GCSE MATHS REVISION Foundation Level Introduction Hello, my name is Alan Young and I would like to welcome you to the very best GCSE Mathematics Revision course on the planet. I want to begin by asking you how important a good grade in your GCSE maths is to you. There is a grade that you are capable of achieving and at the Foundation Level I hope that is a grade C. Given the right materials and a bit of effort, you really can achieve this grade this year. The important thing is to start right now with your revision, even if you have not yet finished covering the syllabus at school or at home, and in this movie I want to show you why the MathSphere material really is head and shoulders above anything else you will find. There is a lot of revision material available in bookshops and on the internet, of course, but there are two problems with all this material. Problem 1 Firstly, the number of examples they give you to practise with is very small and never enough to truly get your teeth into. Problem 2 Secondly, apart from a few questions involving proofs, there is virtually no working out to be seen. They give you some questions and the answers, but the bit in the middle is mostly missing! This raises a very important point: What do you do when you are stuck on a problem and, even after you have looked through the theory, you still cannot see how to apply this to the questions? I am sure this is an experience you have had many times already. You may also have had the experience that some of the revision material available is not even bite sized, it's barely a nibble! What you need is something much more chunky something that shows you the essential processes in solving problems and leads you through the solutions step by step.
MathSphere material gives you complete model answers for a great number of questions. Not only that, it explains the theory being used in the context of the questions and in many cases gives alternative methods and hundreds of hints and tips. Let me demonstrate this to you right now. If you have not already downloaded the Pythagoras Theorem module, please do so and refer to it while you follow through the guidance below. Foundation Level: Pythagoras' Theorem. So, let's have a look at the module. Pages 3, 4, 5 and 6 give you a range of questions to tackle, which we shall look at in a moment, and pages 7 to 19 give you the answers with full working out as promised. So, please take a look at page 3. Normally we do not give you any clues with the questions as explanations are included with the answers, but we have made an exception in this case. Normally we do not give you any clues in the question section, but there is one point that is so important we want to include it here at the beginning of this section. It is this: When solving right angled triangles (that is, when you are trying to find angles or sides given some information about the triangle) you only have two sets of tools available Pythagoras Theorem and Trigonometry there is nothing else. If you have this type of question in the examination, which you are almost certain to have, don t sit there scratching your head. Decide whether to use Pythagoras or Trigonometry and get on with the question. How do you decide? Easy! If the question does not involve angles you are not given angles and you are not asked to find angles given the three sides of a triangle it must be Pythagoras Theorem. If you are given angles to use or are asked to find an angle, you should use Trigonometry. Simple as that!
One of the problems that many people have when they get a question involving right angled triangles is deciding whether to use Pythagoras' Theorem or Trigonometry or something else they can't quite remember. The first speech bubble clears up this confusion by telling you that the only tools you have are Pythagoras' Theorem and Trigonometry and that there is nothing else you can use. That makes it a simple choice between the two. You are also told how to decide. Basically, if the question includes an angle - either you are given one in the question or you are asked to find one you need to use trigonometry. If no angle is mentioned then you need to use Pythagoras. The other clue with Pythagoras' Theorem is that you will be given two sides of a right angled triangle and asked to find the third side. Having made that clear, you can now tackle the questions. You will notice that the questions are given roughly in order of difficulty. Question 2 gives easier examples in which the triangles are drawn for you. It is a simple matter of applying the theorem. 13 m z 12 m Notice, by the way, that part d) involves squaring 12 and 13. It is much quicker in the examination if you know the answers to these squares already as they come up very often. You do not have to waste valuable seconds typing them into your calculator. Question 3 involves drawing and measuring and then using Pythagoras' Theorem to calculate the hypotenuse in each triangle. You should be able to draw with an accuracy better than one millimetre, so the two answers should agree to within this accuracy. Questions 4 to 11 are in written form and you need to know what to do first, which is DRAW A DIAGRAM. I am sure your teachers will have told you this many times. Let me re-assure you by telling you that it is not just your teachers that say this, but every maths teacher in the country, so there must be a good reason for it, and that reason, of course, is so that you can make sense of the question. Question 12 is one of those questions that is quite difficult to describe entirely in words, so a diagram has been drawn to help you. 11 cm 11 cm 9 cm
It might be worth mentioning at this point that the examiners are not out to trick you. They are very experienced in setting GCSE questions and they have a very good idea when they need to draw a diagram to help you and when they can leave it up to you to draw one for yourself. If you know your stuff, you should be able to tackle all the questions with confidence. Mathematics is, therefore, one subject in which the best way to revise is to practise as many questions as you can. Okay, now questions 13 to 19 are beginning to get a bit tricky. If you look at them, you will notice that none of them involve angles, so we must still be with Pythagoras' Theorem here. Problem is that at first glance there are no right angled triangles and without those we are up a gum tree. So, we need to construct a right angled triangle from each diagram or described situation. Looking at Question 13, for example, we see a number of isosceles triangles and we need right angled triangles. So, what can you do to an isosceles triangle to get two right angled triangles? 13. What is the area of each of these isosceles triangles? a) b) 8.4 m 6.7 mm c) 4.3 mm 12 cm 12 cm 8.4 m 6.7 mm 10.2 m 15 cm I am sure you know the answer, but, if not, this is covered in the answers, of course. Now, let's take a look at the answers, beginning on page 7, and this is where MathSphere material is far superior to anything else you will find as we give you fully worked answers to all the problems. Firstly, notice that the final answers to calculations are normally written in a grey box. This is so that if you are very confident with a particular question, you can quickly check your answer to make sure you did not make a silly mistake. The answers are written out very much as you would be expected to write them out in the examination. Occasionally, you could miss out a particularly easy step, providing you are confident enough to handle it. But if you are in any doubt, always write down every step. You will never lose marks for writing down more than is necessary, but you might easily lose marks for missing out essential steps in the calculation.
