Notes, Exercises & Past Year Exam Papers

2012-07-15T21:03:00.000-07:00

Some Challenge probability problems

2010-09-27T10:21:00.000-07:00

1. A large basket of fruit contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana?

Solution:

Oranges = 3
Apples = 2
Bananas = 5

Total = 10

As they've asked either orange or banana, we ADD the probability.

Probability of orange + Probability of banana

3/10 + 5/10 = 8/10

                     = 4/5

2. In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student?

Solution:

Girls = 17
Boys = 13

A grade students = 5
Out of which, girls = 3 and boys = 2
So, 17 - 3 = 14 girls are not A grade students.

Therefore, probability of getting a girl or an A student:

14/30 + 5/30 = 19/30

3. In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wear a seat belt?

Solution:

The probability a person who wears a seat belt is selected = 43/100.

The probability that both of them wear a seat belt is :
43/100 * 43/100 = 1849/10000
   = 18%

4. Three cards are chosen at random from a deck without replacement. What is the probability of getting a jack, a ten and a nine?

Solution:

There are 52 cards in a pack. There are 4 suits i.e. clubs, spades, hearts and diamonds.

Hence, there will be 4 jacks, 4 tens and 4 nines.

Since the cards are selected WITHOUT replacement the total no. of cards will decrease by one each time. Hence,

4/52 * 4/51 * 4/50 = 8/16575

5. A city survey found that 47% of teenagers have a part time job. The same survey found that 78% plan to attend college. If a teenager is chosen at random, what is the probability that the teenager has a part time job and plans to attend college?

Solution:

47/100 * 78/100 = 1833/5000=37%

6. In a school, 14% of students take drama and computer classes, and 67% take drama class. What is the probability that a student takes computer class given that the student takes drama class?

Solution:

Drama = 67/100

Computer and Drama = 14/100

Hence, 67/100 * x = 14/100

Therefore, x = 14/67
                      =21 %

7. In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective?
Solution:

Defective TVs = 6

Total = 100

As the person buys two tvs, one out of hundred and one out of 6 gets subtracted, meaning:

6/100 * 5/100

= 30/9900
=1/330

Sec 2 past year paper for practice

2010-07-18T00:03:00.001-07:00

http://www.ziddu.com/download/10763255/sec2-chungchengsa2-mathsedited.pdf.html

http://www.ziddu.com/download/10763256/S2E_Mid-Yr_Ex_P1.pdf.html

http://www.ziddu.com/download/10763257/S2E_Final_Ex_P1.pdf.html

http://www.ziddu.com/download/10763258/sec2-bp-mathsedited.pdf.html

http://www.ziddu.com/download/10763259/S2E_Final_Ex_P2.pdf.html

http://www.ziddu.com/download/10763260/S2E_Mid-Yr_Ex_P2.pdf.html

P6 past year paper practice

2010-07-18T00:00:00.001-07:00

http://www.ziddu.com/download/10762997/Practise_3_-_2009edited.pdf.html

http://www.ziddu.com/download/10762998/Practise_2_-_2009edited.pdf.html

http://www.ziddu.com/download/10762999/Practise_1_-_2009edited.pdf.html

http://www.ziddu.com/download/10763000/Practise_Paper_1_-_SA1_2009edited.pdf.html

Practise_1_-_2009edited.pdf (453.79 KB)

File Practise_2_-_2009edited.pdf (302.91 KB)

Pyramid problem sum

2010-07-09T23:37:00.000-07:00

Question: The diagram shows a solid which is composed of a pyramid VABCD and a cuboid ABCDEFGH. ABCD is a square of side 8cm, VD is the height of the pyramid, which is 6cm and CG =12 cm. find

(a) the volume of the solid (done!)

(b) the total surface area of the solid.

Click Here to see Diagram

Answer:

Click Here To Download .pdf

Mental Arithmetic Practice

2010-07-08T20:39:00.001-07:00

Practice your math calculation skills...Refresh again and again for more questions.

