OT2: Mathematical problem solving: Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.

The idea

This skill involves reading and creating diagrams to solve problems. You must extract relevant data from given diagrams, such as forces, dimensions, or angles, and construct your own diagrams to model situations, especially in mechanics. For example, from a diagram of a ladder against a wall, you identify forces and distances; then you draw a free-body diagram showing all forces and dimensions to set up equations. Assessment focuses on correct interpretation and accurate construction, including appropriate labels, scales, and conventions.

What earns the marks

• Accurately extract numerical and spatial information from a given diagram, including lengths, angles, forces, and directions.
• Construct clear diagrams that represent the problem, using appropriate conventions such as arrows for vectors and labels for quantities.
• Use diagrams to set up equations or geometric relationships, ensuring all relevant features are included.
• Interpret your constructed diagram to solve the problem, checking that the diagram is consistent with the original information.

Common mistakes and how to put them right

• Misreading the scale or direction of forces in a mechanics diagram.

  Put it right: Check the scale and use arrows to indicate direction, and verify that the diagram matches the written description.

• Omitting key forces or dimensions when drawing a free-body diagram.

  Put it right: Systematically list all forces acting on an object and include them with correct labels and directions.

• Drawing a diagram that is not to scale or is misleading, leading to incorrect geometric conclusions.

  Put it right: Use a ruler and protractor where appropriate, or clearly state that the diagram is schematic and not to scale.

Exam tips

• When extracting information, annotate the given diagram with any additional values you deduce, to avoid losing track of information.
• For mechanics problems, always draw a free-body diagram showing all forces and clearly indicate positive directions.
• Label diagrams fully with quantities and units, as marks may be awarded for correct labelling and clear communication.