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General Mathematics Units 3&4 Free Online - Pack 0

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Paper 1 Combined Independent Practice Booklet - Free Online Pack 0

QCE General Mathematics Units 3&4 Free Online Pack 0 — Paper 1 Combined Independent Practice Booklet - Free Online Pack 0

Read Paper 1 Combined Independent Practice Booklet - Free Online Pack 0 online for free, including every question, worked solution, marking note and diagnostic action. No public PDF download or checkout is provided.

QCE Year 12 Final Exam 2026 Edition - Pack 0 v1.0
Paper 1 Combined Independent Practice Booklet - Free Online Pack 0 is free to read in your browser. There is no public checkout or PDF download.

Exam-pack paper structure

This full-length showcase paper is available to read online.

Paper 1 Combined Independent Practice Booklet - Free Online Pack 0

25 questions

57 marks

Estimated duration: Perusal time 5 minutes; working time 90 minutes

Reading: 5 minutes perusal · Writing: 90 minutes

Read Paper 1 Combined Independent Practice Booklet - Free Online Pack 0 online

Skill Align

Skill Align QCE General Mathematics Paper 1 Combined Independent Practice Booklet - Free Online Pack 0

Original Skill Align Units 3&4 combined independent practice booklet; not a secure QCAA administration replica.

Paper
Paper 1 Combined Independent Practice Booklet - Free Online Pack 0
Reading
5 minutes perusal
Writing
90 minutes
Assessment
57 marks
Given name/s
Family name
Teacher
Class
School name

Any additional response paper must show your name and the relevant question number, and must be attached as directed by your school.

Independent practice conditions

Practice resourcePaper 1 Combined Independent Practice Booklet - Free Online Pack 0
Total time5 minutes perusal; 90 minutes working
  • Answer all questions. Show relevant working, mathematical reasoning and conclusions in the spaces provided.
  • You may use writing equipment, a QCAA-approved handheld scientific calculator and the QCAA formula book.
  • During perusal time, read the questions and make notes only on planning paper supplied by your school.
  • This is a combined independent practice booklet. Record each multiple-choice response by selecting A, B, C or D in this booklet; no separate multiple-choice response sheet is supplied.
  • If you use additional response paper, show your name and the relevant question and part number, then attach it as directed by your school.
  • This independent practice resource is not a secure QCAA examination paper. Complete the candidate details above so printed work can be identified.

Section 1

Questions 1–15 are multiple choice. In this combined independent practice booklet, select the best answer A, B, C or D for each question.

Question 1

1 mark
When it is 5(:)30text( pm) in Brisbane (text(UTC)+10), the time in Singapore (text(UTC)+8) is
  1. 3(:)30text( pm)
  2. 4(:)30text( pm)
  3. 6(:)30text( pm)
  4. 7(:)30text( pm)

Question 2

1 mark
A seasonal index of 0.88 means the seasonal value is usually
  1. 12% below the deseasonalised value
  2. 12% above the deseasonalised value
  3. 88% below trend
  4. 0.88% below trend

Question 3

1 mark
A nominal rate of 4.8% per annum compounded monthly has an effective annual rate closest to
  1. 4.80%
  2. 4.91%
  3. 5.20%
  4. 5.76%

Question 4

1 mark
A maintenance crew must travel from A to E. Which route has the least total weight in the displayed network?
Diagram PreviewABCDE4726394network
  1. A-B-C-D-E, weight 13
  2. A-C-D-E, weight 14
  3. A-B-D-E, weight 14
  4. A-C-E, weight 16

Question 5

1 mark
In a survey, 72% of students who use a study planner submit work on time, compared with 57% of students who do not. The difference is
  1. 15 percentage points
  2. 15% of all students
  3. 21 percentage points
  4. 129 percentage points

Question 6

1 mark
The recurrence A_(n+1)=0.96A_n+180 means each step
  1. decreases by 4%, then adds 180
  2. increases by 4%, then adds 180
  3. decreases by 96%, then adds 180
  4. adds 0.96, then multiplies by 180