Mental Arithmetic Practice

Algebra for practice (download here)

2010-06-30T23:31:00.001-07:00

Download the Algebra here

Exam Techniques, Tips and Tricks

2010-06-07T20:07:00.000-07:00

Here are some of my collected tips and tricks for Exam, you might find some of them useful.
If you’ve got anything yourself to add on, please let me know. I’ll try to keep it up to date in my exam technique.

Part A Preparing for an Exam

1) Revise actively.

Just reading through your notes is the worst possible way to revise. Well, OK, perhaps not the worst possible, but it’s really not very good. The more of your brain you can engage in the revision, the more you will remember. Memory is not a box in one part of your brain that things are either in or out. Memory is spread out everywhere: there’s verbal memory, visual memory, audio memory, muscle memory, all sorts. The more your brain does with the information, the more you will remember.

So don’t just read. Make up poems and mnemonics. Summarise the notes. Set them to music. Extract key points and write them down yourself somewhere – even if you’re just copying them out, this is better than just reading, since more of your brain is involved. Make up quizzes and do them. Write limericks. Above all – do problems. Make up your own if you run out. Get active!

2) Plan revision.

Write a good revision plan, and stick to it. Don’t do just one subject a day, you’ll get tired of it; then again swopping too often means you don’t get the chance to get deep into anything. I used to do mornings on one subject, afternoons on another and evenings on a third.

3) Do past papers – as many as you can lay your hands on.

The web has the last three papers on it. There might be previous years in the library (can anyone confirm this?) if so, get them. Work through them. If you can't do a question, check that it is still in the syllabus (the modules change every year, and it's always worth checking what is new.) With a good revision plan you should be doing nothing in the last week before the exams except working through exam papers and examples sheets making sure you can do them.
I can’t emphasise the importance of this enough. Anyone who doesn’t work through past papers has very little chance of doing well in an exam.
Oh - and do the past papers, and the examples sheets, against the clock. Time is short in an exam, you need to get used to thinking, and writing quickly. Get your hand trained up so it can write fast (but legibly, please).

4) Question-spotting.

This can be risky, but if you're playing the percentages it's worth a try. Look for any topic that was in the exam two and three years ago, but not last year. If you can get hold of papers from further back, try and spot patterns: does any topic come up every other year, for example?
Another good tip is to make a very careful note if the lecturer says at any point "this is new in the course this year". If he does, there's an above average chance that this will be in the exam - it gets harder every year to come up with new questions about the same old subjects, and putting a new topic in the course is an easy "new question" for the examiner.

5) If you can’t do the past papers – ask someone for help.

Study groups work well, provided you don’t think this will mean other people are doing your studying for you. They can’t – that doesn’t work. You have to go and study a subject, or attempt an exam paper by yourselves first, then meet together to discuss your answers. Don’t work through the past papers in the group – the temptation to let other people do the work is too strong. You need to learn to do it yourself. Always remember, exams are not a team exercise.
Failing that, make an appointment to come and ask the lecturer. Lecturers are usually perfectly happy to answer questions of the form “this is how far I’ve got, but I can’t see how to do the next bit – is this right?” However, anyone turning up and asking for the worked solutions to an exam question having made no apparent effort to try themselves first is likely to be told to go away and do some more work. This is for your benefit – if we just tell you how to do a problem, you won’t remember it very well. If you really struggle to get through it yourself, and then with some help finally succeed, you may remember it for the rest of your life. The more effort you put into it, the better it will stick in your memory.

6) If you just can’t understand something, learn it parrot-fashion.

This really is a last-ditch solution. But it gives you at least something to do with the questions on subjects you really don’t understand. Even questions on these subjects usually start off by giving you a few marks for “describing XXX”. Even if you don’t understand it, you can get a few marks by writing down the description straight from the notes.

Part B) The Last 24 Hours

7) Don’t be tired.

