With regard to the line and circle questions, it is useful to remember that where two equations (of either lines or circles) are being sought look for one and generally the other will follow. The line question usually incorporates linear transformations together with the ordinary coordinate geometry of the line and you should ensure that you know all your formulae well, particularly those concerning perpendicular distance from a point to a line and the angles between two lines. For the circle question, it's a while since a question was asked on the determination of tangents to a circle from a point outside a circle and the length of a tangent.

Can you prove that the only right-angled triangle with consecutive sides is the 3,4,5 triangle? Where trigonometry is concerned, you should know the main formulae on page 9. This is the key to solving trigonometric identities. Be particularly mindful of trigonometric identities involving the cosine rule, as it is quite some time since these were asked. Another topic frequently overlooked is the calculation of limits of trigonometric functions. These did come up last year but that is not to say they will not appear again this year. For the practical type questions (usually part c), it is a good idea to fill in any angles or distances obvious to you from the diagram supplied. Break the diagram up into its constituent triangles, isolating, labelling and filling in all information you know about each triangle. Watch out for right angled triangles as you have a huge armoury with which to deal with them – sine, cos, tan and Pythagoras. For non-right angles, bear in mind the sine and cosine rules. If you cannot calculate directly what you are asked to calculate then always calculate anything (and I mean anything) you can calculate.

For Section B, Question 8 is the usual selection as this is heavily based on differentiation and integration. Differential calculus usually appears as part (c) of this question, although last year it did appear, for the first time since 1994, as part (a). With regard to differential calculus, you should bear in mind that more times than not you start with an equation in two variables, with the aid of a key piece of information given you reduce this equation to one variable and then you differentiate with respect to this variable to maximise or minimise. It is worth remembering that this question can be heavily based on the trigonometry parts of your course. It is likely that differential calculus will be back to part (c) this year and that the remainder of the question will be pretty run of the mill stuff.

General Guidelines To Answering Questions

• Make sure you attempt six questions on each paper.
• Attempt every part of every question, leave nothing blank.
• When solving problems do so in a logical, methodical, step by step fashion, writing everything down line by line, even the obvious.
• Take your time; avoid simple errors such as wrong signs, numerical slips.
• Work out even the simple calculations in shown rough-work as this tends to reduce errors.
• Even if the answer to a part of a question seems obvious to you, do not put yourself in a win all or loose all situation. Step out your solution.
• Go for your easiest question first, but remember, if it does not turn out to be so easy do not panic, do what you can and move to your next question.
• catch to it and often the previous part is your clue.
• In attempting difficult parts of questions, always write down all relevant formulae and calculate anything you can calculate, anything at all. At least get the attempt marks.
• Do your thinking on paper, not looking into space and write down all ideas. It is often the case that when you see things written on paper you will see the solution.

Some words of wisdom

• Ensure you get a good night's sleep prior to the exam, as tiredness will affect your basic numeric skills and agility in thinking.
• Do not socialise on the weekend between papers as this will only serve to numb your mind.
• On the morning of the exam, try a few simple maths problems before the exam starts. Like an athlete going into a race, it is a good idea to have a warm up prior to the start. Don't wait to warm up in the examination hall.
• At the very start of the exam, write down any formulae you find difficult to recall as you will probably not recall them correctly later on in the examination.
• When you get into that examination hall, remember there is nothing in this world but you and that paper. Focus intently. Concentrate. Succeed.

Best of Luck
James