Question 7

1 mark
A correlation coefficient of r=0.91 indicates
  1. a strong positive association
  2. a weak positive association
  3. a strong negative association
  4. no association

Question 8

1 mark
Using an Earth circumference of 40,000text( km), the great-circle distance subtended by 45^circ is
  1. 4500text( km)
  2. 5000text( km)
  3. 8000text( km)
  4. 9000text( km)

Question 9

1 mark
In the adjacency matrix of an undirected graph, an edge joining B and D gives entries
  1. a_(BD)=a_(DB)=1
  2. a_(BD)=1,a_(DB)=0
  3. a_(BD)=0,a_(DB)=1
  4. a_(BD)=a_(DB)=0

Question 10

1 mark
A loan charges 0.4% monthly interest and deducts a repayment of AUD 350 after interest. The recurrence is
  1. B_(n+1)=1.004B_n-350
  2. B_(n+1)=0.996B_n-350
  3. B_(n+1)=1.04B_n-350
  4. B_(n+1)=B_n-1.004(350)

Question 11

1 mark
In the displayed project network, the critical path is the path with
Diagram PreviewSABT5476network
  1. the greatest total duration
  2. the smallest total duration
  3. the fewest activities
  4. the most vertices

Question 12

1 mark
A connected graph has an Eulerian circuit when
  1. every vertex has even degree
  2. exactly two vertices have odd degree
  3. every vertex has odd degree
  4. it contains no cycle

Question 13

1 mark
The five-median smooth of 9,14,12,21,17 is
  1. 12
  2. 14
  3. 17
  4. 21

Question 14

1 mark
A perpetuity fund of AUD 600000 earns 5.2% per annum. Its annual payment is
  1. AUD 26000
  2. AUD 30000
  3. AUD 31200
  4. AUD 52000

Question 15

1 mark
If R²=0.72, then approximately
  1. 72% of response variation is explained by the linear model
  2. 28% of predictions are exact
  3. the gradient is 0.72
  4. the correlation coefficient is always 0.72

Section 2

Questions 16–25 are short response. Show relevant working, mathematical reasoning and conclusions.

Question 16

3 marks
A video meeting begins at 2:20 pm in Brisbane (UTC+10).
(a) 1 mark
Find the start time in Singapore (text(UTC)+8).
(b) 2 marks
The meeting lasts 110 minutes. Find the finishing time in Singapore.

Question 17

4 marks
A survey records 54 of 75 bus users and 36 of 60 non-bus users arriving before 8:30 am.
(a) 2 marks
Calculate the early-arrival percentage within each travel group.
(b) 2 marks
State the association supported by these percentages.

Question 18

4 marks
Use Earth circumference 40,000text( km). Two locations lie on latitude 60^circtext( S) and differ by 36^circ longitude.
(a) 2 marks
Estimate the circumference of latitude 60^circtext( S).
(b) 2 marks
Estimate the small-circle distance between the locations.

Question 19

4 marks
A business uses seasonal indices to adjust monthly revenue.
(a) 2 marks
Revenue is AUD 105600 with seasonal index 1.10. Find deseasonalised revenue.
(b) 2 marks
Reseasonalise a later forecast of AUD 102500 using index 0.94.

Question 20

4 marks
A loan starts at AUD 48000, earns 0.55% monthly interest, then receives an AUD 820 repayment.
(a) 2 marks
Find the balance after one month.
(b) 2 marks
Write the balance recurrence.

Question 21

4 marks
The plotted observations show a near-linear increasing sequence for the first six terms.
Graph Preview 12.253.54.7561316.52023.527term nvalue y
(a) 2 marks
Explain why a linear model is reasonable over the observed range.
(b) 2 marks
Use y=10+2.8n to predict y at n=9.

Question 22

5 marks
This question compares a perpetuity with monthly compounding.
(a) 2 marks
A perpetuity pays AUD 22400 annually from a fund earning 4%. Find the principal.
(b) 3 marks
Find the effective annual rate for 0.30% interest per month, to two decimal places.

