Digital resources for QCE General Mathematics. No subscription. Review the free samples before you decide.
QCE General Mathematics Mastery Pack
Data analysis, networks, matrices and financial maths — full Paper 1 + Paper 2 practice External Assessments with fully worked solutions.
General Mathematics Paper 1: Thu 5 Nov, 12:30pm — 26 days away
Explore the study materials
Constructing and Interpreting Scatterplots
Bivariate Data and the Role of Variables
Bivariate data involves the simultaneous collection of two numerical variables from the same individual or unit. Unlike univariate data, which describes a single characteristic, bivariate data allows us to explore whether and how two quantities are related. In the QCAA General Mathematics course, the analysis of bivariate data begins with a clear understanding of the two variable roles: the explanatory variable and the response variable.
The explanatory variable (sometimes called the independent variable) is the variable believed to explain, predict, or cause changes in the other. It is plotted on the horizontal axis (x-axis) of a scatterplot. The response variable (sometimes called the dependent variable) is the one whose values are expected to respond to or depend upon the explanatory variable. It is plotted on the vertical axis (y-axis).
Correctly identifying which variable is explanatory and which is the response is essential before constructing any scatterplot. Ask yourself: Which variable do I think might predict or influence the other? This is a practical, context-driven decision rather than a purely mathematical one.
- Example A: A Queensland researcher collects data on daily maximum temperature (degrees C) and ice cream sales (units) at a Gold Coast kiosk over 20 summer days. Here, temperature is the explanatory variable (x-axis) and ice cream sales is the response variable (y-axis), because we expect temperature to influence how many ice creams are sold.
- Example B: A school records the number of hours per week students spend on revision and their end-of-semester exam score (%). Study hours is the explanatory variable and exam score is the response variable.
Note carefully: the fact that one variable is explanatory does not automatically mean it causes changes in the response variable. Association does not imply causation. This distinction is critical in the QCAA course and is frequently tested in extended-response questions.
Constructing a Scatterplot
A scatterplot (also called a scatter diagram or scatter graph) is a graph that displays the values of two quantitative variables as points on a Cartesian plane. Each point represents a single observation: its x-coordinate is the value of the explanatory variable and its y-coordinate is the value of the response variable.
Steps to construct a scatterplot:
- Step 1: Identify which variable is explanatory (x-axis) and which is the response (y-axis).
- Step 2: Draw and label both axes with the variable name and its units. Choose axis scales that allow all data points to be plotted clearly without excessive white space.
- Step 3: For each observation, locate its x-value on the horizontal axis and its y-value on the vertical axis, then plot the point at the intersection.
- Step 4: Give the scatterplot a descriptive title that references both variables.
Worked Example: Body Mass and Resting Heart Rate in Brisbane Adults
A health researcher collected data from 10 Brisbane adults. The explanatory variable is body mass (kg) and the response variable is resting heart rate (bpm).
| Body Mass (kg) | Resting HR (bpm) |
|---|---|
| 55 | 62 |
| 60 | 65 |
| 68 | 70 |
| 72 | 74 |
| 78 | 72 |
| 85 | 78 |
| 90 | 80 |
| 95 | 85 |
| 100 | 88 |
| 110 | 91 |
Each pair is plotted as a single point: for body mass 55 kg and resting HR 62 bpm, place a point at (55, 62). Repeat for all 10 pairs. The horizontal axis should run from approximately 50 to 115 kg, and the vertical axis from approximately 60 to 95 bpm. Both axes must be clearly labelled with variable names and units.
In QCAA assessments, you may be asked to add a single additional point to an existing scatterplot or identify which point corresponds to a given data pair. Always check both coordinates carefully before plotting.
- cyclical component
- seasonal component
- irregular component
- long-term trend component
Show the worked answer
Answer: B
What's inside General Mathematics
Preview it all free. Unlock when you're ready.
Unlock the original practice exams, answer guides, worked questions and digital flashcards. Complete revision notes are also available free. From $20 once for one subject, with access while the platform operates.
Taking more subjects? Add two more for $30 — three subjects for $50 total, $16.67 each, all yours for life.
