Poor Examiners - they are only HUMAN! (Bless 'em)

An acquaintance of mine phoned me the other day and said his son had just got an Unclassified in his mock GCSE Maths exam and he desperately needed a Grade C to get on the course he wanted to study at the Sixth Form College. Could I give him some lessons, please?

To be honest, it's something I'm trying to give up, but as I knew him reasonably well I agreed.

When I first met his son I gave him a past GCSE Foundation level paper to complete and asked him to post it to me so I could mark it and see what his problems were before we began the lessons.

I could see straight away why he had obtained no more than a Grade U. He had made every mistake in the book.

Stop and think for a moment about all the things your teachers tell you that you must do in the examination to get the best possible mark - show all your working, write so the examiners can read what you have written, show the units of your answer where necessary, read the questions properly, draw construction lines accurately with a sharp pencil and so on and so on.

He hardly did any of these. And when he had to write a sentence as an answer to a question, what he wrote wasn't even proper English. It made me wonder how he will get on in his English examination too.

What you must realise is that the examiners are HUMAN BEINGS. They are the people that will be marking your papers and many of them are teachers just like your own. They have arguments with their husbands/wives/partners. They wake up with headaches. They see that pile of examination papers they have to mark and think about their friends who have the time to be going out or having an early holiday while they have to sit and home at mark them to a deadline. (Typically, an examiner will have something like 400 papers to mark!)

Now I'm not suggesting that the examiners don't do a very good job of marking - they generally go to great pains to do so, but there must be times when a candidate is not awarded a mark he/she may deserve simply because it is buried in some rubbish he/she has written and the examiner can't find it. That may be the mark the candidate needs to push them up to the next grade. And that could be you!

Every year a great number of candidates are just a couple of marks off getting the grade they really want simply because they did not follow the advice of their teacher. I wish I had a pound for every student of mine that had said, 'I know I don't do it now, but I will in the exam, sir.' The truth is they never do because they are so nervous about the exam, everything they thought they would do, but haven't practised, just goes out of the window.

I wish I could show you a pile of typical examination papers. You would be surprised at just how bad some of them are. Many of these candidates could easily score many more marks than they do and a great number could push themselves up not just one grade, but often two. There are thousands of candidates who get a Grade D who could easily get a C or even a B with a bit of effort.

So please make sure this isn't you:

Revise, revise, revise.

Make sure you have all the right equipment for the examinations.

Write in proper sentences when you need to explain an answer.

Draw construction lines accurately with a sharp pencil.

Read the questions properly and make sure you answer the question on the paper - not one you have made up yourself.

Time your answers so you don't spend too long on any one question.

Show all your working.

Give those examiners an easy ride. Sometimes an examiner has to decide whether what you have written deserves a mark or not. If they are in a good mood because your paper shows that you really care about your work, they are much more likely to give you the mark - it's only human nature.

Pythagoras and Trigometry

Higher Level Students: Please go down further to your section.

Foundation Level. At the Foundation level there are no questions on Trigonometry (sines, cosines, tangents and all that stuff), but there is plenty to be careful about with Pythagoras’ Theorem.

Questions on Pythagoras are normally very easy to get if you know what you are doing because there are only a small number of ways these questions can be asked and if you have lots of practice, you are almost guaranteed to get full marks.

1. The first thing to remember is that Pythagoras’ Theorem can only be applied to right angled triangles, but sometimes you sense the question is about Pythagoras’ Theorem, but there is no right angle in sight (or at least not where you want it to be). However, a right angled triangle can normally be found if you look carefully enough.

One common example is that you are given an isosceles triangle. This may be the front of a tent or a flag pole held up with cables, for example. The thing to do here is to draw a line down the middle of the isosceles triangle and, bingo, you have two identical right angled triangles!

In this tent front, for example, drawing a line down the middle gives two right angled triangles 1.5 metres wide and 2.5 metres high. Now you can find the length of the hypotenuse or the area of each triangle.

Another typical variation is to be given a small building such as a shed or lean-to. Here, drawing a line parallel to the floor and passing through the lowest point of the roof gives a right angled triangle.

This construction line gives a right angled triangle 0.7 metres high and 5 metres wide (same as the floor).

Now you can calculate:

a) The sloping length of the roof using Pythagoras’ Theorem √(0.7² + 5²) =  √25.49 = 5.048 = 5.05 metres (3 Sig Figs)

b) The area of the triangle ½ x 0.7 x 5 = 1.75 square metres

c) The area of the rectangle 1.9 x 5 = 9.5 square metres

d) The total area of the side of the building 1.75 + 9.5 square metres.

How easy is that?!

