# A-Level Maths - Mechanics Tips

Mechanics is a subject that requires a lot of diagrams. Don't get lazy and cut corners. Learn the standard diagrams for a given topic so that you can draw them without having to think for too long.

Use standard letters to simplify your work and include these in your diagrams.

## Forces:

- T for tension
- W for weight
- R for reaction (N for normal reaction or contact force can get confused with N for Newtons)
- F or F
_{r}for friction or resistance to motion - F
_{max}or F_{lim}for limiting friction

This will make your work much easier to follow, save you time and possibly less mistakes.

## Velocities and acceleration

Label velocities with a single arrow above or below a particle and a double arrow to show acceleration.

Use u for initial velocities and v for final velocities where possible.

Use subscripts for initial and final velocities of different particles A and B, such as u_{A}, u_{B} and v_{A}, v_{B}

## Common mistakes

When reading a question, take care to see if the weight or the mass is given. Remember, weight = mg and is a force. When weight is given as W, do not write this as Wg Newtons.

Check to see if a question asks for speed rather than velocity. A velocity of -3ms-1 gives a speed of 3ms-1. The same is true for acceleration and deceleration. An acceleration of -5ms-2 gives a deceleration of 5ms-2

When dealing with vector quantities, direction matters. It is very common to see mistakes in solutions where a minus sign has been left out because the direction of motion was in the negative sense. It is always a good idea to get into the habit of defining a positive direction before attempting a solution, especially when doing momentum and impulse questions with particles moving in different directions.

## Guide lines on resolving:

Always aim to resolve in the direction that an object is moving.

If it is moving up a plane, resolve up the plane, if it is moving down the plane then resolve down the plane.

If you resolve in the opposite direction to motion then you will generally find yourself getting into all sorts of problems over acceleration having to be negative.

State the direction you are resolving by using R(left), R(up the plane) etc. Arrows inside the brackets can be used. It makes it clear to the person marking your work what you are intending to do.

## Common phrases or words used in questions

- particle: a point mass
- body: same as a particle (not of the human variety)
- light inextensible string: a string with negligible mass that does not stretch

## Common tags to questions

It is common to see tags at the end of a question where 1 or 2 marks are given. These can be easy marks as often all that is required is a simple statement that requires no working. These questions normally start with "State the assumptions you have made" or "How have you used the fact that the string is light and inextensible?"

Here are a few common answers

- Neglect air resistance - (This is a common reply to questions where a particle falls freely under gravity. If air resistance were a factor in a problem then acceleration would not be constant)
- The string is light - (This is a common reply when dealing with connected particles where a string passes over a pulley. If the string were not light then the mass would change and therefore the acceleration would not be constant).
- The string is inextensible - (An inextensible string will mean that when two particles are connected, as one moves with acceleration a, then the other moves also with the same acceleration a)
- The pulley is smooth - (When a string passes over a smooth pulley the tensions in the string are the same on either side)

## General Exam Comments

Look out for the phrase "Find the exact value ." . Expect to leave answers in surd form, or containing pi, logs or exponentials.

Also take care to read the question. The times a question says find the values and a student gives just one answer. For example when a square root is involved and only the plus answer is given rather than the negative value. Hang on every word!

It is important that you learn formulae. Often you will get marks for just quoting a correct formula for a given situation even if you do not know how to correctly use it.

Always try and have a go at a question. Jot down any ideas or statements that come to mind. An attempt at using a formula or method can sometimes get marks as long as it is reasonably clear.

Show working. This is always written on the front cover of the exam paper. This is so important as it gives the examiners the opportunity of seeing how you achieved an answer and it enables them to follow your lines of thought. By showing working and giving clear introductions to your statements is essential so that you can pick up method marks even if the answer turns out to be incorrect.

Accuracy is also an important element. Too many students round up answers at each stage of a solution and compound their errors. If a question says give your answer to 3 significant figures then throughout the question truncate your answers to several figures beyond this. You will see this repeatedly done in my videos.

Make sure you have a good scientific calculator for the non calculator papers and that you have time to familiarise yourself with the keys and functions. Calculators are always changing with some being easier to use than others. I have listed some of the common calculators.

In an exam you may be anxious to move on to the next question but always check that you have answered the question and to the accuracy that is required. You may easily throw away 1 mark for not answering a question to the required degree of accuracy.

If you attempt a question a solution more than once and are not sure which solution is correct (if either!) it is safer not to cross anything out, then both solutions will be marked and you may gain credit for work seen by the examiner.

This is a summary of what I think are essential points in making progress in mathematics and passing exams. If you can add any more comments that would benefit others then please contact me.

A good text book is also a valuable resource when it comes to revision. I have grouped together study and revision books for each syllabus and module in our bookshop which hopefully you will find useful. You can even see example pages within some of the books!

Good luck with your AS and A-Level

Stuart Sidders