A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Simple probability question. Counting number of occurences of an event in a sample space with given size and finding the probability of the event.

Find a regression equation.

Find a regression equation.

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.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

English sentences which are propositions are given and for each the appropriate proposition  involving quantifiers is to be chosen. 

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

The student must perform an indefinite integration, and include a constant of integration.

A custom marking algorithm identifies the name of the student's constant of integration, and replaces it with 'c' before comparing with the expected answer.

If the student enters something like '2c' instead of 'c', it'll be marked wrong, which is an error in the marking.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

A really simple question which asks the student to multiply two matrices.

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Q1 is true/false question covering some core facts, notation and basic examples.  Q2 has two functions for which second derivative needs to be determined.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Questions which rely on knowledge of standard integrals.

A variety of trigonometric equations which can be solved using inverse operations.

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

several statements are given regarding trig identities. student is to select which are true and which are false

Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.

Some impossible-looking questions about quadratic equations which can be solved with a bit of thinking.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.