Sometimes you have an isosceles triangle on top of a rectangle as in the frontage of a typical garage:

I am sure you can see now how to divide this with a single horizontal line into an isosceles triangle similar to the tent shape and a rectangle. Then you can divide the triangle into two right angled triangles by dropping a vertical line from the top (apex) of the garage roof.

Then you can calculate anything you like: the length of the roof, the area of the triangles and the area of the rectangle. From the last two you can calculate the area of the whole of the front of the garage.

Other examples include questions involving bearings, sightings from the tops of cliffs etc, but there must be right angled triangles in there somewhere which you can find by just adding a few construction lines.

If not, it’s not a Pythagoras question. But if you think about it, what other methods have you been taught to calculate the lengths of lines in these types of diagrams? There aren’t any others.

Need some questions to practise? Go to www.gcsemathematics4u.com

Higher level

Please make sure you are familiar with the ideas in the Foundation Level discussion above. Remember that the Higher Level syllabus includes all of the Foundation Level syllabus!

If you are taking the higher level, you have an additional problem that the Foundation Level students don’t have. You know two ways to solve problems involving right angled triangles, Pythagoras’ Theorem and trigonometry, so the first thing you need to decide is which one to use.

This is surprisingly easy (and pretty obvious once you have realised it). If the triangle involves angles and you are either asked to find the length of a side or the value of an angle, it’s normally trigonometry. If there are no angles mentioned and you are not required to find one it must be Pythagoras’.

But you need to be careful. Sometimes you are given angles as well as the lengths of sides because the questions have more than one part. In the first part you may be asked to use two sides to find a third (which is obviously Pythagoras) and in another part you may need to use the angle information or find an angle (which is trigonometry). So you need to think very carefully about which information you need for each part of the question to help you decide whether to use trigonometry or Pythagoras’ Theorem.

But that’s why it’s called Higher Level.

You, too, may have all sorts of questions where you need to draw some construction lines as with the Foundation Level questions, plus some of your questions may need the answer from one part to calculate the next part or may use the same idea twice in one question. Bearing questions are a good example of this, where a ship, for example, makes the first part of its journey on one bearing and then changes direction for the second part:

Here we have a boat sailing 25 Km on a bearing of 124⁰ and then 32 Km on a bearing of 38^o.    Normally we are asked to find the total distance travelled east and the total distance travelled north etc. A few construction lines will soon give you all the right angled triangles you need:

As with the Foundation level, these are easy marks to get because the number of variations is limited and if you practise them enough you will sail thorough them (sorry about the pun!).

Need some questions to practise? Go to www.gcsemathematics4u.com

GCSE Maths Resits – Who wants them?!

The worst thing in your educational life is to have take a resit. Why? Because it’s lonely and it’s very frustrating. Quite a number of people do not get the grade they want and many do not care. But you are here, so you do care and that means that if you do not get the grade you need you will almost certainly have to take a resit next year. If your friends have the grade they needed and are free to get on with their next set of studies, you will be feeling a bit left out, having to do that extra work that would be unnecessary if only you had tried a bit harder this year

.

There is also the sad fact that although many people do pass a resit, not as many do as you might think. They simply don’t have the motivation to go through the whole examination process with all its associated revision again.

So please make sure you don’t find yourself in that position. Remember that a few extra marks can often push you up over a grade boundary. If you only do what everyone else does in the way of revision, you might get, say, 37% when you need 40% to get the grade you want. By working that bit harder now you can easily get that extra three or four marks and achieve the grade you deserve.

You have been studying mathematics since you were about five years old. Why throw it all away now? 

Alan Young

Publish Post

GCSE Calculator

Which GCSE calculator should you use? The answer is simple - use the calculator your teacher recommends. Schools go to great trouble to choose calculators that are right for you and right for the syllabus you will be studying, so why buy a different type?

And there's another reason for buying the one recommended by your school and that is simply that it makes it a lot easier for your teacher if everyone is using the same model. He/she can tell you which buttons to press if you are not sure without having to visit your desk and waste precious time that could be better used teaching you something that will get you extra marks in the exam. If you are learning how to use a new function on your calculator, your teacher can take the whole class through the process together step by step.

But there's plenty more to say about calculators than that. First of all you should love your calculator and get to know it like you know the back of your hand. The last thing you want to be doing is trying to work out which keys to press in the middle of the examination. You should automatically know which keys to use for each function and you should also know which keys not to use. Remember that scientific calculators are not designed just for GCSE - they can also be used for A-Level and higher maths and so have functions that you will not use unless you study maths at this level.

You will know, of course, that there are two kinds of calculators: simple and scientific and they differ in how they treat mixed calculations. Suppose you have a sum such as 4 + 7 x 5. Technically (that is using the BODMAS rule) you should work out 7 x 5 first because multiplication is always done before addition, and then you should add the 4 at the end. A scientific GCSE calculator will do this automatically, but a simple calculator will do the 4 + 7 first and then multiply the answer by 5. So the scientific calculator will give the answer 39 (correct), but the simple calculator will give 55 (incorrect).

