Mathematical Literacy - Geometry, Measurement and Spatial Reasoning
Geometry, Measurement and Spatial Reasoning tests angle facts, perimeter, area, volume, Pythagoras, similarity and unit conversion, often combined in a single diagram-free description.
Core rules
- Angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal.
- For parallel lines cut by a transversal: corresponding angles are equal, alternate angles are equal, co-interior angles sum to 180°.
- Triangle angle sum is 180°; an exterior angle equals the sum of the two opposite interior angles.
- Polygon interior angle sum = (n − 2) × 180°.
- Circle: circumference C = 2πr, area A = πr². The diameter is twice the radius.
- Pythagoras: in a right triangle, a² + b² = c², where c is the hypotenuse.
- Volume: prism = area of cross-section × length; cylinder = πr²h; cone = (1/3)πr²h; sphere = (4/3)πr³.
- Similar shapes: linear scale factor k; area scale factor k²; volume scale factor k³.
Worked example
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse and the area. Hypotenuse: c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm. Area: (1/2) × 6 × 8 = 24 cm². If the triangle is enlarged by scale factor 3, the new area is 24 × 9 = 216 cm², not 24 × 3.
Traps
- Confusing radius and diameter in circle formulas.
- Using the linear scale factor for area or volume.
- Mixing units (cm with m) before calculating.
- Assuming a triangle is right-angled when the diagram only looks so; check whether the question states it.
- Adding the areas of overlapping shapes twice in composite figures.