External Assessment: The Examination
What the exam demands
The external examination is the major weighting of your result, and it tests the same content as school assessment but under time pressure and without scaffolding. Expect two broad question types: skills and applications (short, procedural, often multi-part) and analysis (multi-step problems requiring interpretation, proof-style justification, or extended modelling). Topics recur across the paper: function notation and transformations, inverse functions, logarithmic and exponential equations, trigonometric equations and identities, differentiation and its applications, integration and area, and probability including conditional probability, the binomial distribution and the normal distribution with its inverse use.
Traps that appear in questions
- Restricted domains. A function written with a stated domain may not be invertible or may change the range; check before applying a rule.
- Losing solutions or accepting spurious ones. Trigonometric equations need the general solution or the specified interval; squaring can introduce extraneous roots, so verify.
- Degrees versus radians. Calculus of trigonometric functions requires radians; a mode error silently ruins a whole question.
- Sign errors in definite integrals. Area between curves requires upper minus lower, and regions below the axis need splitting or absolute value.
- Misreading 'hence'. It means use the previous part; 'hence or otherwise' allows a fresh method.
- Probability traps. Distinguish (P(A\mid B)) from (P(B\mid A)), and use the continuity correction only where appropriate for normal approximations.
Rule of thumb
Budget time by marks, not by interest. Start each question by writing down the given information and what is required; if stuck after a minute, move on and return. Always sanity-check a numerical answer against the context.
Worked example
Solve (2\sin(2x)=1) for (0\le x\le \pi). Then (\sin(2x)=\tfrac12), so (2x=\tfrac{\pi}{6}) or (2x=\tfrac{5\pi}{6}) within (0\le 2x\le 2\pi), giving (x=\tfrac{\pi}{12}) or (x=\tfrac{5\pi}{12}). Checking the extended interval is the step most often missed.