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IGCSE Mathematics: Our Free Notes for 2019

How to use these tips

These tips highlight some common mistakes made by IGCSE Mathematics students. They are collected under various subheadings to help you when you revise a particular topic. Are you generally worried about your studies in IGCSE Mathematics, especially since Mock Exams are coming up? Our team of subject experts at Tutopiya Online Tutoring have arranged a set of resources just for your needs as a Junior College student whether you’re in Singapore or you’re an international student overseas. 

General Advice

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The question papers assume that you will have all the equipment listed on the front cover.
Make sure that you have all the items on this list the day before you go into the examination.

Be aware of which formulae you will be given and which you will need to learn before the exam. We’ve periodically provided content summaries across this article that you can download for free for your homework. 

Make sure that your calculator is set to degree (deg) mode before you enter the examination.

On the papers where you write your answer on the question paper, it is not acceptable to give a
choice of answers on the answer line. Examiners will mark the worst answer in these cases.

In construction questions you are expected to be able to find a locus using just a pair of
compasses and a straight edge. Compass arcs showing your construction method are required
so do not rub them out – they are an important part of your working.

The question papers are set so that you have time to finish them and check your answers. It is
important that you
read the question carefully and not make instant assumptions about what
you are being asked to do

You are advised to show working as well as solutions as marks are awarded for the working
even when answers may be incorrect. Marks are given for the work that you do correctly, not
subtracted for the work that you get wrong

Graph Questions

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 In reading graph questions it is very important that you make sure that you are reading the
scales correctly. The horizontal and vertical axes may be scaled differently.

If you are drawing a graph then you will need to plot points to within 1 mm and if the points lie
on a
curve, you need to join them with a smooth freehand curve.

You should not join points on a curve with a series of straight lines. If the points lie on a straight line, however, then it is important to use a ruler to join them

Most graphs are well behaved, smooth and do not do unexpected things. In particular all
quadratic graphs with a formula such as y = 2x
2 – 3x – 4 have the same shape whatever the
numbers in the formula. They are just in different places on the grid.

If you asked to solve a quadratic equation and give the answer to two decimal places then
this is a clue that the quadratic formula is needed. This is a formula that you need to learn. If
no accuracy is mentioned in the question then it will usually factorise.

In cumulative frequency graphs the top of the graph and the top of the vertical scale are
not always the same number. You need to use the number from the top of the graph in your
calculations. If you are in doubt about which axis to read your answer from, then look at the
labels on the axes, they will match the units or quantity given in the question.

Accuracy

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A minimum of three figure accuracy is required in questions where no accuracy is specified. In
money questions answers to two decimal places are required.

To achieve three figure accuracy in your answer you need to have at least four figures in your
working. Best advice is to use the full calculator display throughout your working

Diagrams in questions having ‘not to scale’ written by them usually require a calculation. Do
not use these
diagrams to take measurements from.

If a triangle is right angled, isosceles or equilateral then the question will say so either specifically or by giving information about the edges or angles.

In probability questions answers should be given in fractions or decimals. Answers in ratio
form or in words are NOT acceptable. If you work with decimals or percentages then the 3
figure accuracy rule applies as well

If you are asked to estimate the size of a number then only 1 significant figure is usually
required.

When rounding numbers to a given number of significant figures, some zeros count and
some do not. Please note that 0.564 is rounded to 3 sf and 5.60 is also rounded to 3 sf.

Paper 1 Tips (Algebra and Fractions) 

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A basic feature of algebra is that multiplication signs are unnecessary – bc means b multiplied
by c.

A question that says factorise will require you to rewrite the expression using brackets.

Write as a fraction in its lowest terms means that you must cancel down the fraction as far as
possible

In fraction questions that have show all your working included, means that the question must
NOT be done on the calculator. A correct answer with no working will not score any marks

Time & Speed Questions: Key Terms 

  1. In the 24 hour clock system answers cannot be bigger than 2400. 2415 must be written
    as 0015.
  2. You must be very careful with decimal amounts of time. 7 hours 30 minutes is NOT
    written as 7.3hours. The correct value would be 7.5 hours as 30 ÷ 60 = 0.5
  3. Answers in the 12 hour clock system must have am or pm included.
  4. You should be careful to check whether a travel graph question is a distance-time graph or a
    speed-time graph as the methods needed in each are very different

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Paper 2 Tips

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 When angles or lines have to be drawn or measured examiners expect them to be accurate to
within 2 mm and 2°. Marks are often not awarded because of poor accuracy.

Answers to bearing questions should always be given as 3 figure answers such as 078° or
265°

 When you are asked to draw a locus you must ensure that it is drawn long enough to answer
the question. For example, the locus of all the points inside a shape must reach the edges of
the shape.

Paper 3 Tips

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You should read all the Paper 1 Tips as any of these topics could appear on paper 3. You may
also find some of the Paper 2 Tips useful as some of your topics can appear on paper 2.

 Questions on this paper are written to test your understanding of Mathematics and parts of
questions will depend on previous parts of the question. You must be careful that you are using
any formula you have learnt appropriately.

Parts of questions are often connected. If you find an answer is unreasonable then it is likely
that you made a mistake in an earlier answer that you have then used. You should have time to
go back and check your earlier work.


In questions with mixed units, you should usually convert all the quantities to the unit required
in the answer before starting to do the questions, usually to decimal places or percentages. 

Paper 4 Tips

This is the only paper where you do not yet answer on the question paper. It is very important
that you
set your work out clearly so that the examiner is able to read what you have written.

Do not write answers to different questions side by side or put any work on the question paper.

It is particularly important that you show ALL your working otherwise you may be awarded very
few marks.

Transformation of Curves: Key Definitions 

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 If the correct term is,…

 1. Rotation: Then you should give the centre as a coordinate and the angle of rotation with direction 

2. ReflectionYou should give the equation of the mirror line

3. Translation: You should say how much it moves in each direction – use a column vector to do this

4. Enlargement: then you should give the centre as a coordinate and scale factor

5. Stretch: then you should give the direction and scale factor.

6. Shear: then you should give the shear factor and the invariant line.

 

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