If you have to stay up all night to do last minute revision, you’ve already failed. It doesn’t work – you end up so tired in the exam you can’t work anything out. It might work for the first one or two exams in a year, but you won’t be able to keep it up throughout a whole series of exams.

8) Eat protein before long exams – not carbohydrates.

An exam is just as much a physical exercise as a race. Well, OK, perhaps not quite as much, but you can’t ignore your body if you want your brain to work at its best. Stuffing it full of sugar, or some Red-Bull type drink just before will work fine for the first hour or so, but by the end of a three-hour exam you’ll have completely run out of energy. You need some food that will slowly release energy. Try pasta, fish or eggs.

9) Get the important facts into short-term memory.

In the last 24 hours it's too late to try and understand anything new. What you can do is cram some facts into short-term memory. This is the time to go through the notes looking at those "key points" sections. If you haven't already done it as part of your revision (and you should have done it), write out a sheet with just the key facts. See how many you can remember. Then write out another sheet with just the ones you forgot. See how many you remember now. Continue until you've either remembered it all, or run out of time.

Also, read through your worked solutions for the last three year's papers. Then, get a good night's sleep, or go for a walk and get some fresh air into your lungs.

Part C) The Exam Itself

10) Planning your campaign

The first thing to do is read over, carefully, the entire exam paper. Spend a good ten minutes reading before you write anything. In this time, work out which questions you are going to answer, which order you are going to answer them in, and plan your time in the exam: how much time you are going to spend answering each question. Take careful note of the marking scheme (see later) when making this plan. Write down the plan on the back sheet of your answer book - you can always score it out later. It helps you feel in control, and that helps keep you calm.
Don't be tempted to do a question on subject X just because it's the subject you know the most about. It might be a real stinker of a question. Are you sure you can do it? Which parts can you do? How many marks do you think you could get on the parts of the question you can do? You might find there is another, much easier question on subject Y, which you might not have chosen because you found subject Y is harder, or because one part of the question looks really difficult. Work it out for each part of each question: which question is likely to get you the most marks? Do that one.
Reading the whole question is also important because many questions lead you through a problem - the answer to part a) is used in part b), etc. There might be clues in later parts of the question about what the examiner is expecting. Make sure you spot them.
As an examiner I am constantly amazed by students who set out to do questions that they've clearly got not the first clue how to do. Surely there would be another question on the paper that they could have got a few marks on at least?
When working out timescales, try and balance the time spend on a part of the question against the marks you will achieve. If it's a 90 minute exam, and it's marked out of 60, then on average you've got 1.5 minutes to get each mark. Plan time accordingly.
Obviously, the plan (with timescales) is not a rigid one, and going a few minutes over on one question is OK – but try and catch it up if this happens.

11) Do the easiest questions first

There is absolutely no reason to do the questions in the order they are printed in the exam. I would recommend doing the easiest one(s) first.
There are two reasons for this. Firstly, getting one question safely under your belt at the start of an exam is a wonderful boost to confidence, and can help stop any feelings of panic that might arise when looking at the harder questions.
The second reason is that the easiest question is likely to take less time than the average. That means you’ll be ahead of schedule from the start – another good confidence boost. It also means that when you get round to the most difficult question, you are free to spend all the time you have left on it, without having to drop it half-way through and come back to it later, if time permits – not a good idea if it can be avoided.

12) Look at the marking schemes – there’s lots of useful material there.

We have strict marking schemes these days – it’s part of the drive to be seen to be fair. So, if there are four marks available for the description of XXX, then the marking scheme will probably have four key points. Mention them all, and you get the marks. Often, for a question like this, I will have a list of five or six points, and give one mark for each of them, up to a maximum of four. One thing you can be (reasonably) certain of: if you haven’t made four key points, you’ve missed something.
Don’t spend half-an-hour writing a long essay for two marks. People still do this. It’s a waste of time – better spent on other parts of the question.

