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.

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.

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

rebelmaths

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

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

Given one of ax^2, ax^3, a/x (where a is a positive integer), calculate f(x+h) and f(x+h)-f(x) 

Calculate R = ap^2 for given positive values of a and p.

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.

Small, simple question.

It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

rebelmaths

A measurement is performed multiple times for the same object, the student will

• calculate the mean result
• calculate the standard error on the mean 
• write the mean±error to the correct precision as defined by the error written to 1 significant figure 

Advice is provided including on performing the calculations in Python or spreedsheets together with further reading. 

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

Use your calculator to calculate a factorial between 5 and 11

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Calculate a factorial, or the difference of two factorials, or a fraction of two factorials.

Used in HELM Book 5.1.1 Exercises

Calculate the product of two randomised scientific notation numbers and give the answer in scientific notation.

Part of HELM Book 1.2

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

The student is shown a diagram with measurements of rooms in a house. They have to enter the measurements in a spreadsheet, then the area of each room, and finally the total area of the house.

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

Divergence of vector fields.

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

This question shows how to use the programming extension's run_code function to run some Python code and use its result in the marking of a non-code part type.

Python is used to calculate the correct answer for a number entry part type. This could be done

The student must write R code to generate samples and calculate CDFs of some common distributions.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

Asks the student to calculate the sum of the triangular numbers (up to some randomised number). 

Steps guide the student through each step in the calculation.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a column graph and asked to calculate the net benefit given the amount invested (randomly generated) and the intervention type (one of seven possible).