Paper 4 (Mechanics): what examiners say, session after session

The Mechanics paper has the most consistent examiner messages of any A Level Math paper. A handful of reminders appear in report after report, often almost word for word. This guide gathers the points that apply to the whole paper. Each topic has its own guide with the mistakes for that topic.

This guide is based on a reading of Cambridge examiner reports for recent sessions. The advice is summarised in our own words.

Message 1: Draw a force diagram

Reports for this paper recommend a well-annotated force diagram, every session. The diagram helps students include all the relevant forces and terms when they form an equilibrium equation, an equation of motion, or a work-energy equation. Examples of what goes wrong without one:

• A weight component on an inclined plane is left out or has the wrong trigonometric ratio.
• The tension in a tow-bar or string is left out, or included in the equation for the whole system, where it should not appear.
• Friction is drawn in the wrong direction.
• The normal reaction is taken to be only a component of the weight, when other forces have a component perpendicular to the plane.

Label every force, the direction of motion, and the angles. Diagrams in the paper should be annotated clearly as well, for full marks.

Message 2: Work to 4 significant figures, answer in 3

• Non-exact numerical answers are required to three significant figures (and angles in degrees to one decimal place), as stated on the front of the paper. This is described as the case in many reports, with examples in several questions each time.
• To obtain a final answer correct to 3 significant figures, carry out all working to at least 4 significant figures. Premature rounding appears in the reports for forces, energy and kinematics alike.
• Only non-exact answers should be approximated. An exact answer, such as one that is a whole number or a simple fraction, does not need to be given to 3 significant figures.

Message 3: Calculus is needed when the acceleration or velocity is a function of time

When a question gives the acceleration, or the velocity, as an expression in t, the constant acceleration equations cannot be used. The reports repeat this in many sessions. Integrate to go from acceleration to velocity to displacement, and differentiate in the opposite direction. When you integrate, include the constant of integration, and use the given information to find it.

When calculating the distance travelled using integration, consider whether the time interval needs to be split. If the velocity changes sign, integrating over the whole interval gives displacement, not distance.

Message 4: Show enough working when the answer is given

• In questions with a given answer, where equations must be solved to find it, do not use an equation solver. It does not show how the answer was found.
• Substitute the given values into your algebraic expression, so that examiners can see them. One report says that if the final answer is wrong and there is no substituted expression, there is no way to know that correct values were used.
• In "show that" questions, show enough detail that the examiner can be sure the result has been shown, not quoted.

Message 5: Do not find an angle you do not need

When a question gives the sine, cosine or tangent of an angle, there is no need to evaluate the angle. All other trigonometric values can be found from the information given, and exact values give a more accurate final answer. The reports give this as a repeated tip.

Other points that appear again and again

• Information in the stem applies to the whole question unless the question says otherwise.
• Check for missing or extra terms in a Newton's second law or energy equation, especially the component of weight on an inclined plane.
• If you make more than one attempt, cross out the work that should not be marked.
• Do not use the same letter for the speeds of different particles.
• Say when you reject a solution, for example a solution that is inconsistent with the motion after a collision.

Before you move on

After every Mechanics worksheet, ask yourself:

1. Did I draw a labelled diagram?
2. Did I check each equation for missing terms and for the right signs?
3. Were my working figures at least four significant figures?
4. Did I use calculus when acceleration or velocity was a function of time?
5. Did I use the information that I was given about an angle without finding it?

Questions students ask

What do examiners say most often about the Mechanics paper?

Draw a force diagram. Reports recommend a well-annotated one every session, to help include all the forces and terms in equilibrium, motion and work-energy equations. Common omissions are the weight component on a slope, tension, friction in the wrong direction, and a normal reaction taken as only part of the weight.

How many significant figures should I use in Mechanics?

Give non-exact answers to three significant figures (angles in degrees to one decimal place), and work to at least four significant figures before the final answer. Premature rounding appears in reports for forces, energy and kinematics alike.

When do I need calculus in Mechanics?

When acceleration or velocity is given as an expression in t. The constant acceleration equations cannot be used then. If the velocity changes sign, split the interval: integrating across the whole interval gives displacement, not distance.

Do I need to find an angle when its sine or cosine is given?

No. When the sine, cosine or tangent of an angle is given, all other trigonometric values follow from it, and exact values give a more accurate final answer.

Can I use an equation solver to reach a given answer?

Not for marks. In questions with a given answer, show how it was found. An equation solver shows none of that.