Use a probability mass function; determine if a given function is a probability mass function; find the probability mass function of a discrete distribution and use it.

Substitute a given value into a formula, and substitute an expression in terms of $x$ into a formula.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Three items of work done on a car. Given total price, and a couple of ratios of prices between pairs of items, work out the cost of one of the items.

Based on question 4 from section 3 of the Maths-Aid workbook on numerical reasoning.

Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.

Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.

Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.

Given the selling price of an item both as a cash amount and as a percentage of the cost of production, find the cost of production and the profit.

Based on question 1 from section 3 of the Maths-Aid workbook on numerical reasoning.

Given cost of production and price of sale of a product; a percentage increase in cost of production; and unit sales before and after; work out the extra profit.

Based on question 6 from section 3 of the maths-aid workbook on numerical reasoning.

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.

Given the cost to produce an item and a desired markup, calculate the appropriate sale price.

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Given a codeword in $w=\mathbb{Z}^4_3$ find and list all codewords at Hamming distance $1$ from $w$.

Given a set in predicate form i.e. $A=\{x|P(x)\}$, find and input the elements of the set.

Given a set $A$, elements of which may also be sets, determine if the given elements or subsets are in $A$.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Enumerate elements of a set given in predicate form.

For example, find all elements of $A=\{x\in\mathbb{Z}\;|\;\;|2x-5|<4\}$.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

English sentences which are propositions are given and for each the appropriate statement 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.

English sentences are given and for each the appropriate statement involving quantifiers is to be chosen. Also choose whether the statements are true or false.

a) Given a recursively defined sequence $t(n)$, find $t(n)$ as a function of $n$.

b) Given a sequence $s(n),\;n \in \mathbb{N}$, find a recursive definition of $s(n)$

Given sentences involving propositions translate into logical expressions.

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given the pdf  $f(x)=\frac{a-bx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q | X \gt t)$.

Three items of work done on a car. Given total price, and a couple of ratios of prices between pairs of items, work out the cost of one of the items.

Based on question 4 from section 3 of the Maths-Aid workbook on numerical reasoning.

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.