Revision:OCR M1 Mathematics

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Here are some basic notes and tips for help answering OCR M1 A Level mathematics exams.

OCR M1 Mechanics

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 ( Don't use N for normal reaction or contact force as it can get confused with N for Newtons )
• F or Fr for friction or resistance to motion
• F_max or F_lim for limiting friction

Aim to use subscripts

For example, if more than one tension acts on a particle: try using T₁ and T₂.

For different reactions that might act on particle A and particle B use R_A and R_B.

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 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
• If a peg is smooth then the tension is uniformly distributed to the string(s) which are subtended at it.

Comments

Originally written by Stuart S on TSR Forums.