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Calculate the heat losses from a model building based on the U values, dimensions and other parameters specified. In addition calculate the annual running costs and payback period for improvements to the building Fabric.

In the first part, the student is asked to enter dimensions of a box in a spreadsheet.

The values are extracted as a list of numbers by changing the interpreted_answer note in the first part's marking algorithm, and the calculated volume is used as the answer to the second part, through adaptive marking.

Using basic derivatives to calculate the gradient function of a hill $y=-e^x+b\ln\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea. 

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

rebelmaths

Student is presented with a clock showing a random time (in 15 minute increments) with an idication of whether it is morning or afternoon, along with a scheduled meeting time (in 24 hour mode). Question asks them to calculate difference between times and whether they are early or late.

how to calculate percentage

Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$. Calculate $f(p,q)$.

Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$. Calculate $f(p,q)$.

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

Calculate the marginal and average cost for a given cost function. Find the corresponding startup/shutdown price.
Maximize the profit function at a given price.

Calculate statistics from a table of unpaired data and conclude whether or not they are from the same underlying population and interpret the result.

Calculate statistics from a table of unpaired data and conclude whether or not they are from the same underlying population and interpret the result.

Using Mohr's Circle to calculate principal stresses in plane stress 2D case.

Calculate the von Mises stress at the base of a post subject to axial compression, bending and torsion.

Calculate invariants and von Mises stress for a general 3D stress state.

Work backwards from hoop strain measurement to calculate prior gauge pressure in a drinks can.

Calculate direct and shear stress in an axially loaded bar in the XY plane.

Knowing the doubling time of a population and the population on day $t$, calculate the initial population and the number of days required for the population to reach a threshold. 

Solving a separable differential equation that describes the rate of decay of radioactive isotopes over time with a known initial condition to calculate the mass of the isotope after a given time and the time taken for the mass to reach $m$ grams. 

Decay Constant - Radioactivity - Nuclear Power (nuclear-power.com)

Students are asked to rearrane the formula giving the voltage drop across a resistor in terms of emf of battery, resistance of resistor and internal resistance of battery to make the internal resistance the subject. They are then asked to calculate the internal resistance given values for the other variables (randomised).

3 Forces Applied to an Eye bolt.  Use force components to calculate the Reaction force.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

A two part question. Students are first given the formula for the time for a ball to come to rest after being dropped on a block. Part a) asks the students to rearrange the formula to make e, the coefficient of restitution, the subject of the formula. Part b) gives students realistic values for variables in the formula and asks them to calculate the coefficient of restitution using the formula derived in part a). 

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.