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Examination 1 Showcase

VCE General Mathematics Units 3&4 Free Online Pack 0 — Examination 1 Showcase

Read Examination 1 Showcase online for free, including every question, worked solution, marking note and diagnostic action. No public PDF download or checkout is provided.

VCE Year 12 Final Exam 2026 Edition - Pack 0 v1.0
Examination 1 Showcase 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.

Examination 1 Showcase

40 questions

40 marks

Reading: 15 minutes · Writing: 1 hour 30 minutes

Read Examination 1 Showcase online

Skill Align

Skill Align VCE General Mathematics Units 3&4 - Free Online Pack 0

Multiple-Choice Question Book | 40 questions | 40 marks

Paper
Examination 1 Showcase
Reading
15 minutes
Writing
1 hour 30 minutes
Assessment
40 marks

Materials supplied: one Multiple-Choice Answer Sheet and one General Mathematics formula sheet. Materials permitted: one approved CAS calculator or CAS software, one scientific calculator, one bound reference that may be annotated, and basic stationery. Record every answer on the separate Multiple-Choice Answer Sheet. Pack 0 remains free online; no public answer-sheet, formula-sheet or PDF download is supplied.

Multiple-Choice Questions

Answer all questions. Choose the best answer for each question and record it on the separate Multiple-Choice Answer Sheet. Each question is worth 1 mark.

Question 1

1 mark
The bar chart shows the number of customer support calls resolved in 2, 3, 4 or 5 minutes. The median resolution time is
Graph Preview
32739455resolution time (minutes)calls
  1. 3 minutes
  2. 3.5 minutes
  3. 4 minutes
  4. 4.5 minutes

Question 2

1 mark
The values 14, 17, 17, 19, 23, 26 and 31 have a median of
  1. 17
  2. 18
  3. 19
  4. 21

Question 3

1 mark
A sample has Q1 = 28 and Q3 = 44. Its interquartile range is
  1. 8
  2. 16
  3. 36
  4. 72

Question 4

1 mark
For a sample with Q1 = 18 and Q3 = 30, the lower outlier fence is
  1. -12
  2. 0
  3. 6
  4. 12

Question 5

1 mark
A normally distributed variable has mean 68 and standard deviation 6. Using the 68-95-99.7 rule, the percentage of values between 62 and 80 is approximately
  1. 68%
  2. 81.5%
  3. 95%
  4. 97.5%

Question 6

1 mark
In a survey of 80 commuters, 34 travel by train. The percentage travelling by train is
  1. 34%
  2. 40%
  3. 42.5%
  4. 46%

Question 7

1 mark
The most appropriate display for comparing the distributions of delivery times from two depots is
  1. a pie chart
  2. parallel boxplots
  3. a segmented bar chart
  4. a single histogram

Question 8

1 mark
The scatterplot shows electricity use against daily maximum temperature. The fitted line is closest to
Graph Preview 121722273218.622.626.630.634.6maximum temperature (degrees C)electricity use (MWh)
  1. use = 9 + 0.8 temperature
  2. use = 22 - 0.8 temperature
  3. use = 0.8 + 9 temperature
  4. use = 9 - 0.8 temperature

Question 9

1 mark
A correlation coefficient of r = -0.76 indicates
  1. a strong negative linear association
  2. a strong positive linear association
  3. no association
  4. a proven causal relationship

Question 10

1 mark
For a regression model, an observed value is 47 and the predicted value is 51. The residual is
  1. -4
  2. 4
  3. 47
  4. 98

Question 11

1 mark
A fitted model is log10(y) = 0.8 + 0.2x. When x = 3, the predicted value of y is closest to
  1. 1.4
  2. 14.0
  3. 25.1
  4. 100

Question 12

1 mark
A power model is linearised as log10(y) = 1.1 + 1.5log10(x). The exponent in the original power model is
  1. 0.1
  2. 1.1
  3. 1.5
  4. 12.6

Question 13

1 mark
The five-point median of 22, 19, 24, 31 and 27 is
  1. 22
  2. 24
  3. 27
  4. 31

