Year 11 Maths Advanced 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.

• Functions and graphsFunctions, domain and range; Linear and quadratic functions; Other graphs: cubics, hyperbolas, circles, absolute value; Composite, inverse, even and odd functions
• Transformations of graphsTranslations; Dilations and reflections; Combined transformations; Circles, hyperbolas and absolute value graphs
• Trigonometric functions and identitiesRadians, arcs and sectors; Exact values and the unit circle; Graphs of trigonometric functions; Identities and equations
• Exponential and logarithmic functionsExponential functions and e; Logarithms and the log laws; Solving exponential and log equations; Graphs and growth or decay models
• Introduction to calculusRates of change; Differentiation from first principles; Rules for differentiation; Tangents and normals
• Probability and discrete distributionsSets, Venn diagrams and the addition rule; Conditional probability and independence; Multi-stage experiments; Discrete random variables

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. Functions and graphsMultiple choice

   x^² − 6x + 9 = 0 has discriminant…

   1. A−36
   2. B0
   3. C36
   4. D72
   Show answer

   B. 0

   36 − 36 = 0.

2. Question 2. Transformations of graphsMultiple choice

   y = f(x/2) is a horizontal dilation by factor…

   1. A2
   2. B4
   3. C−2
   4. D1/2
   Show answer

   A. 2

   f(x/2) = f(ax) with a = 1/2, factor 1/a = 2.

3. Question 3. Transformations of graphs: circles, hyperbolas and absolute value graphs3 marks

   Find the centre and radius of x^² + y^² + 10x − 4y + 20 = 0.

   Show model answer and marking criteria

   Model answer. x^² + 10x + 25 + y^² − 4y + 4 = −20 + 25 + 4, so (x + 5)^² + (y − 2)^² = 9. The centre is (−5, 2) and the radius is 3.

   A full-marks answer:

   • Completes the square in x: (x + 5)^² − 25
   • Completes the square in y: (y − 2)^² − 4, giving (x + 5)^² + (y − 2)^² = 9
   • Centre (−5, 2), radius 3
4. Question 4. Trigonometric functions and identitiesMultiple choice

   sin(5π/6) = …

   1. A√3/2
   2. B1/2
   3. C−√3/2
   4. D−1/2
   Show answer

   B. 1/2

   Quadrant 2, sin positive.

5. Question 5. Trigonometric functions and identities: radians, arcs and sectors3 marks

   A pendulum swings through an arc of 25 cm on a string of length 40 cm. Find the angle of swing in radians and in degrees (1 decimal place), and the area swept out.

   Show model answer and marking criteria

   Model answer. l = rθ, so θ = 25 ÷ 40 = 0.625 radians. In degrees, 0.625 × 180 ÷ π ≈ 35.8°. The area swept out is the sector area ½r^²θ = ½ × 1600 × 0.625 = 500 cm^².

   A full-marks answer:

   • θ = l/r = 25/40 = 0.625 rad
   • In degrees: 0.625 × 180/π ≈ 35.8°
   • Area = ½ × 40^² × 0.625 = 500 cm^²
6. Question 6. Exponential and logarithmic functionsMultiple choice

   log 50 + log 2 = …

   1. A52
   2. B2
   3. C1
   4. Dlog 52
   Show answer

   B. 2

   log 100 = 2 (base 10).

A few of the 94 Year 11 Maths Advanced 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.

• FunctionA relation where each input has exactly one output.
• y = f(x) + cTranslate c units up.
• π radians180°
• a^^m × a^ⁿa^^{m + n}

Set out every step. Senior Maths papers give most of the marks for method, so a right answer with no working can score little on a multi-mark question. Learn the standard derivatives, integrals and identities until they are automatic, then spend your time on mixed questions where you have to choose the method yourself.

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

When you set up Year 11, 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 Advanced in Year 12

Year 12 Maths Advanced study notes and practice questions.

More Year 11 courses

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