ACT Year 12 Mathematical Applications Practice Questions

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ACT Year 12 Mathematical Applications practice questions

Use Skill Align for ACT Year 12 Mathematical Applications practice questions and exercise questions after the relevant topic has been taught. Students can start with the pathway demo, then practise by topic and mode.

27 practice skills

ACT Year 12 Mathematical Applications includes 27 practice skills across Data and statistics, Networks, matrices and modelling, Financial mathematics, and Measurement and applications.

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Sample ACT BSSS Year 12 Mathematical Applications questions

These sample questions are visible on the page before login. They show ACT BSSS Year 12 Mathematical Applications data, finance, matrices, networks, trigonometry, and decision-mathematics explanations before opening the demo.

ACT BSSS Year 12 Mathematical Applications Time series hard forecast graph

1. A trend model predicts 146 bookings for a quarter. The seasonal index for that quarter is 1.08. What is the seasonal forecast, to the nearest whole booking?

Choices

Explanation:

Apply the seasonal index to the trend value: 146 x 1.08 = 157.68, which rounds to 158 bookings.

ACT BSSS Year 12 Mathematical Applications Loans and investments hard finance graph

2. A loan balance follows Bₙ₊₁ = 1.005Bₙ - 520 with B₀ = 18000. What is B₂, to the nearest cent?

Choices

$17,137.85
$17,570.00
$18,090.00
$16,960.00

Explanation:

B₁ = 1.005 x 18000 - 520 = 17570. Then B₂ = 1.005 x 17570 - 520 = 17137.85.

ACT BSSS Year 12 Mathematical Applications Critical path analysis hard critical path diagram

3. A project has three possible branches before final task F: A-C-F takes 4 + 6 + 3 days, B-D-F takes 5 + 7 + 3 days, and B-E-F takes 5 + 4 + 3 days. What is the minimum completion time?

Choices

15 days
13 days
12 days
40 days

Explanation:

The branch totals are 13, 15, and 12 days. The project duration is controlled by the longest required branch, so the minimum completion time is 15 days.

ACT BSSS Year 12 Mathematical Applications Matrices hard transition diagram

4. A row state vector [city, regional] = [480, 320] is multiplied by transition matrix [0.76, 0.24; 0.35, 0.65]. How many customers are expected to be in the city state next period, to the nearest whole customer?

Choices

Explanation:

Use the city column: 480 x 0.76 + 320 x 0.35 = 364.8 + 112 = 476.8, which rounds to 477.

ACT BSSS Year 12 Mathematical Applications Expected value hard weighted score chart

5. A promotion gives a $120 prize with probability 0.18, a $40 prize with probability 0.35, and no prize otherwise. Entry costs $25. What is the expected net gain per entry?

Choices

$10.60
$35.60
$25.00
-$10.60

Explanation:

Expected winnings are 120 x 0.18 + 40 x 0.35 = 21.60 + 14.00 = $35.60. Subtract the $25 entry cost to get an expected net gain of $10.60.

ACT BSSS Year 12 Mathematical Applications Bivariate data hard regression graph

6. A regression model predicts demand with y = 52 + 1.8x. For x = 14, actual demand is 81. What is the residual, using actual - predicted?

Choices

3.8
-3.8
77.2
81

Explanation:

The predicted value is 52 + 1.8 x 14 = 77.2. The residual is 81 - 77.2 = 3.8.

For parents comparing ACT BSSS Year 12 Mathematical Applications support

ACT BSSS Year 12 Mathematical Applications practice should make data, finance, matrices, networks, trigonometry, and decision-mathematics feel structured rather than guessable. These examples preview that style before the no-login Mathematical Applications demo.

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What this practice and exercise page covers

Mathematical Applications practice sits inside ACT BSSS Year 12 mathematics planning coverage across Essential Mathematics, Mathematical Applications, Mathematical Methods, Specialist Methods, Specialist Mathematics, algebra, calculus, statistics, probability, finance, and modelling, with Skill Align keeping the route focused on the selected maths pathway.

Senior practice is organised by pathway, unit, topic, and mode so students can revise targeted areas rather than sitting a full-paper workflow every time. Skill Align treats practice questions and exercise questions as the same learning workflow: students answer curriculum-aligned questions, review explanations, and move between exercise mode and test mode.

Start with the public sample questions to check the question style, then use the curriculum coverage page to choose a topic that matches the student's current classwork.

Preview question styles

Data and statistics: Students practise data and statistics through short targeted questions, explanations, and mode-specific feedback.
Networks, matrices and modelling: Students practise networks, matrices and modelling through short targeted questions, explanations, and mode-specific feedback.
Financial mathematics: Students practise financial mathematics through short targeted questions, explanations, and mode-specific feedback.

Suggested first practice steps

Preview the public sample practice and exercise questions before creating a saved student session.
Choose one focus area that has already been introduced at school.
Use exercise mode for immediate explanations, then test mode when the student is ready for delayed feedback.

Example focus areas

View full curriculum coverage

These examples are not the full topic list. Use the curriculum coverage page for the complete mapped pathway.

Data and statistics
Networks, matrices and modelling
Financial mathematics
Measurement and applications

Who it is for

ACT students studying Mathematical Applications.

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