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100+ Free QCAA General Maths EA Practice Questions

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Key Facts: QCAA General Maths EA Exam

50%

External assessment contributes 50% to the final General Mathematics result

QCAA General Mathematics 2025 syllabus

Two papers

Paper 1 (30%, simple familiar) and Paper 2 (20%, complex familiar and unfamiliar)

QCAA General Mathematics 2025 syllabus

15 multiple choice

Paper 1 Section 1 has 15 multiple-choice questions; Section 2 has 10 short-response questions

QCAA 2025 General Mathematics Paper 1 question and response book

60/20/20

Approximate mark split of simple familiar, complex familiar and complex unfamiliar questions

QCAA General Mathematics 2025 syllabus

Units 3 and 4

Examination questions relate to Units 3 and 4, with assumed knowledge from Units 1 and 2

QCAA General Mathematics 2025 syllabus

5 topics in Unit 3

Bivariate data, bivariate data 2, time series, sequences, and Earth geometry and time zones

QCAA General Mathematics 2025 syllabus

3 topics in Unit 4

Loans, investments and annuities; graphs and networks; networks and decision mathematics

QCAA General Mathematics 2025 syllabus

100

Free original practice questions provided here

OpenExamPrep

The QCAA General Mathematics external assessment is Queensland's common Year 12 examination for the QCE General Mathematics subject, developed and marked by the QCAA and worth 50% of the final result. It has two papers covering Units 3 and 4: Paper 1 (simple familiar, 30%) has 15 multiple-choice questions and 10 short-response questions; Paper 2 (20%) is complex familiar and complex unfamiliar short response. Mark allocation is about 60% simple familiar, 20% complex familiar and 20% complex unfamiliar. Topics include bivariate data and time series, sequences, Earth geometry and time zones, loans and annuities, and graphs and networks. This 100-question bank gives original multiple-choice practice across every Unit 3 and Unit 4 topic.

