Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

In four parts, the student builds up the definition of a class representing a rectangle. First they write the constructor, then add methods to compute area and perimeter.

In the final part, they must use the methods to write a function which determines if a rectangle's area is larger than its perimeter.

This is the simplest demonstration of the "code" part type I could think of: assign x = 1.

An alternative answer gives a hint if the studen'ts code doesn't define x at all.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an unusual chart and asked one of six possible questions.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a column graph and asked to calculate the net benefit given the amount invested (randomly generated) and the intervention type (one of seven possible).

Used for LANTITE preparation (Australia).SP = Statistics & Probability strand. NC = Non Calculator strand. Students are shown an infographic and asked two of five possible true/false questions.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. SP = Statistics & Probability strand. Students read a percentage from the chart, and calculate that percentage of the number of children (randomly generated).

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of people that are fed with 200g of rice (randomised), and the total number of people to be fed (randomised). They need to calculate the weight of rice using proportional reasoning.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of pages read (randomised) and number of pages remaining (randomised), and asked to write the proportion read as a simple fraction.

A test of basic concepts to do with SI units and concentrations of solutions.

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.

Here you'll see a first example of how a map can arise from a system of differential equations and gain some first insight into the dynamics of 1D maps.

Integrating a function of the form $\frac{a}{x}$ using a table of integrals / anti-derivatives.

Given the exchange rate between two currencies, calculate how much of one currency you will get for $x$ amount of the other

Given the exchange rate between two currencies and the bank's commission rate, calculate how much of one currency you will get for $x$ amount of the other

Given the ratio of copper to zinc in brass, calculate how much more copper than zinc is used to create a given amount of brass.

Used for chemistry/materials

Given the ratio of male to female gym members, calculate how many more women than men use the gym

Given x and y, calculate (x-y) as a percentage of y.  Chemistry context.

Calculating rates and scaling rates. Drops per mL and drops per minute questions unit rate to equivalent rate.

Students are given a diagram with 2 triangles. They are given 2 randomised lengths, and a randomised angle of depression.

They need to compute an angle by subtracting the angle of depression from 90°. Then they need to use the sine rule to calculate a second angle. Then they need to use the alternate angles on parallel lines theorem to work out a third angle. They use these to calculate a third angle, which they use in the right-angle triangle with the sine ratio to compute the third side. They then use the cos ratio to compute the length of the third side.

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years. 

Integrating a polynomial functions which describe the rate of change of a population over time to find and use an equation that describes the total population according to time.

Use a substitution to simplify an integral.

A demonstration of the random person extension, which picks representative names of people.

Integration by susbtitution. Use the letter C for the constant.