A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the mean.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Choosing whether given random variables are qualitative or quantitative.

No description given

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

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.

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

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 $X$.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

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.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

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.

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

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.

Given descriptions of  3 random variables, decide whether or not each is from a Poisson or Binomial distribution.

Integration by susbtitution, no hint given

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Given three vectors with integer components, find the corresponding magnitude and direction.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Given the graph of the line determine the equation of the line.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.