Evaluate a composition of functions for a randomised numerical input. The functions are 3t+2 and t+3. This is part of HELM Book 2.1.3.

Given f(x)=(x+a)/(x+b) and g(x) = 1/x, compute f(g(x)) and g(f(x)).

a and b are randomised integers.

Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value

Given 2 randomised functions f (linear) and g (quadratic), find one of f(f), f(g), g(f) or g(g)

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.

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.

Plot the Fourier series coefficients for a piece-wise linear function.  Write a Python script to reproduce the same figure.

Shows how to use the programming extension's preload function to load files from the question resources into the Python or R code runners.

Look at the question's JavaScript preamble.

Given f(x)=1/(a-x)^2, evaluate f(x/z) where a is a randomised constant, and z is a randomised letter.

Give f(x)=ax^2+b a simple function input (like 6x-3) and evaluate. Constants and variables, and the function input are all randomised.

evaluate a function with randomised alphanumeric expressions as inputs.

Evaluate a linear function at 3 numerical inputs.

Evaluate a given, randomised, linear function at a given, randomised, value.

"Explain what is meant by the argument of a function."

Unmarked: Answer: "The argument is the input."

Student is shown a simple (randomised) function and asked to describe its behaviour. This is an information only question. Students need to view the advice to check their answer.

Given a function definition in words, evaluate the function with various variable and numeric inputs

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

evaluate the function y=ax+b for given values of a,b and x, each of which may be positive or negative.

Shows how to switch to the 3D graphics view of a geogebra applet using an extension function.

This question shows a JSXGraph diagram above a mathematical expression input, containing a plot of the expression the student enters.

Turning points of a cubic function

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.

No description given

The statement contains two blank geogebra applets: one with the computer algebra view, which can be used as a calculator, and the other with algebra and geometry views.

There are custom functions which set the perspective of a geogebra applet and show the toolbar or algebra input line. These will probably be included in the geogebra extension eventually.