Calculate 95% CI given, mean, sd and sample size.

Using geogebra to draw lines tangent to a curve and calculate their gradient.

Calculate distance given speed and time.

Given speed and time, calculate distance.

Given the total cost, insurance cost, and daily cost of hiring a bicycle, calculate the number of days the bicycle was hired for.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

Given n-1 angles inside a polygon, students have to calculate the value of the last internal angle.

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. 

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

Given a student discount, calculate a discounted price.

This question assesses

• the students ability to apply both theoretical and experimental probability to calculate expected values 
• the students understanding of how to calculate the relative frequency of an outcome

The question also helps to show students how using experimental probability and theoretical probability results in different expected values of an outcome.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

This question assesses the students ability to calculate and convert between different types of compound units, including rates of pay, speed and unit pricing.

Find the original price before a discount by dividing the new price by the percentage discount.

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.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are shown an infographic, and need to calculate a percentage from the information supplied. There are 7 different versions of this question.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given the number of years worked, and the price paid. They use the table to look up the percentage discount, then calculate the full price. The number of years and price paid are randomised.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given sales and years of service. They read the retainer and commission from two tables, then calculate before-tax income. The sales and years of service are randomly generated.

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Calculate the average speed in km/h and m/s given distance in kilometres and time in hours and minutes.

Given the vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate $(\mathbf a \times \mathbf b) \times \mathbf c$ and $\mathbf a \times (\mathbf b \times \mathbf c)$.

Calculate the vector product between two vectors.

Given three 3-dimensional vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate the scalar product between $\mathbf a$ and $\mathbf b$, the angle between $\mathbf a$ and $\mathbf b$, and $\mathbf a (\mathbf b \cdot \mathbf c)$,

Given three 2-dimensional vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate the scalar product between $\mathbf a$ and $\mathbf b$, the angle between $\mathbf a$ and $\mathbf b$, and $\mathbf a (\mathbf b \cdot \mathbf c)$,

Given two side-lengths and an angle of a triangle, use the sine rule to calculate an unknown angle.

Given an equation of the form $m=m_0 e^{-kt}$ to model the mass of a radioactive material, calculate the decay constant $k$ and the time taken for the material to reach a certain percentage of its initial mass. 

Given an equation of the form $T=T_0 e^{kt}$ to model temperature, calculate the temperature after a given time, the time taken to reach a certain temperature, and the time taken for the temperature to double.

Given the polar coordinates of a point $P$, calculate the equivalent cartesian coordinates