IB DP Physics (2025) SK.13 Adding and Subtracting Vectors Skill Pack

IB DP Physics skill pack: adding and subtracting vectors, SL and HL, first assessment 2025. Tip to tail, scale diagrams and components, up to three vectors. 35 answered items, 43 student pages.

What this pack is, and what it is not

The IB asks this technique to be practised inside the topics that need it, so this is a supplement to integrated teaching, not a taught unit: reference and remedial material for a class that adds two forces on one line and stops dead when the second is at an angle.

This pack is worked, not taught: any teaching duration quoted for it, about 285 minutes, is student working time across the whole pack, not classroom delivery time. Seven sittings of about forty minutes.

Where this pack starts

Right-angled trigonometry is assumed. Resolving into components is recapped on a single card, not taught: a companion skill pack drills it.

What students learn

• An arrow drawn to scale, and a magnitude read back off one.
• Vectors on one line as signed values, and two at right angles by Pythagoras and the inverse tangent.
• Tip to tail, the parallelogram, and the range a resultant of two vectors can take.
• Subtraction as adding the reverse, including a change in velocity.
• Up to three vectors at any angle: resolve, add along each direction, recombine.

Six rule cards with an example each and three worked examples, then nine fluency drills, ten applied questions and seven exam-style items (four multiple choice). 213 marks and 19 figures; three constructions are drawn with ruler and protractor on printed grids.

IB skills this pack teaches and practises (Tool 3: Mathematics)

• Adding and subtracting vectors in the same plane (taught).
• Constructing and using scale diagrams (taught).
• Drawing and labelling vectors (taught).
• Resolving vectors into perpendicular components (practised).
• Calculations with trigonometric ratios (practised).
• Arithmetic and algebra to solve problems (practised).

What’s included

• Student Worksheet, 43 pages, colour and B&W
• Teacher Key, 59 pages, every item answered with marking guidance
• The editable worksheet, a self-contained HTML file

Worksheet and key are two projections of one source, so no answer file can drift. Opens in any browser, nothing to install, worksheet editable. SI units and IB command terms throughout. It declares no syllabus topic: these are IB skills in the study of physics. Grades 11-12 (ages 16-19).

Related resources:

• Resolving Vectors, the companion pack that takes a vector apart
• Resultant Force, Inertia and Newton’s First Law, where the resultant is put to work
• Foundations of Motion: Distance and Displacement, the free demo lesson

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