Question 23

4 marks
Use the displayed weighted network.
Diagram PreviewABCDE2356978network
(a) 2 marks
State the edges in one minimum spanning tree.
(b) 2 marks
Find its total weight.

Question 24

5 marks
A café records advertising spend x (hundreds of dollars) and weekly sales y (thousands of dollars): (2,11),(4,15),(6,18),(8,23),(10,26). Technology gives hat y=7.2+1.9x and R²=0.97.
Graph Preview 2468101114.7518.522.2526advertising x ($100)weekly sales y ($000)
(a) 2 marks
Interpret the gradient in context.
(b) 1 mark
Predict weekly sales for x=7.
(c) 2 marks
Interpret R² and state the observed domain.

Question 25

5 marks
Use the displayed project network.
Diagram PreviewSABCDT5476543network
(a) 2 marks
Find the critical-path duration.
(b) 3 marks
An activity has earliest start 6 and latest start 9. Find its float and explain the result.

Queensland Certificate of Education (QCE) subjects and external assessments are administered by the Queensland Curriculum and Assessment Authority (QCAA). Skill Align is an independent publisher and is not affiliated with, authorised by, sponsored by, approved by, or endorsed by QCAA or the Queensland Government.

Copyright (c) 2026 Skill Align. Free for personal, non-commercial online viewing at https://skillalign.au. You may share the Skill Align page link. Except as permitted by law or with Skill Align's prior written permission, the pack itself must not be resold, copied, redistributed, republished, automatically extracted, or uploaded to a question bank.

Worked Solutions And Marking Guide

Section 1 Question 1

Answer: 3(:)30text( pm)

Singapore is two hours behind Brisbane.

Mark allocation

  • 1 mark: select 3(:)30text( pm). Evidence: Singapore is two hours behind Brisbane.

Section 1 Question 2

Answer: 12% below the deseasonalised value

An index of 0.88 is 0.12 below 1.

Mark allocation

  • 1 mark: select 12% below the deseasonalised value. Evidence: An index of 0.88 is 0.12 below 1.

Section 1 Question 3

Answer: 4.91%

(1+0.048 / 12)¹²-1approx0.0491.

Mark allocation

  • 1 mark: select 4.91%. Evidence: (1+0.048 / 12)¹²-1approx0.0491.

Section 1 Question 4

Answer: A-B-C-D-E, weight 13

Adding the edge weights gives 4+2+3+4=13, which is less than the alternatives.

Mark allocation

  • 1 mark: select A-B-C-D-E, weight 13. Evidence: Adding the edge weights gives 4+2+3+4=13, which is less than the alternatives.

Section 1 Question 5

Answer: 15 percentage points

Compare the two conditional percentages: 72-57=15 percentage points.

Mark allocation

  • 1 mark: select 15 percentage points. Evidence: Compare the two conditional percentages: 72-57=15 percentage points.

Section 1 Question 6

Answer: decreases by 4%, then adds 180

The multiplier 0.96 retains 96%, a decrease of 4%.

Mark allocation

  • 1 mark: select decreases by 4%, then adds 180. Evidence: The multiplier 0.96 retains 96%, a decrease of 4%.

Section 1 Question 7

Answer: a strong positive association

The coefficient is positive and close to 1.

Mark allocation

  • 1 mark: select a strong positive association. Evidence: The coefficient is positive and close to 1.

Section 1 Question 8

Answer: 5000text( km)

((45) / (360)) × 40000=5000text( km).

Mark allocation

  • 1 mark: select 5000text( km). Evidence: ((45) / (360)) × 40000=5000text( km).

Section 1 Question 9

Answer: a_(BD)=a_(DB)=1

Adjacency is symmetric for an undirected edge.

Mark allocation

  • 1 mark: select a_(BD)=a_(DB)=1. Evidence: Adjacency is symmetric for an undirected edge.