Sample QCAA General Maths EA Practice Questions

Try these sample questions to test your QCAA General Maths EA exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In a two-way frequency table, 60 of 150 students who play sport also study music, while 20 of 100 students who do not play sport study music. Comparing the column percentages, what does this suggest?
A.There is no association between playing sport and studying music
B.Sport players are more likely to study music
C.Sport players are less likely to study music
D.All sport players study music
Explanation: Among sport players, 60/150 = 40% study music; among non-players, 20/100 = 20% study music. Because the percentages differ markedly, an association is suggested, and sport players are more likely to study music.
2When constructing a scatterplot to investigate whether hours studied explains exam score, which variable should be placed on the horizontal axis?
A.Exam score, the response variable
B.Hours studied, the explanatory variable
C.Either variable, it does not matter
D.Whichever has the larger values
Explanation: By convention, the explanatory (independent) variable is placed on the horizontal axis and the response (dependent) variable on the vertical axis. Here hours studied is used to explain exam score, so hours studied goes on the horizontal axis.
3A scatterplot shows points scattered closely around a line that falls from upper-left to lower-right. Which description best fits the correlation?
A.Strong positive
B.Strong negative
C.Weak positive
D.No correlation
Explanation: Points tightly clustered around a downward-sloping line indicate a strong negative linear correlation: as one variable increases the other decreases, with little scatter.
4A least-squares line is given by y = 3.5x + 12, where y is predicted sales (in $1000s) and x is advertising spend (in $1000s). What is the predicted increase in sales for each extra $1000 of advertising?
A.$12,000
B.$3,500
C.$15,500
D.$3,500,000
Explanation: The slope is 3.5, so for each 1-unit increase in x (one extra $1000 of advertising) y increases by 3.5 units, i.e. $3500 in sales. The intercept of 12 is the predicted sales when advertising is zero.
5For a least-squares regression line, the correlation coefficient is r = 0.8. What is the coefficient of determination, and how is it interpreted?
A.0.64; about 64% of the variation in the response is explained by the regression
B.0.8; about 80% of the variation is explained
C.0.9; about 90% of the variation is explained
D.0.64; about 64% of points lie on the line
Explanation: The coefficient of determination is r squared = 0.8 squared = 0.64. It is interpreted as the proportion (about 64%) of the variation in the response variable that is explained by the linear relationship with the explanatory variable.
6A least-squares line predicts y = 2x + 5. The actual data point at x = 4 has y = 15. What is the residual at this point?
A.2
B.13
C.-2
D.10
Explanation: Residual = actual minus predicted. Predicted y = 2(4) + 5 = 13, and actual y = 15, so residual = 15 - 13 = 2. A positive residual means the point lies above the line.
7Data were collected for ages 10 to 18 years and a least-squares line was fitted. Using the line to predict a value at age 25 is an example of:
A.Interpolation, which is generally reliable
B.Extrapolation, which may be unreliable
C.Smoothing
D.Calculating a residual
Explanation: Age 25 lies outside the data range of 10 to 18 years, so predicting there is extrapolation. Extrapolation can be unreliable because the relationship may not continue beyond the observed data.
8A correlation coefficient of r = 0.95 is found between ice-cream sales and drowning deaths across the year. What is the most appropriate conclusion?
A.Ice-cream sales cause drownings
B.The strong correlation proves causation
C.A third variable such as hot weather may explain both, so correlation does not imply causation
D.There is no real relationship between the variables
Explanation: A strong correlation does not establish causation. A confounding variable such as hot weather increases both ice-cream sales and swimming (hence drownings), explaining the association without one causing the other.
9To find a least-squares line, the means are x-bar = 5 and y-bar = 20, and the slope is calculated as 3. What is the y-intercept?
A.5
B.20
C.15
D.-5
Explanation: The least-squares line passes through the mean point (x-bar, y-bar). Using y = a + bx: 20 = a + 3(5), so a = 20 - 15 = 5. The y-intercept is 5.
10Which value of the correlation coefficient r indicates the strongest linear relationship?
A.r = 0.45
B.r = -0.88
C.r = 0.10
D.r = -0.30
Explanation: Strength of a linear relationship depends on the magnitude of r, regardless of sign. The largest magnitude here is |-0.88| = 0.88, so r = -0.88 indicates the strongest (negative) linear relationship.

About the QCAA General Maths EA Exam

The QCAA General Mathematics external assessment is the common statewide examination for Queensland Year 12 students studying General Mathematics under the Queensland Certificate of Education (QCE). It is developed and marked by the QCAA, administered under the same conditions on the same day, and contributes 50% to the final subject result alongside three internal assessments. The examination consists of two papers covering Units 3 and 4: Paper 1 (simple familiar, 30%) contains 15 multiple-choice questions and 10 short-response questions, while Paper 2 (20%) contains complex familiar and complex unfamiliar short-response questions. Mark allocation is approximately 60% simple familiar, 20% complex familiar and 20% complex unfamiliar. Content spans bivariate data and time series analysis, growth and decay in sequences, Earth geometry and time zones (Unit 3), and loans, investments and annuities, graphs and networks, and networks and decision mathematics (Unit 4), with assumed knowledge from Units 1 and 2.

Assessment

Two papers. Paper 1 (simple familiar, weighted 30%): 15 multiple-choice questions (Section 1) and 10 short-response questions (Section 2). Paper 2 (weighted 20%): short-response complex familiar and complex unfamiliar questions. Both papers draw on Units 3 and 4.

Time Limit

Each paper allows about 90 minutes working time plus 5 minutes perusal; the two papers together form the external assessment.

Passing Score

No single pass mark. The external assessment contributes 50% to the final General Mathematics result (the three internal assessments contribute the other 50%), and results feed the A-E subject grade and the QCE/ATAR.

Exam Fee

There is no separate fee for the external assessment for students enrolled in Queensland schools; it is part of the QCE General Mathematics subject and is developed and marked by the QCAA. (Queensland Curriculum and Assessment Authority (QCAA))

QCAA General Maths EA Exam Content Outline

28%

Bivariate data and time series analysis

Unit 3 Topics 1-3. Two-way frequency tables and column percentages, scatterplots, Pearson correlation and its interpretation, least-squares regression lines, interpreting slope and intercept, residuals, interpolation versus extrapolation, the coefficient of determination, and time series methods including trend, seasonal indices, moving-average smoothing and deseasonalising data.

