Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

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 the original amount when told that $p\%$ is $x$. The value given can be non-integer.

Calculating the original amount when told that $p\%$ is $x$. The value given and the original values are both integers.

Given the number of international students enrolled on a course of $n$ students, calculate the percentage of 'home' students.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

This question asks the student to calculate three points of a given linear function then plot these points in a JSXGraph item and find the x and y intercepts of the line.

Calculate P(A|B) given a Venn diagram.

Calculate P(A|B) given a two way table.

Given a discrete random variable (as a formula) calculate:
E(X), Var, std dev, cumulative distribution and probabilties.

Calculate an intersection probability given a two way table.

Calculate P(A|B) given a two-way table.

Calculate P(A|B) given a venn diagram including P(A) and P(B) and intersection.

Calculate P(A u B) given P(A), P(B) and intersection.