Each game plan is a decision routine, a fixed set of questions that takes you from reading a QCAA question to knowing what to do first.
Keep the game plans beside you while you work through past papers. The goal is that by the exam you no longer need them.
Start with Game plan 0 every time, because it decides which of the others you need. The game plans choose the method. The Topic guides teach it, and carry the worked exam questions and the practice questions. Each game plan points you to the right part of the right guide.
Start here
The first question
Ask these in order every time you start a question, and stop at the first yes.
Which one?
Stop at the first yes
1Is anything joined to anything else, and does the question ask what something is called, how many faces there are, whether a route exists, the shortest route between two places, or the shortest round trip through every place? → Game plan 6, Graphs and networks
2Is anything joined to anything else, and does the question want the cheapest way to connect everything, the minimum completion time or a float time, the maximum flow, or an allocation? → Game plan 7, Network optimisation
3Is there money and a compound interest rate you are given: an investment or loan, an annuity or a perpetuity? → Game plan 5, Finance
4Do you need a distance on the Earth’s surface from latitudes and longitudes, or the time somewhere else from longitudes or time zones? → Game plan 4, Earth geometry and time zones
5Is one quantity listed against seasons, quarters or months, so the question is about smoothing, seasonal indices or deseasonalising? → Game plan 2, Time series
6Are two variables being compared to see how they are related: a two-way table, a scatterplot, $r$, $R^2$ or a least-squares line? → Game plan 1, Bivariate data
7Is something changing step by step, by the same amount or the same factor each time? → Game plan 3, Growth and decay in sequences
Some Paper 2 questions need two game plans. Start with the first thing you have to find, then ask the first question again for the next stage. Game plan 8 lists the questions that have done this, and gives the answer shape for every evaluate, advise and justify question.
Habit
Name the game plan in your head before you pick up your pen. The full version, with the two papers, rounding, units and the setup for sequence and finance questions, is Game plan 0, The first question.
Which game plan?
Here are the openings of eight real QCAA exam questions. Read each one, run the first question, and pick the game plan you would open first. You do not need to solve them.
1 · 2024 Paper 2 Question 3
“Table 1 shows the latitude, x, and ultraviolet index, y, for Australian locations at noon on the first day of autumn. Table 2 categorises the ultraviolet index. …
A person in Hobart (43° S 147° E) at noon on the first day of autumn receives a phone app notification that the ultraviolet index is high.
Use the equation for the least-squares line for the data in table 1 and the information in table 2 to evaluate the reasonableness of the phone app notification.”
The tables are not reproduced here.
The latitude is the explanatory variable in a least-squares line, and you need no distance or time from it.
2 · 2022 Paper 2 Question 1
“The table shows a swimwear company’s seasonally adjusted swimsuit sales (in thousands). …
The long-term seasonal indices for spring, summer and winter are 1.11, 1.42 and 0.62 respectively.
Determine the actual swimsuit sales for autumn.”
The table is not reproduced here.
Seasonal indices and seasonally adjusted sales mean you find the missing index and reseasonalise.
3 · 2025 Paper 2 Question 2
“A vehicle’s value ($) depreciates geometrically each year. The table shows the value, $t_n$, where $n$ is the number of years since the end of 2020. …
Determine if the value at the end of 2028 will be lower than one third of the value at the end of 2021.”
The table is not reproduced here.
There are dollars but no interest rate, and the depreciation ratio is yours to find from the table, so it is a geometric sequence.
4 · 2024 Paper 2 Question 7
“A non-stop flight departs Sydney (UTC +10) at 9:50 pm Tuesday local time and arrives in Los Angeles (UTC −8) at 6:50 pm Tuesday local time. Flight speed is assumed to be constant.
Determine the local time and day in Sydney when the flight distance travelled is 4828 km, with 7242 km remaining.”
Two time zones and a local time to find put you in Game plan 4, and the constant speed is a proportion on top.
5 · 2022 Paper 2 Question 2
“Tam deposits a fixed amount at the end of each month into an account paying 8.6% p.a. compounding monthly. From an initial zero balance, she accumulates $51 343.85 in four years. …”
Regular deposits into an account with a given interest rate are a future value annuity.
6 · 2024 Paper 2 Question 2
“The table shows the travel time (minutes) between five islands in the Torres Strait for a ferry service. …
Construct a weighted graph and use it to calculate the total travel time for a ferry that completes a Hamiltonian cycle beginning at Waiben.”
The table is not reproduced here.
A table of times between places is a network, and a round trip through every vertex is a Hamiltonian cycle, which belongs to Game plan 6.
7 · 2024 Paper 2 Question 5
“A flying doctor coordinator allocates a plane from each of three airbases, A, B and C, to fly to one of three sites, P, Q and R, to provide medical care. Distances (km) are shown in the table. …
Determine the optimal allocation for each plane and the minimum total distance flown.”
The table, with two distances to find from the coordinates of A, P and R, is not reproduced here.
An allocation stops you at question 2 of the list, and Game plan 4 then fills the two missing distances from the coordinates.
8 · 2023 Paper 2 Question 5
“At 9:00 am, a security guard begins their patrol of the eight work sites represented in the network diagram, starting and ending at site A. They drive at 40 km/h on the roads between sites and check every site once for 15 minutes.
The length (km) of each road corresponds to the terms of the arithmetic sequence $t_n = t_1 + 2(n - 1)$, where $t_1 = 1$.
Determine the earliest possible time the security guard can finish their patrol, and identify the route they must follow.”
The network diagram is not reproduced here.
A round trip through every site is a Hamiltonian cycle, so it stops at Game plan 6, and you run Game plan 3 first for the road lengths.
The game plans
Start with Game plan 0 and finish any judgement question with Game plan 8. Game plans 1 to 7 hold the routines for each topic, and each one links back to the Topic guide parts it draws on.
Sources: QCAA General Mathematics external assessment papers, marking guides and subject reports, 2020 to 2025. General Mathematics General Senior Syllabus 2025 and the 2025 formula book.
