Geometry and Measurement
Core content
Candidates should know angle relationships, triangle properties, congruence and similarity, the Pythagorean theorem, special right triangles, and circle theorems involving chords, tangents, arcs, and inscribed angles. Compute perimeter, area, surface area, and volume for standard and composite figures. Use coordinate geometry, including distance, midpoint, slope, and transformations. Measurement includes unit conversion, scale drawings, precision, and dimensional consistency.
Trap watch
Confuse radius with diameter, and height with slant height, at your peril. In similar figures, lengths scale by k, areas by k^2, and volumes by k^3. An inscribed angle is half the corresponding central angle, not equal to it. When converting square or cubic units, apply the conversion factor twice or three times. Composite figures often invite double counting of shared edges or overlapping regions. Diagrams are not always to scale, so rely on stated measurements and geometric relationships.
Worked example
A cylinder has radius 3 cm and height 5 cm, so its volume is pi x 3^2 x 5 = 45pi cubic centimetres. If every dimension is doubled, the new volume is 8 x 45pi = 360pi, because volume scales by the cube of the linear scale factor.
Rule of thumb: label every dimension with its unit and ask whether the required quantity is one-, two-, or three-dimensional.