Question 14

1 mark
The line graph shows monthly bookings. The largest month-to-month decrease is
Graph Preview
1234565248.54541.538384347524549monthbookings
  1. 3
  2. 5
  3. 7
  4. 12

Question 15

1 mark
Quarterly seasonal indices are 0.82, 0.96, 1.08 and k. The value of k is
  1. 0.86
  2. 1.04
  3. 1.14
  4. 1.22

Question 16

1 mark
Actual winter sales are 378 units and the winter seasonal index is 0.90. The deseasonalised sales are
  1. 340 units
  2. 378 units
  3. 420 units
  4. 468 units

Question 17

1 mark
AUD 4,200 is invested at 0.45% per month for 24 months. The balance is
  1. 4200(1.0045)²⁴
  2. 4200(0.0045)²⁴
  3. 4200 + 24(1.0045)
  4. 4200(1.045)²⁴

Question 18

1 mark
A reducing-balance asset model is V(n+1) = 0.88V(n). The annual depreciation rate is
  1. 8%
  2. 12%
  3. 88%
  4. 112%

Question 19

1 mark
An AUD 28,000 vehicle depreciates by 15% per year. Its value after two years is
  1. AUD 19,600
  2. AUD 20,230
  3. AUD 23,800
  4. AUD 25,270

Question 20

1 mark
Under unit-cost depreciation, equipment loses AUD 18,000 over 6000 operating hours. The depreciation per hour is
  1. AUD 2
  2. AUD 3
  3. AUD 6
  4. AUD 12

Question 21

1 mark
A perpetuity of AUD 18,000 per year earns 4.5% per annum. The required principal is
  1. AUD 81,000
  2. AUD 180,000
  3. AUD 400,000
  4. AUD 810,000

Question 22

1 mark
A loan balance follows B(n+1) = 1.006B(n) - 850. The term 850 represents
  1. the interest charged each period
  2. the repayment made each period
  3. the initial loan
  4. the number of repayments

Question 23

1 mark
A nominal annual rate of 7.2% compounded monthly has a monthly rate of
  1. 0.06%
  2. 0.6%
  3. 6%
  4. 7.2%

Question 24

1 mark
An annuity satisfies A(0) = 1000 and A(n+1) = 1.004A(n) + 300. The value of A(1) is
  1. AUD 1,204
  2. AUD 1,300
  3. AUD 1,304
  4. AUD 1,400

Question 25

1 mark
For A = [[3, -1], [2, 5]], the value of a(2,1) is
  1. -1
  2. 2
  3. 3
  4. 5

Question 26

1 mark
If A = [[1, 4], [2, 3]] and B = [[5, 0], [-1, 2]], the entry in row 1, column 2 of AB is
  1. 2
  2. 5
  3. 8
  4. 13

Question 27

1 mark
The determinant of [[4, 1], [2, 3]] is
  1. 5
  2. 10
  3. 12
  4. 14

Question 28

1 mark
The matrix [[k, 3], [2, 6]] is singular when
  1. k = -1
  2. k = 1
  3. k = 3
  4. k = 9

Question 29

1 mark
A transition matrix column contains 0.72 and p. The value of p is
  1. 0.18
  2. 0.28
  3. 0.72
  4. 1.72

Question 30

1 mark
A two-state transition model predicts next month's state vector as [156, 84]. The total population is
  1. 72
  2. 156
  3. 240
  4. 13 104

Question 31

1 mark
If A has order 3 by 2 and B has order 2 by 5, the order of AB is
  1. 2 by 2
  2. 2 by 5
  3. 3 by 5
  4. 5 by 3

Question 32

1 mark
In an adjacency matrix M, the entry (M³)(A,D) counts
  1. direct edges from A to D
  2. two-step walks from D to A
  3. three-step walks from A to D
  4. vertices adjacent to both A and D