Section 1 Question 10

Answer: B_(n+1)=1.004B_n-350

Apply the interest multiplier, then subtract the repayment.

Mark allocation

  • 1 mark: select B_(n+1)=1.004B_n-350. Evidence: Apply the interest multiplier, then subtract the repayment.

Section 1 Question 11

Answer: the greatest total duration

The longest-duration path determines the earliest completion time.

Mark allocation

  • 1 mark: select the greatest total duration. Evidence: The longest-duration path determines the earliest completion time.

Section 1 Question 12

Answer: every vertex has even degree

An Eulerian circuit returns to its starting vertex and requires all degrees even.

Mark allocation

  • 1 mark: select every vertex has even degree. Evidence: An Eulerian circuit returns to its starting vertex and requires all degrees even.

Section 1 Question 13

Answer: 14

Ordered values are 9, 12, 14, 17, 21.

Mark allocation

  • 1 mark: select 14. Evidence: Ordered values are 9, 12, 14, 17, 21.

Section 1 Question 14

Answer: AUD 31200

600000 × 0.052=31200.

Mark allocation

  • 1 mark: select AUD 31200. Evidence: 600000 × 0.052=31200.

Section 1 Question 15

Answer: 72% of response variation is explained by the linear model

The coefficient of determination measures explained response variation.

Mark allocation

  • 1 mark: select 72% of response variation is explained by the linear model. Evidence: The coefficient of determination measures explained response variation.

Section 2 Question 16

(a) 12(:)20text( pm).

Singapore is two hours behind Brisbane.

(b) 2(:)10text( pm).

Add 1 hour 50 minutes to 12:20 pm.

Mark allocation

  • Part a (1 mark): Evidence: Singapore is two hours behind Brisbane. Required result: 12(:)20text( pm).
  • Part b (2 marks): Evidence: Add 1 hour 50 minutes to 12:20 pm. Required result: 2(:)10text( pm).

Section 2 Question 17

(a) Bus: 54 / 75=72%. Non-bus: 36 / 60=60%.

Evidence: use the two group totals as conditional denominators and report both percentages.

(b) The bus-user early-arrival rate is 12 percentage points higher, so the data support an association between bus use and early arrival.

Evidence: calculate 72-60=12 percentage points and state the direction without claiming causation.

Mark allocation

  • Part a (2 marks): Evidence: use the two group totals as conditional denominators and report both percentages. Required result: Bus: 54 / 75=72%. Non-bus: 36 / 60=60%.
  • Part b (2 marks): Evidence: calculate 72-60=12 percentage points and state the direction without claiming causation. Required result: The bus-user early-arrival rate is 12 percentage points higher, so the data support an association between bus use and early arrival.

Section 2 Question 18

(a) 40000cos60^circ=20000text( km).

Evidence: scale the equatorial circumference by cos60^circ.

(b) ((36) / (360)) × 20000=2000text( km).

Evidence: use the longitude fraction of the latitude-circle circumference and include kilometres.

Mark allocation

  • Part a (2 marks): Evidence: scale the equatorial circumference by cos60^circ. Required result: 40000cos60^circ=20000text( km).
  • Part b (2 marks): Evidence: use the longitude fraction of the latitude-circle circumference and include kilometres. Required result: ((36) / (360)) × 20000=2000text( km).

Section 2 Question 19

(a) AUD 96000.

105600 / 1.10=96000.

(b) AUD 96350.

102500 × 0.94=96350.

Mark allocation

  • Part a (2 marks): Evidence: 105600 / 1.10=96000. Required result: AUD 96000.
  • Part b (2 marks): Evidence: 102500 × 0.94=96350. Required result: AUD 96350.

Section 2 Question 20

(a) AUD 47444.

48000(1.0055)-820=47444.

(b) B_(n+1)=1.0055B_n-820, B_0=48000.

Apply interest, then subtract the repayment.

Mark allocation

  • Part a (2 marks): Evidence: 48000(1.0055)-820=47444. Required result: AUD 47444.
  • Part b (2 marks): Evidence: Apply interest, then subtract the repayment. Required result: B_(n+1)=1.0055B_n-820, B_0=48000.

