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). 

Students are given lengths of 3 sides of a triangle (all randomised) and asked to find one of the angles in degrees. Requires use of the cosine rule.

Students are given two angles and the length of the side between them, they are asked to find the length of the side opposite angle A. Can be completed with the ine rule.

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

 Question asks student to find zeros of a quadratic equation. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

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.

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

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. 

Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down. 

Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem. 

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem. 

The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.

The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $ p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.

Estimating the proportion of sodium carbonate in a solutionat a specific timepoint and vice versa, depicted as a quadratic graph.

Interpreting line graphs depicting the decrease of temperature in a mixture over time. Estimating the temperature of the mixture at a given time point and vice versa.

Calculations involving Standard form.

Convert numbers between 0 and 1 intro standard form/scientific notation.

Convert numbers greater than 1 into standard form/scientific notation.

Dividing amounts in ratios

Picking a ratio out of a list that is not equivalent to the others.

Proportional calculation in context.

Convert a fraction into a decimal.

Convert a decimal to a fraction.

Convert a percentage to a fraction.

Put fractions in size order.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions.