Year 12 Maths Standard study notes and practice questions

For Year 11 and 12 students sitting the HSC, VCE, QCE, SACE, WACE and more. Each unit has short study notes, flashcards and practice questions, and the app builds timed practice exams from the whole course.

• Networks and pathsNetwork terminology; Shortest paths; Minimum spanning trees; Critical path analysis
• Simultaneous equations and non-linear modelsSimultaneous linear equations; Break-even analysis; Exponential models; Quadratic and reciprocal models
• Rates and ratiosRates and unit conversions; Ratios; Scale drawings and maps; Fuel consumption
• Investments and loansFuture and present value; Depreciation; Annuities; Loans and credit cards
• Bivariate data analysisScatter plots and association; The correlation coefficient; The least-squares regression line; Interpolation, extrapolation and causation
• The normal distributionProperties of the normal distribution; z-scores; The 68–95–99.7 rule; Applications and comparisons
• Right-angled and non-right-angled trigonometryRight-angled triangles; Elevation, depression and bearings; Sine rule and cosine rule; Area of a triangle and radial surveys

4 multiple choice and 2 written questions. Try each one before you open the answer. Written answers show the model answer and what a full-marks response needs.

1. Question 1. Networks and pathsMultiple choice

   A network has degrees 3, 2, 3, 2, 2. How many edges?

   1. A6
   2. B5
   3. C12
   4. D10
   Show answer

   A. 6

2. Question 2. Simultaneous equations and non-linear modelsMultiple choice

   h = −5t^² + 30t. Maximum height…

   1. A30 m
   2. B45 m
   3. C3 m
   4. D90 m
   Show answer

   B. 45 m

   At t = 3.

3. Question 3. Simultaneous equations and non-linear models: exponential models3 marks

   A car bought for $32 000 depreciates by 18% per year. Write a model for its value after t years and find its value after 4 years.

   Show model answer and marking criteria

   Model answer. Each year 82% of the value remains, so V = 32 000(0.82)^^t. After 4 years V = 32 000 × 0.82^⁴ ≈ 14,467.90 dollars.

   A full-marks answer:

   • V = 32 000(0.82)^^t
   • V(4) = 32 000 × 0.82^⁴
   • ≈ $14,467.90
4. Question 4. Rates and ratiosMultiple choice

   Which is cheapest per litre?

   1. A2 L for $3.50
   2. B3 L for $5.40
   3. C600 mL for $1.20
   4. D1 L for $1.90
   Show answer

   A. 2 L for $3.50

   $1.75/L.

5. Question 5. Rates and ratios: rates and unit conversions3 marks

   On a map with scale 1 : 25 000, a walking track is 18.4 cm long. Find the real length and the time to walk it at 4 km/h.

   Show model answer and marking criteria

   Model answer. Real length = 18.4 × 25 000 = 460 000 cm = 4.6 km. At 4 km/h the walk takes 4.6 ÷ 4 = 1.15 hours, which is 1 hour 9 minutes.

   A full-marks answer:

   • Real length 18.4 × 25 000 = 460 000 cm
   • = 4.6 km
   • Time 4.6 ÷ 4 = 1.15 h = 1 h 9 min
6. Question 6. Investments and loansMultiple choice

   An annuity with $100 at the end of each year for 2 years at 10% p.a. is worth…

   1. A$200
   2. B$210
   3. C$220
   4. D$221
   Show answer

   B. $210

   100 × 1.1 + 100.

A few of the 105 Year 12 Maths Standard flashcards. In the app they use spaced repetition: rate each card Again, Hard, Good or Easy and it comes back just before you would forget it.

• Degree of a vertexNumber of edges at the vertex.
• Solution of simultaneous equationsThe point of intersection of the graphs.
• RateComparison of quantities with different units.
• Future valueFV = PV(1 + r)^ⁿ

Most marks come from applying a method to a real situation: a loan, a network, a data set. Write the formula, substitute with units and say what the answer means in context. Practise with your formula sheet so you know where everything is before the exam.

Press Study for me and the app builds a 15 to 20 minute session from the cards that are due, the mistakes that are due and questions on your weakest topics. Practice questions come in three levels, and anything you get wrong comes back 1, 3 and 7 days later until you get it right. When an exam is close, sit a timed practice exam with AI marking.

Your state, your exam

Maths Standard goes by different names around Australia. In the app the course shows under your state’s name: NSW: Maths Standard; VIC, QLD, SA, TAS, ACT, NT: General Mathematics; WA: Mathematics Applications.

When you set up Year 12, you pick your state (NSW, VIC, QLD, SA, WA, TAS, ACT or NT) and your subjects. The AI then pitches explanations and marking at your certificate’s level. Courses differ between states, so compare the units above with your course outline, and turn your class notes into extra decks for anything that’s different.

Maths Standard in Year 11

Year 11 Maths Standard study notes and practice questions.

More Year 12 courses

Year 12 Maths Advanced, Year 12 English, Year 12 Modern History, Year 12 Biology, Year 12 Chemistry, Year 12 Business Studies, Year 12 Legal Studies, Year 12 PDHPE. All Year 11–12 subjects.