Compare 1, 3 or 5 subjects ▾
- 1 subject — $20 once
General Mathematics onlyUnlock 1 - 3 subjects — $50 once
$16.67 a subject · pick the rest after you payUnlock 3 - 5 subjects — $60 once
$12 a subject · pick the rest after you payUnlock 5
Each selected subject includes its complete Mastery Pack. Choose how many subjects you need. Full pricing page →
No account needed · one-time payment in AUD · digital resources · by purchasing you agree to our Terms.
General Mathematics Paper 1: Thu 5 Nov, 12:30pm — 26 days away
Our promise: see the real material before you pay — a worked exam question, the opening of a real revision note and the full contents list of all 20 revision notes and 20 practice exams are on this page, free. If you unlock it and it isn't what this page described, email hello@atarmaxxing.com.au and we'll refund it — no form, no argument. We won't promise you an ATAR; we promise the material is what we said it was.
Everything you unlock
All 20 practice exams
- Exam 1 — Time series analysis: 4-quarter centred moving averages, ratio-to-moving-average seasonal indices, deseasonalising (divide by SI), and reseasonalised next-year forecasting of Queensland seasonal rainfall across four weather stations; Bivariate data: scatterplots, Pearson's r, coefficient of determination R², least-squares regression and prediction (rainfall vs reservoir inflow); Arithmetic and geometric sequences and recurrence relations modelling annual rainfall trend and drought storage decay
- Exam 2 — Bivariate data analysis: scatterplots, Pearson's r, coefficient of determination R-squared, least-squares regression, residuals, correlation vs causation (reef health score vs water temperature); Time series analysis: trend/seasonal/cyclical/irregular components, 4-point centred moving averages, ratio-to-moving-average seasonal indices, deseasonalising, regression-based forecasting (Great Barrier Reef visitor numbers); Growth and decay in sequences: arithmetic and geometric rules and recurrence relations, simultaneous equations for unknown terms, threshold/doubling problems
- Exam 3 — Bivariate data: Pearson r, R-squared, least-squares regression, residuals (cane yield vs rainfall); Time series: trend/seasonal/cyclical/irregular, centred moving averages, seasonal indices, deseasonalising, forecasting (quarterly cane crush); Arithmetic and geometric sequences and recurrence relations (annual sugar cane harvest growth; machinery depreciation)
- Exam 4 — Unit 4 Networks: weighted directed graphs, adjacency matrices, Dijkstra's shortest path, Euler/Hamilton, TSP; Unit 4 Decision maths: minimum spanning trees (Kruskal/Prim), max-flow min-cut, Hungarian assignment, critical path analysis (forward/backward pass, float); Unit 4 Finance: compound interest with varied compounding, reducing-balance loans and amortisation, annuities (FV) and perpetuities
- Exam 5 — Project network critical path analysis: precedence table to activity network, dummy activities, forward/backward pass, EST/EFT/LST/LFT, float, critical activities, crashing; Graph and network theory: adjacency matrices, Euler's formula, Eulerian/Hamiltonian graphs, Dijkstra shortest path, travelling salesman; Decision mathematics: minimum spanning trees (Kruskal/Prim), maximum-flow minimum-cut, bipartite assignment
- Exam 6 — Bivariate data: least-squares regression, Pearson r and r-squared interpretation in context; Time series: 4-quarter centred moving averages, seasonal indices, deseasonalising actual data; Arithmetic and geometric sequences: equipment depreciation and ore-stockpile decay modelling
- Exam 7 — Unit 4 Topic 1 financial mathematics as the spine — compound interest with monthly compounding (A=P(1+r/n)^nt and recurrence A_{n+1}=(1+i)A_n), future value of a regular-deposit annuity, reducing-balance loan recurrence, and perpetuity — set in a Sunshine Coast investment-property renovation-savings context; Full seven-topic EA coverage: bivariate data (Pearson's r, R^2, least-squares line), time series (seasonal indices, deseasonalisation, centred moving averages, reseasonalised forecasts), arithmetic and geometric sequences and recurrence relations, earth geometry (parallel and meridian distances) and time zones; Networking and decision mathematics: graph terminology and degree/edge counting, Euler's formula, Dijkstra shortest path, minimum spanning tree (Kruskal/Prim), and critical path analysis with full forward/backward pass, float times and critical-activity identification