Question 33

1 mark
The network shown contains an Euler circuit because
Diagram PreviewABCDE
  1. every vertex has even degree and the network is connected
  2. exactly two vertices have odd degree
  3. every edge has the same weight
  4. there is a Hamiltonian path

Question 34

1 mark
A tree with 11 vertices has
  1. 9 edges
  2. 10 edges
  3. 11 edges
  4. 12 edges

Question 35

1 mark
For the weighted network shown, the minimum spanning tree has total weight
Diagram PreviewABCD628793
  1. 9
  2. 10
  3. 11
  4. 13

Question 36

1 mark
A cut crosses source-to-sink edges of capacities 7, 4 and 6. The capacity of the cut is
  1. 7
  2. 10
  3. 17
  4. 168

Question 37

1 mark
Two edge-disjoint routes have bottleneck capacities 5 and 8. Their combined possible flow is
  1. 5
  2. 8
  3. 13
  4. 40

Question 38

1 mark
Routes from P to T have lengths 14, 17, 19 and 22. The shortest-path distance is
  1. 3
  2. 14
  3. 17
  4. 72

Question 39

1 mark
The minimum assignment uses costs 7, 4, 6 and 5 for four worker-task pairs. The total cost is
  1. 18
  2. 20
  3. 22
  4. 24

Question 40

1 mark
An activity has earliest start 9 days and latest start 12 days. Its float is
  1. 0 days
  2. 3 days
  3. 9 days
  4. 21 days

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Worked Solutions And Marking Guide

Question 1

Answer: 4 minutes

There are 24 calls. The 12th and 13th observations both lie in the 4-minute category.

Question 2

Answer: 19

The fourth value in the ordered list is 19.

Question 3

Answer: 16

The interquartile range is 44 - 28 = 16.

Question 4

Answer: 0

The IQR is 12, so the lower fence is 18 - 1.5(12) = 0.

Question 5

Answer: 81.5%

The interval extends from one standard deviation below the mean to two standard deviations above it. Using the 68-95-99.7% rule, 34%+34%+13.5%=81.5%.

Question 6

Answer: 42.5%

34 divided by 80 is 0.425, or 42.5%.

Question 7

Answer: parallel boxplots

Parallel boxplots compare centre, spread and possible outliers for two numerical distributions.

Question 8

Answer: use = 9 + 0.8 temperature

The fitted line rises by about 0.8 units per degree and crosses the use axis near 9.

Question 9

Answer: a strong negative linear association

The magnitude is large and the sign is negative; correlation alone does not establish causation.

Question 10

Answer: -4

Residual = observed - predicted = 47 - 51 = -4.

Question 11

Answer: 25.1

The transformed prediction is 1.4, so y = 10^1.4, approximately 25.1.

Question 12

Answer: 1.5

For log(y) = log(a) + b log(x), the power is b = 1.5.

Question 13

Answer: 24

After ordering, 19, 22, 24, 27, 31, the middle value is 24.

Question 14

Answer: 7

Bookings fall from 52 to 45 between the fourth and fifth months, a decrease of 7.

Question 15

Answer: 1.14

Four quarterly indices sum to 4, so k = 4 - 2.86 = 1.14.

Question 16

Answer: 420 units

Deseasonalised sales = 378 / 0.90 = 420.

Question 17

Answer: 4200(1.0045)²⁴

Monthly compounding uses a multiplier of 1.0045 for 24 periods.

Question 18

Answer: 12%

A multiplier of 0.88 retains 88% of the value, so 12% is lost.

Question 19

Answer: AUD 20,230

The value is 28000(0.85)² = 20230.

Question 20

Answer: AUD 3

18000 / 6000 = AUD 3 per operating hour.

Question 21

Answer: AUD 400,000

Principal = annual payment / rate = 18000 / 0.045 = 400000.

Question 22

Answer: the repayment made each period

Interest is applied by the multiplier, then AUD 850 is subtracted as the repayment.

Question 23

Answer: 0.6%

Divide the nominal annual rate by 12: 7.2% / 12 = 0.6%.

