Units 3 and 4 · External exam revision
Mathematical Methods: External Game plan
Every technique and formula you need for the external exam, gathered in one place. Each game plan is a set of questions you ask yourself in order. They take you from reading a QCAA question to knowing which technique to use.
The six exam game plans assume you already have the mechanics down. They come into their own in the last two months before the external. If a step in one of them feels shaky, go back to The Mechanics of Methods first and come back when it feels automatic.
Start here
The First Question
Ask yourself these every time you start an external exam question, in this order. They tell you which game plan to use. Check the statistics wording first, because some statistics questions need calculus along the way.
Step 1
Is it a statistics question?
Ask these in order and stop at the first yes.
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Step 2 · If every answer in step 1 was no
“Am I required to differentiate or integrate in this question?”
The most common mistake I see in practice exams is reaching for the wrong technique. Answer these questions first, before you touch your calculator.
Which game plan?
Here are the openings of eight real QCAA exam questions. Read each one, ask the First Question in order, and pick the game plan you would reach for. You do not need to solve them.
The game plans
Start with The Mechanics of Methods during the year. The other six are for the exam itself, and each one links back to the Topic Guide sections it draws on.
Game plan 0
The Mechanics of MethodsDifferentiation and integration techniques, finding the equation of a graph, and the unit circle.
Work on these all year. Every other game plan assumes you have them down.
Game plan 1
CalculusDifferentiation, integration and the applied calculus techniques that build on them.
Reach for it when the question asks for a rate, gradient, velocity, maximum, tangent, area or total change.
Game plan 2
TrigonometrySine and cosine rules, area, bearings and modelling.
Reach for it when the question is not calculus and not statistics.
Game plan 3
Discrete random variablesBernoulli trials, binomial distributions and general discrete distributions.
Reach for it when the question defines success and failure, says “binomial”, or gives a table of outcomes.
Game plan 4
Probability density functionsContinuous random variables, area, mean and variance.
Reach for it when you are given a function on an interval that is zero everywhere else.
Game plan 5
The normal distributionProbabilities, quantiles and z-scores.
Reach for it when the question says “normally distributed”.
Game plan 6
Sample statisticsSample proportions, margin of error and confidence intervals.
Reach for it when you see a sample proportion, a margin of error or a confidence level.
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