About this unit
How accurately can we know a length, an angle or a direction — and what does that uncertainty do to everything we calculate from it?
Sections in this unit
Factual
- What does a bearing of 250 degrees mean, and what is its back bearing?
- How do you find the angle between a line and a plane in a solid?
- What are the bounds of a length given to the nearest centimetre?
Conceptual
- Why does the ratio of two sides depend only on the angle?
- Why does the exact value always go in the denominator of a percentage error?
- Why does the maximum of a quotient come from the largest numerator and the smallest denominator?
Debatable
- How accurate is accurate enough?
- Is an answer given to more figures than the measurement justifies actually wrong?
Skills
Students should be able to:
- Select and apply an appropriate technique in an unfamiliar situation.
- Work backwards from a given result to an unknown condition.
- Judge the reasonableness of an answer, including its accuracy, its bounds and its units.
- Interpret a mathematical result in the context it came from, and say whether it is good enough for the decision being made.
- Verify a result by an independent route or an estimate.
How you are assessed
- Maximising area investigation, Criteria B and C
- Bearings, bounds and error, Criteria C and D
Before you start
Students arrive with:
- Pythagoras' theorem in two dimensions and the three right-angled trigonometric ratios.
- Area and volume of prisms, and the area of a circle.
- Rounding to decimal places and significant figures, and the compass directions.
- Angle rules including angles in parallel lines, which back bearings depend on.
- From Unit 2, exact values in surd form; from Unit 4, gradient, which connects to the angle of inclination.
Check what you remember
Circles