we can use a pair of compasses, a straight edge and sometimes a protractor, to cut lines and angles in half and to draw triangles accurately. We then consider drawing plans that illustrate loci. We use all of these skills to complete a variety of tasks throughout the title. You can then Test Yourself in the questions following Chapter Six.

Measures

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

In this title, we�re going to consider the common units of measurement for length, mass and capacity. We�ll also briefly look at how these measurements came to be used. We�ll then consider what happens when we combine measurements together to get compound measures. Finally, we�ll define the term �3D� and discuss how this relates to measurements and formulae. If we keep our eyes open, we may even find the mystical fourth dimension!

Perimeter and Area

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

It is very important to recognise the difference between perimeter and area, so this title will define these terms. Chapters One and Two consider perimeters of squares, rectangles and circles. The perimeter of a circle is called its circumference. Circles rely on diameters and radius. Half a diameter is a radius, often mixed up by students. Circles also use pi, which is often rounded to 3.14 in exam papers. The title then looks at finding the areas of squares, rectangles, triangles, parallelograms and trapeziums. Formulae start to be used here, which are put into simple terms to help you remember them. Chapter Four shows how circle areas are worked out. All these shapes can be joined together to form compound shapes. Chapter Five stresses the ideas of strategies and sketches to earn method marks to solve compound area problems.

Pythagoras' Theorem

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title looks at how we use Pythagoras' theorem. Pythagoras' Theorem applies to right angled triangles, and allows us to work out a missing side if we know two of the sides. We consider this theorem using different examples, including some real-life situations. For those sitting the Higher level paper, we then move on to consider using Pythagoras' Theorem in 3D objects, such as cubes and cuboids. You can then �Test Yourself' using the questions that follow Chapter Three, and by using the accompanying worksheet.

Transformations and Vectors

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

This title considers symmetry and tessellations. It then moves on to look at properties of shapes and how transforming shapes affects them. It explores reflection, rotation, enlargement and translation in detail. Congruence and similarity, as well as vectors, are also covered. It's important to work as neatly as you can when drawing diagrams and to make sure that you have the necessary equipment available. For example, a sharp pencil, ruler and tracing paper. The title deals mostly with 2 dimensional shapes. A small section of the chapter on symmetries refers to 3 dimensional shapes. But otherwise, when a shape is referred to, the assumption is that it's a flat, 2 dimensional shape.

Trigonometry - Higher Level Only

feeds@gcsepod.co.uk (GCSEPod Feeds) — Thu, 01 Jan 1970 01:00:00 +0100

Pythagoras' Theorem allows us to find missing side lengths in right-angled triangles. Trigonometry enables us to find out areas, missing angles and missing sides, not just of right angled triangles, but of any triangle. This all revolves around the use of the trigonometric functions, sine, cosine and tangent. These may seem difficult at first, but once you've seen and drawn their graphs and have practiced applying the functions to different questions, they'll be much more familiar.