Section 2 Question 21

(a) The points lie close to a straight increasing pattern.

There is little curvature or irregular scatter over the six observations.

(b) 35.2.

10+2.8(9)=35.2.

Mark allocation

  • Part a (2 marks): Evidence: There is little curvature or irregular scatter over the six observations. Required result: The points lie close to a straight increasing pattern.
  • Part b (2 marks): Evidence: 10+2.8(9)=35.2. Required result: 35.2.

Section 2 Question 22

(a) AUD 560000.

22400 / 0.04=560000.

(b) 3.66%.

(1.003)¹²-1approx0.0366.

Mark allocation

  • Part a (2 marks): Evidence: 22400 / 0.04=560000. Required result: AUD 560000.
  • Part b (3 marks): Evidence: (1.003)¹²-1approx0.0366. Required result: 3.66%.

Section 2 Question 23

(a) AB,BC,CE,CD.

These four low-weight edges connect all five vertices without a cycle.

(b) 16.

2+3+5+6=16.

Mark allocation

  • Part a (2 marks): Evidence: These four low-weight edges connect all five vertices without a cycle. Required result: AB,BC,CE,CD.
  • Part b (2 marks): Evidence: 2+3+5+6=16. Required result: 16.

Section 2 Question 24

(a) Each additional 100 of advertising is associated with an increase of about 1,900 in predicted weekly sales.

Evidence: interpret one x-unit as 100, one y-unit as 1000, and retain association language.

(b) hat y=7.2+1.9(7)=20.5, or 20,500.

Evidence: substitute x=7 and convert the response unit.

(c) About 97% of the variation in weekly sales is explained by the linear model over the observed domain 2le xle10.

Evidence: interpret explained response variation and give the numeric advertising domain.

Mark allocation

  • Part a (2 marks): Evidence: interpret one x-unit as 100, one y-unit as 1000, and retain association language. Required result: Each additional 100 of advertising is associated with an increase of about 1,900 in predicted weekly sales.
  • Part b (1 mark): Evidence: substitute x=7 and convert the response unit. Required result: hat y=7.2+1.9(7)=20.5, or 20,500.
  • Part c (2 marks): Evidence: interpret explained response variation and give the numeric advertising domain. Required result: About 97% of the variation in weekly sales is explained by the linear model over the observed domain 2le xle10.

Section 2 Question 25

(a) 17 days.

Path S-A-C-T has duration 5+7+5=17, the greatest shown.

(b) Float =3 days; it can be delayed three days without delaying the project.

Float equals latest start minus earliest start.

Mark allocation

  • Part a (2 marks): Evidence: Path S-A-C-T has duration 5+7+5=17, the greatest shown. Required result: 17 days.
  • Part b (3 marks): Evidence: Float equals latest start minus earliest start. Required result: Float =3 days; it can be delayed three days without delaying the project.

