Geometry and Measurement
Core concepts
Candidates need solid command of angle relationships (parallel lines, triangles, polygons), congruence and similarity, the Pythagorean theorem, and area and volume formulas for standard figures. Know that similar figures have equal angles and proportional sides, with areas scaling as the square of the ratio and volumes as the cube. Circle facts-central and inscribed angles, chords, tangents-appear regularly, as do coordinate-geometry tools such as midpoint and distance formulas.
Traps to watch
- Using the diameter instead of the radius in circle formulas.
- Applying a length ratio directly to an area or volume.
- Forgetting that the exterior angle of a triangle equals the sum of the two opposite interior angles.
- Mixing units, for example centimetres with metres, before computing.
- Assuming a triangle is right-angled when the diagram merely looks so.
Worked example
Two similar cylinders have heights in the ratio 3 : 5. If the smaller has volume 54 cm³, the volume ratio is 3³ : 5³ = 27 : 125. So 54/27 = 2, giving the larger volume as 2 × 125 = 250 cm³.
Rule of thumb
Write the ratio you are given, then ask whether the quantity is one-dimensional (length), two-dimensional (area), or three-dimensional (volume) before you raise it to a power.