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This is a set of practice questions for the non-right-angle trig component of the Australian year 12 Mathematics Standard 2 course.

It asks questions about

• finding sides and angles of right angle triangles,
• finding areas of triangles,
• using the sine rule,
• using the cos rule,
• bearings, and
• radial surveys.

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$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Small demo using the JME implementation of JSXGraph inline in a multiple choice question. This version uses a JME variable to store the expressions and then calls a function wherever a plot is required.

Small demo using the JME implementation of JSXGraph inline in a multiple choice question.

This is my first trial of Numbas.

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A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

Solve unknown on one side

Solve $\displaystyle ay + b = cy + d$ for $y$.

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Solve an exponential equation

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Introduces students to the floor and ceiling functions

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

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This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

This question demonstrates sending commands to geogebra and getting geogebra values and using them as part of a marking algorithm.

Slightly harder introductory exercises about the power set.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Converting between metres (m) and centimetres (cm). 

Round random numbers to the closest whole number, 1 to 3 decimals places. Also rounding that could show common misunderstandings.