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. 

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.

Asks students to apply laws of logical equivalence to prove the equivalence between two logical statements. The quiz should accept any correct answer (as long as each step is included, with one law per step), and provides detailed feedback on mistakes.

Convert between improper fractions and mixed numerals

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. 

Converting between giga, mega, kilo, base, milli and micro, nano. Metres, grams and litres.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Simplify an algebraic fraction that is fully factorised with common factors between the numerator and denominator, and one of the variables has a larger index on the denominator. Part of HELM Book 1.4

Calculating the angle between a vector and the positive $x$-axis.

Asks students to add and multiply two integers modulo another integer.  The modulus is a random number between 30 and 70, the summands are set to be large enough that modular reduction will be necessary.

Asks students to compute the multiplicative inverse of $a$ in $\mathbb{Z}_n$ where $n$ is an odd number between 31 and 61 and $a$ is an integer coprime to $n$ that lies between $n/4$ and $3n/4$.

Use your calculator to calculate a factorial between 5 and 11

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Given a data sheet with distances between cities and costs for different forms of transport, and some information about modes of transport used, fill in a form for a journey.

A quick practice set of problems for education students to take in preparation for their numeracy test.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

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

Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

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.

Calculating the angle between two vectors.

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

Convert speeds from m/s to km/h

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

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