Geometry and Trigonometry

Five to seven questions. Much of what you need is on the built-in reference sheet, so the efficient move is to learn precisely what isn't.

#On the reference sheet (don't memorise)

Circle area and circumference, triangle area, the Pythagorean theorem, the 30-60-90 and 45-45-90 side ratios, volumes of cylinder/cone/sphere/pyramid, 360° = 2π radians, 180° in a triangle.

#Not on it (do memorise)

• SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
• sin(θ) = cos(90° − θ). Complementary angles swap sine and cosine — a question type in its own right.
• sin²θ + cos²θ = 1.
• Circle equation: (x − h)² + (y − k)² = r², centre (h, k), radius r. Given an expanded form, complete the square to find the centre.
• Arc length = rθ (θ in radians). Sector area = ½r²θ.
• Inscribed angle = half the central angle on the same arc.

#Similar triangles

The most reused idea in this domain. Triangles are similar if their angles match — which happens automatically when a line is parallel to a side, or when two triangles share an angle and both have a right angle.

Similar means corresponding sides are proportional. Set up the proportion carefully: corresponding sides, in the same order, on both sides of the equation. Most errors here are pairing the wrong sides, not the arithmetic.

Scale factor k: lengths scale by k, areas by k², volumes by k³.

#Angles

• Vertical angles are equal.
• A line crossing two parallel lines makes corresponding and alternate angles equal, and co-interior angles supplementary.
• Angles on a straight line sum to 180°; around a point, 360°.
• Interior angles of an n-gon sum to (n − 2) × 180°.

#Radians

π radians = 180°. To convert, multiply by 180/π or π/180 — pick whichever makes the unit you don't want cancel.

#The habit that matters most

Draw the figure, and label every value on the drawing as you derive it. Many of these questions describe a shape in words without a picture, and holding a geometric configuration in your head is much harder than sketching it badly on the scratch paper you're given.

When a figure is given, it may not be to scale — but unless it says "not drawn to scale", it is, and you can sanity-check an answer by eye. An angle that looks like 30° is not 120°.