Diagnostic Checklist

TopicQuestionsMarksMarks LostAction
Time Zones Q1 1 ___ Convert departure and arrival times through UTC, track the calendar date before applying the destination offset, and explain any International Date Line adjustment.
Time Series Q2 1 ___ Use an odd centred moving mean or median, derive actual-to-trend ratios before averaging a seasonal index, and match the index to the forecast period when reseasonalising.
Loans and Investments Q3 1 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Graphs and Networks Q4 1 ___ Audit vertex degrees and connectivity, apply the relevant Euler, planar, shortest-path or spanning-tree condition, and justify the operational route consequence.
Two-way Tables and Association Q5 1 ___ Calculate conditional percentages using each group total as the denominator, compare percentage-point differences, and separate association from causation.
Sequences Q6 1 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Bivariate Data Q7 1 ___ Enter every ordered pair, report the least-squares equation, r and R², calculate residual as observed minus predicted, and check domain before interpreting a prediction.
Earth Geometry Q8 1 ___ Choose the correct great-circle or latitude-circle circumference, apply the angular fraction with the cosine latitude factor where required, and retain kilometres throughout.
Graphs and Networks Q9 1 ___ Audit vertex degrees and connectivity, apply the relevant Euler, planar, shortest-path or spanning-tree condition, and justify the operational route consequence.
Loans and Investments Q10 1 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Project Networks Q11 1 ___ Complete forward and backward event-time scans, identify zero-float activities and the critical path, then calculate and interpret float from earliest and latest times.
Graphs and Networks Q12 1 ___ Audit vertex degrees and connectivity, apply the relevant Euler, planar, shortest-path or spanning-tree condition, and justify the operational route consequence.
Time Series Q13 1 ___ Use an odd centred moving mean or median, derive actual-to-trend ratios before averaging a seasonal index, and match the index to the forecast period when reseasonalising.
Loans and Investments Q14 1 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Bivariate Data Q15 1 ___ Enter every ordered pair, report the least-squares equation, r and R², calculate residual as observed minus predicted, and check domain before interpreting a prediction.
Time Zones Q16 3 ___ Convert departure and arrival times through UTC, track the calendar date before applying the destination offset, and explain any International Date Line adjustment.
Two-way Tables and Association Q17 4 ___ Calculate conditional percentages using each group total as the denominator, compare percentage-point differences, and separate association from causation.
Earth Geometry Q18 4 ___ Choose the correct great-circle or latitude-circle circumference, apply the angular fraction with the cosine latitude factor where required, and retain kilometres throughout.
Time Series Q19 4 ___ Use an odd centred moving mean or median, derive actual-to-trend ratios before averaging a seasonal index, and match the index to the forecast period when reseasonalising.
Loans and Investments Q20 4 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Sequences Q21 4 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Loans and Investments Q22 5 ___ Match payment timing and interest period before selecting a present-value, future-value, perpetuity or recurrence model; retain unrounded values until the final financial decision.
Graphs and Networks Q23 4 ___ Audit vertex degrees and connectivity, apply the relevant Euler, planar, shortest-path or spanning-tree condition, and justify the operational route consequence.
Bivariate Data Analysis Q24 5 ___ Enter every ordered pair, report the least-squares equation, r and R², calculate residual as observed minus predicted, and check domain before interpreting a prediction.
Project Networks Q25 5 ___ Complete forward and backward event-time scans, identify zero-float activities and the critical path, then calculate and interpret float from earliest and latest times.

What is included

Paper 1 Combined Independent Practice Booklet - Free Online Pack 0 questions (57 marks)

Paper 2 Question and Response Book - Free Online Pack 0 questions (38 marks)

Worked solutions and marking guidance shown online

Diagnostic checklist shown online

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No PDF or downloadable file

Independent practice resource

Queensland Certificate of Education (QCE) subjects and external assessments are administered by the Queensland Curriculum and Assessment Authority (QCAA). Skill Align is an independent publisher and is not affiliated with, authorised by, sponsored by, approved by, or endorsed by QCAA or the Queensland Government.

Each exam pack is listed with a pack label so parents do not buy the same pack twice. Future packs will use the next label for that state or curriculum.

Related Online Practice and curriculum

Pack 0 is a free online resource. These links open the related subscription practice, curriculum coverage, and free public sample questions.

QCE Year 12 General Mathematics practice questions Browse QCE General Mathematics curriculum coverage Try QCE General Mathematics public sample questions

Questions about this exam pack

What is included in General Mathematics Units 3&4 Free Online - Pack 0?

Pack 0 includes 2 full-length showcase papers, worked solutions, marking guidance and diagnostic checklists, all shown online.

Is Pack 0 really free?

Yes. Pack 0 can be read online without checkout or a monthly subscription.

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No. Pack 0 is intentionally online-only and no downloadable PDF is provided.

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No. The questions are original Skill Align material. Skill Align is independent and is not affiliated with, authorised by, sponsored by, approved by, or endorsed by any state assessment authority.