- Exam 8 — Earth geometry: latitude/longitude positions, great-circle and same-meridian/same-parallel distances using the QCAA formula (R = 6400 km); Longitude-based time differences (15 degrees = 1 hour) and International Date Line day changes across the Pacific; Bivariate data: scatterplots, Pearson's r, the coefficient of determination R squared, and least-squares regression with contextual interpretation
- Exam 9 — Geometric sequences and recurrence relations (herd growth with culling); Arithmetic sequences and series; Time series: seasonal indices, deseasonalising, moving-average smoothing, trend forecasting
- Exam 10 — Bivariate data analysis (Pearson's r, R squared, least-squares regression, prediction, correlation vs causation); Time series analysis (4-point centred moving averages, seasonal indices, deseasonalising, forecasting, seasonal vs cyclical vs structural change); Arithmetic and geometric sequences and recurrence relations (growth/decay modelling, simultaneous equations)
- Exam 11 — Bivariate data: scatterplots, Pearson's r, R-squared, least-squares regression and prediction (solar install cost vs panel count); Time series: trend/seasonal/cyclical/irregular components, 4-quarter centred moving averages, seasonal indices, deseasonalising and forecasting; Arithmetic and geometric sequences and recurrence relations modelling panel installation rates and output degradation
- Exam 12 — Networks and decision mathematics (graph terminology, adjacency matrices, Euler's formula, Eulerian and Hamiltonian paths/circuits, Dijkstra's shortest path, travelling salesman, minimum spanning trees via Kruskal's and Prim's, maximum-flow minimum-cut, critical path analysis) applied to a South-East Queensland multimodal public transport network; Bivariate data and least-squares regression, Pearson's r and R-squared; Time series analysis: trend, seasonal indices, centred moving averages, deseasonalising and forecasting
- Exam 13 — Bivariate data: Pearson's r, R-squared and least-squares regression with contextual interpretation (Q16, Q27); Time series: 3-point moving averages, seasonal indices, deseasonalising by division, and forecasting (Q17, Q18, Q26, Q27); Arithmetic and geometric sequences via recurrence relations for passenger/route growth (Q6, Q7, Q19)
- Exam 14 — Earth geometry: latitude/longitude positions, great-circle meridian arc distance (d = angle/360 x 2 pi R, R = 6400 km), three-figure bearings and reverse bearings; Time zones and the International Date Line: AEST (UTC+10) to Vanuatu (UTC+11) conversions, longitude-to-time, eastbound IDL day adjustment; Bivariate data: scatterplots, Pearson r, coefficient of determination R-squared, least-squares regression line, interpolation/extrapolation and contextual interpretation
- Exam 15 — Bivariate data: two-way frequency tables, association between categorical variables, Pearson's r, least-squares regression and R-squared evaluation (UQ research-funding context); Time series: centred moving averages, seasonal indices, deseasonalisation and forecasting of quarterly grant income; Sequences: arithmetic and geometric models with recurrence relations for research output growth and funding
- Exam 16 — Time series analysis: trend, seasonal indices, deseasonalisation and deseasonalised-trend forecasting (Queensland Health flu vaccination context); Bivariate data: Pearson's r, coefficient of determination R^2, least-squares regression, residuals and two-way tables; Arithmetic and geometric sequences and recurrence relations (dose delivery and cold-chain decay)
- Exam 17 — Sequences & recurrence relations (arithmetic/geometric, loan-balance modelling); Financial mathematics: perpetuities, annuities, reducing-balance loans, amortisation, compound interest with varied compounding; Bivariate data & least-squares regression (Pearson's r, prediction)
- Exam 18 — Bivariate data: scatterplots, Pearson's r, R-squared, least-squares regression, residuals (Mackay cable cost vs length); Time series: seasonal indices, deseasonalising, centred moving averages, trend and forecasting (desalination water demand); Arithmetic and geometric sequences and recurrence relations (cable-laying schedule, maintenance cost escalation)
- Exam 19 — Bivariate data analysis: scatterplots, Pearson's r, coefficient of determination R-squared, least-squares regression, interpolation vs extrapolation, residuals (athlete age vs finish time); Time series analysis: trend/seasonal/cyclical/irregular components, 4-point centred moving averages, seasonal indices, deseasonalising, forecasting (annual triathlon entries); Arithmetic and geometric sequences: nth-term and recurrence relations, series sums (entry growth, prize pools)
