Units 3 and 4 · External exam revision
Specialist Mathematics: External Game plan
In Methods, the hard part was working out which topic a question came from. In Specialist, the topic usually names itself. Marks are lost when you choose the wrong method inside the topic, and each game plan is built to stop that happening.
So the question to ask is what form the mathematics is in, and what form you need it in. The one place where working out the situation is genuinely hard is motion, which is why the game plans open with The Motion Map.
Three kinds of formula
Each formula in the game plans carries one of these labels, so you know how to treat it.
Printed in the QCAA formula book. You don’t need to learn it, but you do need to know where to find it.
Not in the formula book. Learn it by heart for both papers.
Not on the sheet, but you can work it out from formulas that are. The game plan shows you how.
Habit
Before the exam, test yourself on the labels. Can you find every formula on the sheet in under five seconds, and say every one you need to memorise? If so, the only thing left to practise is choosing the right method.
The game plans
Start with The Motion Map whenever something is moving. Each of the other nine covers one area of the course and links back to the Topic Guide sections it draws on.
Game plan 0
The Motion MapFive kinds of question all begin “a particle moves…”. Three questions send you to the right game plan.
Start here whenever something is moving.
Game plan 1
Complex numbersConverting form, arithmetic in polar form, roots, and factorising over the complex numbers.
Reach for it when you see $i$, $\text{cis}\,\theta$ or a polynomial over $\mathbb C$.
Game plan 2
Induction and trigonometric proofsSummation and divisibility proofs, De Moivre’s theorem and multi-angle identities.
Reach for it when you see “prove by mathematical induction” or “using De Moivre’s theorem”.
Game plan 3
Vectors and 3D geometryLines, planes and spheres, angles, intersections and vector proofs.
Reach for it when you see points in three dimensions, or the equation of a line, plane or sphere.
Game plan 4
Motion in a planePaths, collisions, projectiles and circular motion.
Reach for it when you see position as a vector function of time, a projectile, circular motion or two particles that might meet.
Game plan 5
MatricesMatrix equations, systems of equations, the three cases, and Leslie and dominance matrices.
Reach for it when you see a matrix, a system of equations, or a Leslie or dominance context.
Game plan 6
IntegrationChoosing a technique, areas and volumes, Simpson’s rule and the exponential distribution.
Reach for it when you see any integral sign, an area or volume, Simpson’s rule, or an exponential PDF.
Game plan 7
Rates of change and differential equationsRelated rates, implicit differentiation, separable differential equations, the models you are given and slope fields.
Reach for it when you see related rates, implicit differentiation, a differential equation to solve, a growth or cooling model, or a slope field.
Game plan 8
Motion in a line and forcesForce diagrams, choosing the form of acceleration, air resistance, simple harmonic motion and momentum.
Reach for it when you see named forces, an inclined plane, air resistance, simple harmonic motion or momentum.
Game plan 9
Statistical inferenceStatistics and parameters, sample means and confidence intervals.
Reach for it when you see a sample mean, a confidence interval, a margin of error, or a claim to judge.
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