This is something you need to keep in mind for certain kinds of calculation such as finding the mean of a set of numbers. Suppose you need to find the mean of 23, 45, 67 and 98. With a simple calculator you must add up the numbers 23, 45, 67 and 98 and press the '=' key to get 233. Then you divide by 4 to get the correct mean of 58.25.

Now you might think a GCSE scientific calculator will take care of all this for you, but you would be wrong.

If you type 23 + 45 + 67 + 98/4 into a scientific calculator, it will think you only want the last number divided by 4 and the answer will be 159.5, which is obviously rubbish. With a scientific calculator you have two choices. You can either add up the four numbers first as with the simple calculator and then divide the answer by 4. Or you can put brackets around the addition part of the sum and divide by 4 at the end, like this: (23 + 45 + 67 + 98)/4 and this will give you the correct answer.

There are many other traps you can fall into too. Now perhaps you can see how important it is to be really familiar with your calculator before you go into the examination.

Now here's a strange thing. Have you ever thought of buying two calculators of the same type? Probably not. Well, it's a very small chance, but you could misplace your calculator just before the exam or have it stolen by some unscrupulous person who has not bothered to get their own. What are you going to do then? 

With the price of calculators at just a few pounds each these days, you could easily have two just as you would take two pens, pencils etc into the exam. I am always flabbergasted by the number of people who will spend hundreds of pounds on something like an XBox 360, but skimp on buying essential equipment for an examination or the very best revision material. Still, that's human nature I suppose.

So, make sure you know your calculator inside out and treat it as your best friend - at least until the exams are over.

GCSE Mathematics - Getting Ready

Some of you will be on the modular courses in which you sit examinations at regular intervals and some will be on the do or die courses in which everything depends on the results of the final examinations at the end of your course. Whichever you are on, there are a number of things you can do to make sure you get the best grade you possibly can. As a teacher I have seen time and again students turning up to examinations (examinations that will affect the rest of their lives) with no calculator, no ruler, only one pen etc. And some of them even arrive late without good reason.

All this indicates a very poor attitude and these people are often the ones who have not bothered to revise very much either.

The fact that you are subscribed to this blog tells me that you are unlikely to be in this group, but even so you might not be sure how to proceed or you might make a serious mistake without realising it. For example, many students stay up far too late on the night before an examination revising, thinking that they can cram in that last fact or two that is going to make all the difference to their results. What actually happens is that they turn up for the examination far too tired to produce their best work and, particularly in mathematics, they cannot get their head around problems that they would normally find quite easy to tackle. If you begin your revision early enough you will know just about everything you need to know to tackle the papers efficiently.

So here are some general guidelines that I hope you will find helpful:

1. Download the GCSEMathematics4U Revision Guide which gives you good advice about how to separate the planning of revision from the revision itself and shows you how to tackle revision in small sections in a non-stressful way. If you follow this advice you will be surprised at how much extra work you will cover compared to that of other students and what a head start that will give you!

2. Make sure you get a fair bit of exercise. If you are a fitness fanatic you will be doing this already, but if you are a bit of a couch potato who spends far too long on your computer playing with Facebook, then put it away and get some exercise instead. Do what you like to do. Whether it is just a walk, a run, a game of tennis - it doesn't matter. The point is that exercise puts oxygen in your brain and that helps with the thinking process, so do some between your revision sessions. It's obvious really, but it's surprising how many people don't do it. And try to get a little exercise just before an examination too. A quick walk around the block or walking the last kilometre to school will put enough oxygen in your brain to give you a burst of intellectual energy during the examination.

3. Revise with a partner if you can. When I was taking my last examinations at Uni, a friend and I 'borrowed' a blackboard from a store cupboard and set it up in my room. We had many sessions together working through problems and I know it helped us both. When one was stuck, the other could help. We could discuss in detail why our method worked instead of just being happy with getting the answer right. This helped us with other similar problems, of course.

4. Make sure you have all the right equipment. I shall have more to say about calculators in particular in a later posting, but please remember that mathematics is a subject that needs equipment (like a good ruler with no dents along the edges!), so make sure you have yours all in good condition.

5. On the night before an examination, by all means look up a fact or two that are worrying you, but don't do any more than that. Make sure you get a good night's sleep - that will help you far more than anything else.

And lastly (and this is a point I shall mention in these posting more than once) remember this:

If you only do what everyone else is doing, you will only achieve what everyone else achieves. If you want to get a higher grade, you need to do that bit more. Unfortunately, most people only realise this far too late in life. Please don't be one of those people!