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Free Practice Questions for VCE Foundation Mathematics

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Key Facts: VCE Foundation Mathematics Exam

Administered by the Victorian Curriculum and Assessment Authority (VCAA).

Assesses 4 Areas of Study: Financial Mathematics, Data Analysis & Probability, Space & Measurement, and Algebra, Number & Structure.

The external written examination is 2 hours long with 15 minutes reading time (100 marks total).

External exam contributes 40% towards the VCE Study Score (out of 50), with internal SACs contributing 60%.

Focuses on practical, real-world applications including Australian financial, tax, and spatial measurement contexts.

VCE Foundation Mathematics Units 3 & 4 practice question bank for senior secondary exam revision.

Sample VCE Foundation Mathematics Practice Questions

Try these sample questions to review concepts for the VCE Foundation Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Round 0.004072 to two significant figures.
A.0.0041
B.0.0040
C.0.004
D.0.00407
Explanation: Leading zeros are not significant, so the first two significant figures of 0.004072 are the 4 and the 0. The next digit is 7, which is 5 or more, so the second significant figure rounds up from 0 to 1, giving 0.0041.
2A concrete mix uses cement, sand and aggregate in the ratio 1 : 2 : 4. A batch has a total mass of 21 kg. What mass of cement is required?
A.3 kg
B.5.25 kg
C.7 kg
D.2.1 kg
Explanation: The ratio 1 : 2 : 4 has 1 + 2 + 4 = 7 parts in total. One part is 21 kg divided by 7, which is 3 kg. Cement is 1 part, so 3 kg of cement is needed.
3A steel rod should be 5.00 m long. A measurement records it as 4.85 m. What is the percentage error of the measurement?
A.3%
B.1.5%
C.15%
D.0.3%
Explanation: Percentage error is the size of the difference divided by the true value, expressed as a percentage. The difference is 5.00 - 4.85 = 0.15 m, so the percentage error is 0.15 / 5.00 x 100 = 3%.
4The circumference of a circle is given by C = 2 x pi x r. A circular garden bed has a circumference of 31.4 m. Correct to one decimal place, what is its radius?
A.5.0 m
B.10.0 m
C.15.7 m
D.9.9 m
Explanation: Transpose the formula to make r the subject: r = C / (2 x pi). Substituting gives r = 31.4 / (2 x 3.1416) = 31.4 / 6.2832 = 5.0 m.
5The cost y of a job varies directly with the number of hours x worked. When x = 4.5 hours the cost is AUD 18.00. What is the cost for 7 hours?
A.AUD 28.00
B.AUD 25.00
C.AUD 31.50
D.AUD 20.50
Explanation: Direct variation means y = kx. From 18 = k x 4.5, the constant of variation is k = 4. For x = 7 hours, y = 4 x 7 = AUD 28.00.
6Six landscapers can complete a job in 10 days. Assuming all work at the same rate, how long would 4 landscapers take to complete the same job?
A.15 days
B.6.7 days
C.12 days
D.20 days
Explanation: This is inverse variation, so the number of worker-days stays constant. The job takes 6 x 10 = 60 worker-days. With 4 workers the time is 60 / 4 = 15 days.
7A market stall has costs C = 500 + 8n dollars and revenue R = 18n dollars, where n is the number of items sold. How many items must be sold to break even?
A.50 items
B.28 items
C.63 items
D.100 items
Explanation: Break-even occurs where revenue equals cost. Setting 18n = 500 + 8n gives 10n = 500, so n = 50 items.
8For a stall with costs C = 500 + 8n and revenue R = 18n dollars, what is the total revenue at the break-even point?
A.AUD 900.00
B.AUD 500.00
C.AUD 400.00
D.AUD 1,400.00
Explanation: Break-even occurs at n = 50 items, because 18n = 500 + 8n gives 10n = 500. Revenue is then R = 18 x 50 = AUD 900.00, which equals the total cost of 500 + 8 x 50 = AUD 900.00.
9Which of these numbers is irrational?
A.The square root of 50
B.0.75
C.22/7
D.3.14
Explanation: An irrational number cannot be written as a ratio of two integers, and its decimal expansion never terminates or repeats. 50 is not a perfect square, so its square root is irrational. The other three values are ratios of integers or terminating decimals.
10A 3.5 litre tin of paint covers 42 square metres. How many litres are needed to cover 90 square metres at the same coverage rate?
A.7.5 L
B.6.0 L
C.10.5 L
D.8.4 L
Explanation: The coverage rate is 42 / 3.5 = 12 square metres per litre. Covering 90 square metres requires 90 / 12 = 7.5 litres.