- Exam 20 — Financial mathematics: simple and compound interest, reducing-balance loans, annuities/savings plans, effective interest rates, depreciation, GST, CPI/inflation; Applied trigonometry: Pythagoras, right-angled trig, sine rule, cosine rule, area of triangles, bearings, angles of elevation/depression; Graphs and networks: minimum spanning trees, shortest path, vertex degree/handshake lemma, connected weighted graphs
All 20 revision notes
- Constructing and Interpreting Scatterplots
- Calculating and Interpreting r
- Regression Line Equation, Prediction and Residuals
- Identifying Association Between Categorical Variables
- Constructing Plots and Identifying Components
- Centred Moving Averages and Linear Trend Lines
- Computing Seasonal Indices, Deseasonalising and Forecasting
- Arithmetic Sequence Rules and Recurrence Relations
- Geometric Sequence Rules and Recurrence Relations
- Locating Positions and Calculating Distances on Earth
- Time Differences, Travel Problems and the Date Line
- Compound Interest with Variable Compounding Periods
- Modelling Loans with Recurrence Relations and Repayment Calculations
- Present Value, Future Value of Annuities and Perpetuities
- Graph Types, Adjacency Matrices and Euler's Formula
- Walks, Eulerian and Hamiltonian Graphs, and the Travelling Salesman Problem
- Shortest Path Problems Using Dijkstra's Algorithm
- Kruskal's and Prim's Algorithms for Minimum Spanning Trees
- Activity Networks, Critical Path and Float Times
- Maximum Flow, Bipartite Graphs and the Hungarian Algorithm
Common questions about QCE General Mathematics
Which units of QCE General Mathematics are on the external assessment?
Units 3 and 4 only. Units 1 and 2 are assessed at school and are not examined directly by QCAA, although their consumer arithmetic, measurement, trigonometry and matrix content sits underneath nearly every Unit 3 and 4 question, so it still needs to be fluent by the time you sit the papers.
How many exam papers are there in General Mathematics?
Two. Paper 1 assesses simple familiar questions and contributes 30% of the subject result; Paper 2 assesses complex familiar and complex unfamiliar questions and contributes 20%. Each has 5 minutes perusal and 90 minutes working time. Historical raw mark totals are not a fixed 2026 specification.
Has the General Mathematics syllabus changed since 2019?
Yes. The 2025 syllabus applies to students completing in 2026. QCAA highlights calculation of both r and r squared using technology, activity-on-arc critical path analysis, Hungarian algorithm minimisation and maximisation up to 5 by 5, and an updated formula book. Use older papers as practice after checking their content and conditions against the current syllabus.
What is the QCAA subject report and should I read it?
A subject report is published for each cohort alongside the papers and marking guide. It describes how students statewide handled each question and where responses commonly fell short, which makes it more useful than the marking guide alone when you are working out why a method that looked right did not earn full marks.
Does QCE General Mathematics scale up or down?
General Mathematics scales down, and by a wide margin against Mathematical Methods. In QTAC's 2024 ATAR report the median raw result of 68 scaled to 60.48 out of 100. Scaling is recalculated every year, so this describes a past cohort rather than the year you are sitting.
What is included in the QCE General Mathematics Mastery Pack?
Original practice exams with answer guides, worked questions, digital flashcards and revision notes for General Mathematics. Complete revision notes are also available free. Official past papers are free external links, not material we sell. Preview the sample note, worked question and contents here. Paid resources unlock with a one-time purchase from $20, with access while the platform operates.
Where can I buy QCE General Mathematics notes and practice exams?
You can buy the General Mathematics Mastery Pack here as a one-time purchase: original practice exams with answer guides, revision notes, worked questions and flashcards. Printed study guides, trial-exam packs and student note marketplaces are other options, and official QCAA past papers are free — see the past-paper index for this subject.
Is the QCE General Mathematics Mastery Pack a subscription?
No. It is a single payment per subject with no renewal, and access continues while the platform operates. You can preview a sample note, a worked question and the full contents before paying.
More detail: the syllabus explained · every official past paper by topic · how General Mathematics scales · all 20 General Mathematics revision notes · General Mathematics practice exams with worked solutions