In the GCSE mathematics examinations, in all but the simplest of questions, marks are given for working as well as getting the right answer. Examiners can only give marks for what they can see, not what they think you might have thought! And remember, a couple of lost marks could you drop you down a grade from the one that you really deserve. You will notice hints and tips scattered throughout the answers, normally in speech bubbles. If you look at the answer to Question 2, part b) on page 7, you will see a very useful piece of advice that if you are asked to round an answer to three significant figures (in this case a square root) you only need to write down the first four figures from your calculator to do the rounding. On those questions where you need to round to three significant figures when you take a square root, you need only write down the first four significant figures because you are only going to look at the fourth one to see if it is 5 or more. Any other figures you write down are going to be ignored, so what s the point? Some people write down every figure on their calculator. There is no point in doing this and it will use up a few more of those valuable seconds in the examination. In the answer to Question 3 at the top of page 9, there is a reminder that it is very important to label the points on the diagram. No letters were given in the question, so you can use whatever letters you like. If you think about it, some people will use A, B and C, some will use X, Y and Z and so on. Some people will use A, B and C going around the triangle one way and some the same letters going around the other way. How is the examiner going to know which points you are referring to in your answer if you do not label them on the diagram? The answer to Question 7 at the bottom of page 11 reminds you to be very careful when using Pythagoras' Theorem to make sure you know whether you should be adding the squares of the sides or subtracting them. I would estimate that more marks are lost by adding when you should be subtracting or subtracting when you should be adding than for any other reason. Why throw marks away?
7. 31 m 22 m x 2 = 31 2 22 2 = 961 484 = 477 i.e. x = 477 = 21.84 Distance of cable anchor from pole = 21.8 m (Corr to 3. S.F.) x Be careful about whether the question involves a subtraction or an addition and don t forget to correct your answer. In the answer to Question 12 on page 13 you are reminded to keep the examiner happy with good explanations. I can you tell from my years of marking papers that examiners have to mark quite a bit of utter rubbish! This is normally produced by people who think they know better than their teachers and that the examiners will somehow know what they were thinking and give them full marks for it. If you can't tell what the person next to you is thinking right now, how can an examiner be expected to know what you were thinking in the exam, perhaps several weeks before? General Comments Examiners are only human, believe it or not. Many of them are teachers just like your own. They have arguments with their partners, headaches and suffer from all the usual traumas of everyday life just as you and I do. The best way to please an examiner is to write your answers clearly, lay out your calculations in a logical way and label all your diagrams. I can promise you that if you do this, you will be way ahead of most of the other candidates in the country. So. I hope that now you have a good idea of how our revision modules work. There are a large number of questions. Try to answer as many as you can. Some you will find very easy and all you want to do is to check your answers. Some of the more difficult questions you will have some idea about, but perhaps lack the confidence to be sure your answers are correct. For these questions, have a go and try to get to the end of the question. Then take some time to go through our solution and check to see how it corresponds with your answer. If you did well after all, you can pat yourself on the back.
If you had a few difficulties, check to see where you got stuck and what to do about it. Then have another go a little later. Finally, there will be some questions you won't have a clue about. For these questions, it is always worth having a go first because there may be one or two parts that you can do. Can you draw a diagram that corresponds to the information in the question? Can you write Pythagoras' Theorem in relation to this question? When you have got as far as you can, even if it's just a very small way, take a long look at our solution and then immediately go back and have another go while it is still fresh in your mind. Have a third go a little later to make sure you can do the question now and check again to see that you have fully understood it and included all the necessary working. Whether you find the question moderately difficult or very difficult, do make sure you have another go later and, if necessary, a further go in a few days' time. Because examination mathematics involves convergent thinking, that is thinking that leads to a definite answer, and is generally made up of questions whose answers can be written down step by step, the best way to revise is to tackle as many questions as possible. That way you will quickly be able to identify the gaps in your knowledge. You won't be able to do that by reading your text book in bed. Reading a text book will certainly point out some things that perhaps you were not too sure about, but it is only by tackling questions that you will be able to pinpoint those specific difficulties that could hold you up with the longer questions. So, that's how it all works. By tackling the fourteen modules we have available for Foundation Level, you can very quickly improve your mathematical ability by identifying and rectifying points of weakness. If you would like another module to try, please fill in your name and email address on the home page of our website (www.gcsemathsrevision.net) and we will send you a link to another one and a pdf document giving you tips on how to revise and improve your grades. Don't worry, we keep email addresses confidential and never reveal them to anyone else. So, download the next module now and you will have two you can be working on. See how quickly you become more able and confident.