Question 24

Answer: AUD 1,304

A(1) = 1.004(1000) + 300 = 1304.

Question 25

Answer: 2

Row 2, column 1 contains 2.

Question 26

Answer: 8

Row 1 of A dotted with column 2 of B gives 1(0) + 4(2) = 8.

Question 27

Answer: 10

The determinant is 4(3) - 1(2) = 10.

Question 28

Answer: k = 1

The determinant is 6k - 6, which is zero when k = 1.

Question 29

Answer: 0.28

Transition probabilities in a column sum to 1, so p = 1 - 0.72.

Question 30

Answer: 240

The total is 156 + 84 = 240.

Question 31

Answer: 3 by 5

The inner dimensions match; the outer dimensions are 3 and 5.

Question 32

Answer: three-step walks from A to D

Entries of the third power count walks of length three.

Question 33

Answer: every vertex has even degree and the network is connected

A connected network has an Euler circuit exactly when every vertex has even degree.

Question 34

Answer: 10 edges

Every tree with n vertices has n - 1 edges.

Question 35

Answer: 11

Selecting AC = 2, CD = 3 and AB = 6 connects all four vertices without a cycle for a total of 11.

Question 36

Answer: 17

Cut capacity is the sum 7 + 4 + 6 = 17.

Question 37

Answer: 13

The two routes can carry 5 + 8 = 13 units.

Question 38

Answer: 14

The shortest path is the route with minimum total length, 14.

Question 39

Answer: 22

Add the chosen assignment costs: 7 + 4 + 6 + 5 = 22.

Question 40

Answer: 3 days

Float = latest start - earliest start = 12 - 9 = 3 days.

