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. 

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Divide $ f(x)=x ^ 4 + ax ^ 3 + bx^2 + cx+d$ by $g(x)=x^2+p $ so that:
$\displaystyle \frac{f(x)}{g(x)}=q(x)+\frac{r(x)}{g(x)}$

Choosing whether given random variables are qualitiative or quantitative.

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 sample data find mean, standard deviation, median, interquartile range.

Note that there are different versions of the upper and lower quartiles, so you may want to include your own versions - see the user defined functions in the question.

Find a regression equation.

Given vectors  $\boldsymbol{A,\;B}$, find the angle between them.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given vectors $\boldsymbol{A}$ and $\boldsymbol{B}$, find their inner product.

Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

The students are given the magnitude and angle (in degrees) of a vector. They have to find its alpha and beta components.

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Calculate the concentration of a dilute acid given the amount and concentration of dilute alkali to neutralise it. Cribbed from this Bitesize problem.

There are steps to break down the calculation, and the student must give units at each step.

Preparing solutions to given concentrations/dilutions.

Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

Expression of the (a+bx)^n is given and a couple of coefficients are asked for.

Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

The student must calculate the number of digits a given decimal number would have when written in a different base. Alternative answers catch some common mal-rules and give appropriate feedback.

Based on table 2 from "diagnosing student errors in e-assessment questions" by Philip Walker, D. Rhys Gwynllyw and Karen L. Henderson.

Given some numbers in standard index form, convert to decimal form.