13) One thing to try if you can’t quite get a derivation to work out

What you could consider doing in questions of the form “derive the result shown below” where you’re not sure of all the steps: start at the top of the page, state the assumptions clearly, and write down the equations where you’re going to start. About a page and a half later, write the result, and start working backwards from there. Where the two halves meet, write “Clearly,”
This gives the examiner a problem. Provided you’ve got the steps right, and the two halves almost meet up, it’s hard for him to know whether the missing step is clear to you or not. It might be. You could get the benefit of the doubt.
Of course, there is some risk here, if you have made a mistake, and your “clearly” connects two lines that can not possible agree. While the strict marking schemes we use these days make it hard to penalise students directly for this sort of thing, it will tend to put the examiner in a poor frame of mind, and he might start being less generous in marking other sections of the paper where he has some discretion.

14) Don’t get stuck. Move on.

Avoid writer's block, you haven't got time for it. If you get stuck on a question, move on. Start doing another one. Staring at a question you don’t know how to answer is a waste of time, and you’d be amazed how often, when coming back to a question after half-an-hour, it suddenly becomes clear.

15) Take a bottle of water in with you. Sip it slowly throughout.

It’s a good way of remaining calm. Also, you can get through a lot of nervous sweat during a hard exam. Your body will work better if you replace it.

16) Use common sense.

If the answer to “how high is the radio tower” is 217 miles, or to “what is the electron density in the semiconductor” is 0.003 electrons per cubic metre, then you’re probably wrong. Even if you don’t have time to go back and find the mistake, at least write something to indicate that you know it’s wrong. You might get some credit for that.

17) Always explain what you are doing.

Too many times I find an exam script where the student has written an equation with variables in it, and not told me what the variables represent. If the answer is right, then I can usually figure out what the variables must be, and the student gets the marks. But if the answer is wrong, then sometimes it's impossible to work out what they were supposed to be. In this case the students gets zero for an incomprehensible answer.
Don't just write long lines of mathematics. Explain what you're trying to do with the derivation before you set off, and add comments as you go. It's easy, and can gain a lot marks for method, even when the answer is wrong.

18) If you're running out of time.

Suppose you've got time left to do one question, but two questions left to do. Which one do you choose? The way to maximise your marks is to do the first half of both of them. You gain marks faster at the start of a question than at the end.
If you don't have time to write sentences, but you do know what to do, then just write bullet points. If you don't have time to do the calculations, write and explain what calculations you would do. You can get marks for method.

19) Never leave an exam early.

The only possible excuse for this is when you are absolutely sure that you have got 100%. There is always something you can do to improve your paper. Check, and check again. When you’ve finished, start back at the beginning, and try to do the questions in different ways, and check they agree. Add more explanations.

If you've got time left at the end, try remembering the mnemonic: ACUTE.
Assumptions (have you explained them all, even when not explicity asked)

Calculations (have you checked them all - doing things different ways if possible and time permits. Did you press those calculator buttons right? Do the answers to different parts of the question agree? Check, and check again.)

Units (do the units for all formulas make sense and agree - this is a very powerful technique for checking that your derivations are right and you're using the right formula)

Truth (have you done all the parts of all the sections in the questions? If asked to make a list and explain why, don't just make a list. This is probably the biggest cause of unnecessary lost marks - read the question and answer the question, the whole question, and nothing but the question. Just like the truth in a court of law)

Explanations (have I explained what I'm doing at all stages - good explanations will get marks for method even if the answer is wrong; miss out the explanation and you're throwing away easy method marks)

**I have never left an exam early in my life.**

Ratio

2010-06-01T17:39:00.000-07:00

A ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

The ratio of quantities A and B can be expressed as:

the ratio of A to B (fractional notation)
A is to B
A:B

For example, the "ratio of men to women" in the group. if there are 50 people, 20 are men. Then the ratio of men to women is 20 to 30.Notice that, in the expression "the ratio of men to women","men" came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been "the ratio of women to men", then it will be "30 to 20".Expressing the ratio of
men to women as "20 to 30" is expressing the ratio in words. There are two other notations for this "20 to 30" ratio:

Odds notation: 20 : 30

Fractional notation: ²⁰/₃₀

You should be able to recognize all three notations; you will probably be expected to know them for your test.Given a pair of numbers,
you should be able to write down the ratios. For example:

There are 25 goats and11 chicken in a certain park. Express the ratio of goats to chicken in all three formats.

25:11, 25/11, "25 to11"

Consider the above park. Express the ratio of chicken to goats
in all three formats.

11:25, 11/25, "11 to 25"

The numbers were the same in each of the above exercises, but the order is different. In ratios, order is very important.

Let's return to the15 men and 20 women in our original group. I had expressed the ratio as a fraction, namely, ¹⁵/₂₀. This fraction reduces to
³/₄. This means that you can also express the ratio of men to women as
³/₄, 3 : 4, or "3 to 4".

This points out something important about ratios: the numbers used in the ratio might not be the absolute measured values. The ratio "15 to 20"
refers to the absolute numbers of men and women, respectively, in
the group of thirty-five people. The simplified or reduced ratio "3 to 4"
tells you only that, for every three men, there are four women. The
simplified ratio also tells you that, in any representative set of seven
people (3 + 4 = 7) from this group, three will be men. In other words, the men comprise ³/₇ of the people in the group. These relationships and reasoning are what you use to solve many word problems:

In a certain class, the ratio of passing grades to failing grades is
7 to 5. How many of the 36 students failed the course?zabeth St

The ratio, "

" (or

7 : 5

⁷/₅

), tells me that, of every

(7 + 5 = 12

)students, five failed. That is,

⁵/₁₂

of the class . Then

( ⁵/₁₂ )(36) =

15 students failed.

In the park mentioned above, the ratio of goats to chicken is
25 to 11. How many of the 360 animals are chicken?

The ratio tells me that, of every

+ 11 = 36

animals,

are chicken. That is,

¹¹/₃₆

of the animals are chicken. So there are

( ¹¹/₃₆ )(360) = 110

chicken.

Generally, ratio problems will just be a matter of stating ratios or simplifying them. For example:

Express the ratio in simplest form: $10 to $45

This exercise wants me to write the ratio as a

reduced

fraction:

¹⁰

/₄₅

= ²/₉.

This reduced fraction is the ratio's expression in simplest fractional form. Note that the units (the "dollar" signs) "cancelled" on the fraction, since the units,"$", were the same on both values. When both values in a ratio have the same unit, there should be no unit on the reduced form.

Express the ratio in simplest form: 240 km to 80 minutes

When I simplify, I get (

240

km) / (

0 min) = (

km) / (

min), or

3 km per minute.

In this exercise the answer did need to have units on it, since the units on both parts of the ratio, the "km" and the "minutes", do not "cancel" with each other.

Ratios are the comparison of one thing to another (meter to centimeter, km to minutes, goats to chicken, etc). But this is useful in the setting up and solving of proportions.

Keys To Solve PSLE Math Problems

2010-05-26T04:17:00.000-07:00

What can you do when you are stumped? Too many students sit and stare at the page, waiting for inspiration to strike — and when the solution doesn’t crack their heads open and step out, fully formed, they complain: “Math is too hard!”

How to solve a tough problem

Ask yourself these 4 questions:

1. What do I know?

List the facts or information given in the problem.

Underline or circle any key words, such as factor, multiple, area, or perimeter.

Watch out for mixed units!

Express the facts in math symbols, if you can.

2. What do I want?

Describe the goal, what the problem is asking you to find.

Underline or circle any key words, such as sum, product. (Small words are easy to miss!)

Express the goal in math symbols, if you can.

3. What can I do?

Combine the given facts. Can you get closer to the goal?

Try a tool from your Problem Solving Tool Box.

Do one little step at a time.

4. Does it make sense?

When you get an answer, always look back at the original problem one more time.

Does your answer make sense?

Do you have the correct units (m, cm2, kg, etc.)?

Can you think of a way to confirm that your answer is right?