Unit Overview

Geometry and Trigonometry

IB Mathematics Applications and Interpretation SL· 5 min read 📊 12-14% of overall IB AI SL exam

1. Unit at a Glance

This unit builds from basic 2D and 3D measurement up to applied trigonometry and two AI SL-specific core topics: sinusoidal modelling and Voronoi diagrams. Skills build incrementally, with early trigonometry concepts reused in later applications and modelling work.

Approximately half of the unit's exam marks come from applied problems, so we focus on connecting formulas to real-world contexts throughout the sub-topics, which aligns with AI SL's assessment focus.

All sub-topics in this unit, ordered for sequential learning:

Volume and surface area of 3D solids

Calculate volume and surface area for common 3D solids and composite solids.

★★⏱ 10 min

Right-angled triangle trigonometry

Use SOHCAHTOA and Pythagoras' theorem to solve for unknown sides and angles.

★★⏱ 12 min

Sine rule, cosine rule for non-right triangles

Apply the sine and cosine rules to find unknown sides and angles in any triangle.

★★★⏱ 15 min

Bearings and trigonometric applications

Solve real-world navigation problems using bearings and combined trigonometric rules.

★★★★⏱ 15 min

Sinusoidal functions: amplitude, period, translation

Model periodic phenomena with transformed sine and cosine functions.

★★★★⏱ 20 min

Voronoi diagrams and closest site problems

Construct and interpret Voronoi diagrams for closest facility spatial problems.

★★★⏱ 18 min

Triangle area formula for non-right triangles

Calculate the area of any triangle using the $r a c 12 ab s in C$ formula.

★★⏱ 8 min

2. Common Pitfalls

Wrong move:

Forgetting to convert bearings to the internal angle of a triangle before applying trig rules

Why:

Bearings are measured clockwise from north, so they do not directly give the required triangle internal angle

Correct move:

Draw a north line at each vertex and use parallel line/angle sum rules to find the internal angle

Wrong move:

Confusing the formula for the period of a sinusoidal function $y = sin (k x)$

Why:

Many students incorrectly use $p er i o d = k /2 π$ instead of the correct relationship

Correct move:

Remember $p er i o d = 2 π /∣ k ∣$ for sinusoids in the standard transformed form

Wrong move:

Double-counting overlapping faces when calculating surface area of composite 3D solids

Why:

When two solids are joined, the overlapping faces are no longer on the surface

Correct move:

Subtract twice the area of the overlapping face from the sum of individual surface areas

3. Quick Reference Cheatsheet

Concept	Key Formula / Rule
Volume of a sphere	$V = \frac{4}{3} π r^{3}$
Surface area of a sphere	$S A = 4 π r^{2}$
Sine Rule	$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$
Cosine Rule (for side $a$ )	$a^{2} = b^{2} + c^{2} - 2 b c cos A$
Area of any triangle	$A r e a = \frac{1}{2} ab sin C$
Period of $y = sin (k x)$	$P er i o d = \frac{2 π}{∣ k ∣}$
Voronoi edge property	All points on an edge are equidistant from the two adjacent sites

What's Next

Start with the first sub-topic of this unit below to build your foundational 3D measurement skills, then work through each sub-topic in order to progress to more complex applications and modelling. After completing all sub-topics in this unit, you can move on to the next unit overview for Statistics and Probability.