Geometry and Measurement
What to know
Candidates need perimeter, area, volume, and surface area formulas for standard figures; angle relationships (vertical, complementary, supplementary, and parallel lines cut by a transversal); triangle angle sum and the triangle inequality; the Pythagorean theorem and its converse; similarity and congruence; circle circumference and area; coordinate geometry (distance, midpoint, slope); transformations; and unit conversion and scale drawings.
Traps
- Radius versus diameter: area uses r, so halve a given diameter before squaring.
- Units follow the operation: perimeter is linear, area is square, volume is cubic. Converting cm² to m² divides by 10,000, not 100.
- Composite figures may require subtracting an unshaded region rather than adding shapes.
- For similar figures with scale factor k, lengths scale by k, areas by k², and volumes by k³.
- Complementary angles sum to 90°; supplementary angles sum to 180°.
- Surface area counts every face; a common error is omitting the base or counting a shared face twice.
Worked example
Two rectangles are similar with a scale factor of 3. The smaller has area 12 cm². Because areas scale by k², the larger area is 12 × 3² = 12 × 9 = 108 cm². Rule of thumb: before computing, write the formula, substitute with units attached, and ask whether the answer should be linear, square, or cubic.