Geometry — Objectives | Mathematics Department

Area, Volume and Surface Area

1. Calculate the area of compound shapes built from rectangles, triangles, parallelograms, trapezia and circles.
2. Calculate the volume of prisms, including cylinders.
3. Calculate the volume of pyramids and cones using $V = \tfrac{1}{3} \times \text{base area} \times h$.
4. Calculate the surface area of prisms and cylinders, including curved surfaces.
5. Rearrange a mensuration formula to make a chosen variable the subject.

6. Use SOH-CAH-TOA to find missing sides and angles in right-angled triangles.
7. Apply Pythagoras' theorem and right-angle trigonometry inside 3D solids (space diagonals, slant heights).
8. Apply the sine rule to find missing sides and angles in non-right-angled triangles.
9. Apply the cosine rule to find missing sides and angles in non-right-angled triangles.
10. Apply the area-of-a-triangle formula $\tfrac{1}{2}ab\sin C$.

11. Read and draw bearings as three-figure angles measured clockwise from north.
12. Solve navigation and surveying problems using bearings together with right-angle and non-right-angle trigonometry.
13. Round answers to a given number of decimal places or significant figures and decide on an appropriate level of accuracy.
14. Calculate the percentage error between an approximate and an exact value, using the absolute-value convention.
15. Combine $\pm$ measurement errors through sums and products, and discuss the effect on the final answer.