An IB DP Physics skill pack on resolving vectors into two perpendicular components (SL and HL, first assessment 2025): a rules reference, six worked examples, thirteen figures and more than 100 answered practice items.

It drills the technique in every frame the course uses: the angle at the horizontal or at the vertical, along and perpendicular to a slope, a bearing measured clockwise from north, and an obtuse angle at a bridge joint. That breadth, not the trigonometry, is what a class stalling on a ramp is short of.

The syllabus assumes this technique but no topic owns it: the IB asks for it to be practised inside the topics that need it, so this is not a taught unit but a supplement to integrated teaching.

This pack is worked, not taught: the teaching duration shown is student working time across the practice bank, about 185 minutes, not classroom delivery time. It runs as three sittings of about 63, 79 and 47 minutes.

What students learn:

• The component lying along the direction the angle is measured from takes the cosine: a property of the triangle, not the memorised “the horizontal takes the cosine”
• Resolving along and perpendicular to a slope, and working the angle out first for a bearing or an obtuse angle
• Recombining with Pythagoras and the inverse tangent: the magnitude tests the arithmetic, the angle tests the decision

Three tiers: A, five fluency tables and a five-part error hunt, 80 answers; B, seven applied items and 20 marked parts; C, four multiple-choice items with every distractor explained, and three structured questions worth 28 marks.

IB skills (Tool 3: Mathematics): the pack teaches resolving a vector into perpendicular components; students practise trigonometric ratios, vector addition in the same plane, drawing and labelling a vector, and using a scale diagram.

What’s included:

• Student Worksheet, 27 pages, answers stripped out, colour and B&W
• Teacher Key, 37 pages, every answer and model solution, plus teaching notes
• The editable worksheet as a self-contained HTML file

Worksheet and key are two projections of one source, so no answer file can drift. Grades 11-12 (ages 16-19).

Related resources:

• Projectile Motion I: Theory and Components, where resolving is taught in a topic
• Projectile Motion II: Calculations, where it is used to get an answer
• Foundations of Motion: Distance and Displacement, the free demo lesson