Diagnostic Checklist

TopicQuestionsMarksMarks LostAction
Data Analysis Q1 1 ___ Redo the calculation from its defining rule: There are 24 calls. The 12th and 13th observations both lie in the 4-minute category.
Data Analysis Q2 1 ___ Redo the calculation from its defining rule: The fourth value in the ordered list is 19.
Data Analysis Q3 1 ___ Order the data, calculate Q1, median and Q3 using the stated convention, then apply the 1.5 × IQR fences before comparing distributions.
Data Analysis Q4 1 ___ Order the data, calculate Q1, median and Q3 using the stated convention, then apply the 1.5 × IQR fences before comparing distributions.
Data Analysis Q5 1 ___ Standardise with z=((x-mu) / (sigma)), then interpret the sign and magnitude in standard-deviation units.
Data Analysis Q6 1 ___ Redo the calculation from its defining rule: 34 divided by 80 is 0.425, or 42.5%.
Data Analysis Q7 1 ___ Order the data, calculate Q1, median and Q3 using the stated convention, then apply the 1.5 × IQR fences before comparing distributions.
Data Analysis Q8 1 ___ Redo the calculation from its defining rule: The fitted line rises by about 0.8 units per degree and crosses the use axis near 9.
Data Analysis Q9 1 ___ Redo the calculation from its defining rule: The magnitude is large and the sign is negative; correlation alone does not establish causation.
Data Analysis Q10 1 ___ Calculate residual = observed - predicted, then use its sign or the residual-plot pattern to assess the model.
Data Analysis Q11 1 ___ Redo the calculation from its defining rule: The transformed prediction is 1.4, so y = 10^1.4, approximately 25.1.
Data Analysis Q12 1 ___ Redo the calculation from its defining rule: For log(y) = log(a) + b log(x), the power is b = 1.5.
Data Analysis Q13 1 ___ Redo the calculation from its defining rule: After ordering, 19, 22, 24, 27, 31, the middle value is 24.
Data Analysis Q14 1 ___ Redo the calculation from its defining rule: Bookings fall from 52 to 45 between the fourth and fifth months, a decrease of 7.
Data Analysis Q15 1 ___ Divide by the seasonal index to remove seasonality, multiply by it to restore seasonality, and align the forecast with the correct season.
Data Analysis Q16 1 ___ Divide by the seasonal index to remove seasonality, multiply by it to restore seasonality, and align the forecast with the correct season.
Recursion and Financial Modelling Q17 1 ___ Redo the calculation from its defining rule: Monthly compounding uses a multiplier of 1.0045 for 24 periods.
Recursion and Financial Modelling Q18 1 ___ Choose the stated depreciation model, calculate adjacent values around any threshold, and retain the required scrap-value or domain constraint.
Recursion and Financial Modelling Q19 1 ___ Choose the stated depreciation model, calculate adjacent values around any threshold, and retain the required scrap-value or domain constraint.
Recursion and Financial Modelling Q20 1 ___ Choose the stated depreciation model, calculate adjacent values around any threshold, and retain the required scrap-value or domain constraint.
Recursion and Financial Modelling Q21 1 ___ Use annual payment = principal × effective annual rate, allowing for any stated costs before distributing earnings.
Recursion and Financial Modelling Q22 1 ___ Iterate the loan recurrence with interest applied before each repayment; reduce the final repayment when the interest-adjusted balance is below the regular payment.
Recursion and Financial Modelling Q23 1 ___ Redo the calculation from its defining rule: Divide the nominal annual rate by 12: 7.2% / 12 = 0.6%.
Recursion and Financial Modelling Q24 1 ___ Redo the calculation from its defining rule: A(1) = 1.004(1000) + 300 = 1304.
Matrices Q25 1 ___ Redo the calculation from its defining rule: Row 2, column 1 contains 2.
Matrices Q26 1 ___ Redo the calculation from its defining rule: Row 1 of A dotted with column 2 of B gives 1(0) + 4(2) = 8.
Matrices Q27 1 ___ Redo the calculation from its defining rule: The determinant is 4(3) - 1(2) = 10.
Matrices Q28 1 ___ Use the printed matrix dimensions and row-by-column products, then interpret the requested entry or vector in context.
Matrices Q29 1 ___ Use the printed matrix dimensions and row-by-column products, then interpret the requested entry or vector in context.
Matrices Q30 1 ___ Multiply the matrix by the state column vector using the printed row-and-column convention, then apply any stated culling, restocking or total constraint.
Matrices Q31 1 ___ Redo the calculation from its defining rule: The inner dimensions match; the outer dimensions are 3 and 5.
Matrices Q32 1 ___ Use the printed matrix dimensions and row-by-column products, then interpret the requested entry or vector in context.
Networks and Decision Mathematics Q33 1 ___ Redo the calculation from its defining rule: A connected network has an Euler circuit exactly when every vertex has even degree.
Networks and Decision Mathematics Q34 1 ___ Redo the calculation from its defining rule: Every tree with n vertices has n - 1 edges.
Networks and Decision Mathematics Q35 1 ___ Apply Kruskal's or Prim's algorithm, reject any edge that closes a cycle, and confirm that all vertices are connected.
Networks and Decision Mathematics Q36 1 ___ Construct a feasible source-to-sink flow, calculate a matching cut capacity, and use equality of the flow and cut to prove maximality.
Networks and Decision Mathematics Q37 1 ___ Redo the calculation from its defining rule: The two routes can carry 5 + 8 = 13 units.
Networks and Decision Mathematics Q38 1 ___ Use Dijkstra's algorithm: make the smallest temporary label permanent, update adjacent labels, and trace predecessor labels for the route.
Networks and Decision Mathematics Q39 1 ___ Redo the calculation from its defining rule: Add the chosen assignment costs: 7 + 4 + 6 + 5 = 22.
Networks and Decision Mathematics Q40 1 ___ Complete forward and backward scans, identify every zero-float path, and recalculate all affected paths after a duration change.

What is included

Examination 1 Showcase questions (40 marks)

Examination 2 Showcase questions (60 marks)

Worked solutions and marking guidance shown online

Diagnostic checklist shown online

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Related Online Practice and curriculum

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

Questions about this exam pack

What is included in General Mathematics 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.

Can I download Pack 0 as a PDF?

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

Are these official assessment authority examination questions?

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.