16%

Sequences (growth and decay)

Unit 3 Topic 4. Arithmetic sequences and their nth-term rule, geometric sequences and exponential growth and decay, recursion and first-order linear recurrence relations, and modelling practical growth and decay situations without logarithms.

12%

Earth geometry and time zones

Unit 3 Topic 5. Latitude and longitude, distances along meridians and great circles using arc length, nautical miles, and converting times between locations using standard time zones and the date line.

22%

Loans, investments and annuities

Unit 4 Topic 1. Simple and compound interest, effective annual interest rate, future and present value, depreciation, reducing-balance loans and amortisation tables, annuities and perpetuities, and using recurrence relations and finance solvers to analyse repayments and investments.

22%

Graphs, networks and decision mathematics

Unit 4 Topics 2-3. Graph and network terminology, degree, adjacency matrices, connected graphs and planarity, Euler and Hamilton paths and circuits, shortest path, minimum spanning trees (Prim/Kruskal), maximum flow, bipartite matching, and critical path analysis with earliest and latest start times and float.

How to Pass the QCAA General Maths EA Exam

What You Need to Know

  • Passing score: No single pass mark. The external assessment contributes 50% to the final General Mathematics result (the three internal assessments contribute the other 50%), and results feed the A-E subject grade and the QCE/ATAR.
  • Assessment: Two papers. Paper 1 (simple familiar, weighted 30%): 15 multiple-choice questions (Section 1) and 10 short-response questions (Section 2). Paper 2 (weighted 20%): short-response complex familiar and complex unfamiliar questions. Both papers draw on Units 3 and 4.
  • Time limit: Each paper allows about 90 minutes working time plus 5 minutes perusal; the two papers together form the external assessment.
  • Exam fee: There is no separate fee for the external assessment for students enrolled in Queensland schools; it is part of the QCE General Mathematics subject and is developed and marked by the QCAA.

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

QCAA General Maths EA Study Tips from Top Performers

1Learn the QCAA formula and reference sheet so you can quickly find interest, sequence and Earth-geometry formulas during the exam.
2For bivariate data, practise interpreting the least-squares slope and intercept in context and distinguishing interpolation from extrapolation.
3For sequences, be confident moving between recursive rules and explicit nth-term rules for both arithmetic and geometric patterns.
4For finance, set up reducing-balance loan and annuity recurrence relations carefully and check whether the rate is per period or per annum.
5For networks, practise reading adjacency matrices and applying minimum spanning tree, shortest path and critical path methods step by step.
6Use past external assessment papers and marking guides to rehearse timing and to see how complex unfamiliar questions are structured.

Frequently Asked Questions

Does the QCAA General Mathematics external assessment include multiple-choice questions?

Yes. Paper 1 Section 1 contains 15 multiple-choice questions worth simple familiar marks, followed by 10 short-response questions in Section 2. Paper 2 is short response only.

How is the General Mathematics external assessment structured?

There are two papers covering Units 3 and 4. Paper 1 (simple familiar) is weighted 30% and Paper 2 (complex familiar and complex unfamiliar) is weighted 20%, together forming the 50% external assessment.

What topics are assessed?

Unit 3 covers bivariate data and time series analysis, growth and decay in sequences, and Earth geometry and time zones. Unit 4 covers loans, investments and annuities, graphs and networks, and networks and decision mathematics.

How much is the external assessment worth?

The external assessment contributes 50% to the final General Mathematics subject result. The three internal assessments contribute the remaining 50%.

What is the difficulty mix of the questions?

Marks are allocated approximately 60% simple familiar, 20% complex familiar and 20% complex unfamiliar, within plus or minus 2% as set out in the syllabus specifications.

Are these official QCAA questions?

No. These are original OpenExamPrep practice questions modelled on the syllabus topics and assessment objectives. The QCAA publishes official past papers and marking guides separately.