Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Apply the Kruskal-Wallis test on some data to determine if a measurement differs between groups.

Given a piecewise CDF $F_X(b)$ which is discontinuous at several points, find the probabilities at those points and also find the value of $F_X(b)$ at a continuous point and the expectation.

This cdf is a step function and is therefore the cdf of a discrete random variable. This should be stated somewhere in the statement or the solution. Apart from this the question is correct.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

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 two distributions, calculate the measures of average and spread and make some decisions based on the results.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Some questions on working with surds.

Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

Round some large integers to the a given power of ten.

Given some coordinates, recognise which quadrant a point lies in, or which axis a point lies upon.

Given results from a survey about what people eat for breakfast, where some people eat one or both of cereal and toast. Student is asked to pick the probability of eating either one or the other from a list. Distractors pick out common errors.

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

Some questions to do with measures of distance and length.

This question tests the student's ability to identify the factors of some composite numbers and the highest common factors of two numbers. 

Given arithmetic sequences with some terms missing, fill in the missing terms.

Some conceptual questions about parallel lines - fill in the gaps in some statements.

Identify the lines corresponding to given equations, and the lines parallel to lines with given equations.

Present some given data in a frequency table.

This question assesses the student's ability to use some given information involving two different units of measurement to rewrite the information as a compound measure.

Decide whether statements about square and cube numbers are always true, sometimes true or never true.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Translation to Dutch of 

"Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop."