IB DP Physics skill pack on proportionality and scaling: SL and HL, first assessment 2025. Six modelled examples, five figures and 30 answered questions.

The IB asks for these techniques to be practised inside the topics that need them, so this is a supplement to integrated teaching and not a taught unit of the course. It is reference and remedial material for a technique the syllabus assumes but no topic owns, and it earns its place with a class that substitutes correctly and still cannot say what trebling the radius does to the force.

This pack is worked, not taught: the 220 minutes shown is student working time across the practice bank, not classroom delivery time. It splits into three sittings of about 75, 70 and 75 minutes, marked on the page.

Where it stops: the constant is read straight off a gradient, without the best-fit lines and the uncertainty a Paper 1B analysis puts on it.

What students learn:

• Stating a proportionality, and whether it is positive, negative or neither
• Scaling by the ratio method, as a factor or a percentage, and backwards
• Rearranging before reading the power, and scaling two changes at once
• The shape each relationship draws, and how to sketch it
• Straightening a curve by choosing what to plot, and what its gradient equals

Three tiers: A, five fluency items, four drill tables, 28 rows, 67 answers; B, twelve applied items, 32 lettered parts; C, four multiple-choice items, every option explained, and three structured questions worth 34 marks.

IB skills (Tool 3: Mathematics). Taught: direct and inverse proportionality, with positive and negative relationships; the effect of a change in one variable on another; sketching graphs with labelled but unscaled axes. Practised: selecting and manipulating equations; ratios, reciprocals and exponents; arithmetic and algebra; linearizing graphs where appropriate; interpreting graph features.

What’s included (6 files):

• Student Worksheet, 30 pages, answers stripped out, colour and B&W
• Teacher Key, 42 pages, every answer, 21 worked solutions and teaching notes
• The editable worksheet, a self-contained HTML file
• READ ME FIRST guide with the licence

Worksheet and key are two projections of one source, so no answer file can drift. Opens in any browser, nothing to install, worksheet editable. It declares no topic and no understanding, deliberately: this belongs to the IB skills in the study of physics. Grades 11-12 (ages 16-19), as homework, reference or revision.

Related resources:

• Graphical Analysis of Motion, where a gradient is read inside a topic
• Measuring the Acceleration of Free Fall, the practical that straightens a curve (free)
  - SUVAT Equations II, where the free-fall relationship it scales is taught