About the VCE Foundation Mathematics Exam

VCE Foundation Mathematics Units 3 & 4 practice questions aligned with VCAA Study Design requirements.

Exam sponsor: Victorian Curriculum and Assessment Authority (VCAA). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official 2026 VCAA scored assessment: Unit 3 SAC 40%, Unit 4 SAC 20%, written examination 40%. This practice bank provides English-language multiple-choice study questions and is not an official-format simulation.

Time Limit

15 minutes reading time + 2 hours writing time (2026 VCAA written examination session).

Passing Score

Not pass/fail. Results contribute to a VCE study score out of 50 (scaled for ATAR).

Exam / Certification Fees

Included in standard Victorian secondary/VCE enrolment; fee-paying international students are invoiced VCAA administration fees through their school (see VCAA Fees and charges).

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

50%

Unit 3 - Area of Study 1 & 2

Core knowledge for Unit 3.

50%

Unit 4 - Area of Study 1 & 2

Advanced applications for Unit 4.

Preparing for the VCE Foundation Mathematics Exam

What You Need to Know

  • Passing score: Not pass/fail. Results contribute to a VCE study score out of 50 (scaled for ATAR).
  • Assessment: Official 2026 VCAA scored assessment: Unit 3 SAC 40%, Unit 4 SAC 20%, written examination 40%. This practice bank provides English-language multiple-choice study questions and is not an official-format simulation.
  • Time limit: 15 minutes reading time + 2 hours writing time (2026 VCAA written examination session).
  • Exam / certification fees: Included in standard Victorian secondary/VCE enrolment; fee-paying international students are invoiced VCAA administration fees through their school (see VCAA Fees and charges). Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

VCE Foundation Mathematics: Suggested Study Strategy

1Always check whether GST is being added to a pre-tax amount (multiply by 1.10) or extracted from a GST-inclusive total (divide by 11).
2Convert interest rates and time periods to matching units before applying simple ($I = P r t$) or compound interest ($A = P(1 + r)^n$) formulas.
3Pay attention to scale factors when working with maps: square the linear scale factor when converting areas (1 cm² on map = k² cm² in real life).
4For statistical measures, always arrange raw data in ascending order first before identifying medians, quartiles, and interquartile ranges.
5Ensure all units are converted consistently (e.g. metres to centimetres, hours to minutes) before evaluating practical measurement formulas.

Frequently Asked Questions

What is VCE Foundation Mathematics Units 3 & 4?

VCE Foundation Mathematics Units 3 & 4 is a senior secondary mathematics study designed to equip VCE students with practical, everyday mathematical skills for employment, small business management, personal finance, and further vocational training.

How is VCE Foundation Mathematics assessed by VCAA?

Assessment includes School-Assessed Coursework (SACs) contributing 60% of the overall study score and a 2-hour external written examination contributing 40%.

Does this 100-question practice bank contain worked calculations?

Yes. Every calculation question includes step-by-step numerical workings in Australian Dollars (AUD) or metric units, making it ideal for building exam confidence.

Are scientific and CAS calculators permitted in VCE Foundation Mathematics exams?

Yes, approved scientific calculators and CAS (Computer Algebra System) / graphics calculators are permitted during the external examination.

What topics are covered under Financial Mathematics?

Topics include simple interest, compound interest, gross vs net income, pay as you go (PAYG) tax, GST calculations, unit prices, simple budgeting, credit card interest, and vehicle operating costs.