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Approximate $f(x)=(a+h)^{m/n}$ by $f(a)+hf^{\prime}(a)$ to 5 decimal places and compare with true value.

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An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

Use the Hungarian algorithm to find the optimal assignment of workers to tasks.

Questions on the least upper bounds and greatest lower bounds of sets of the form $\{ f(x) : x \in \mathbb{Z} \text{ or } \mathbb{R} \}$.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

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 $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Finding the coordinates and determining the nature of the stationary points on a polynomial function

Find a regression equation given 12 months data on temperature and sales of a drink. 

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.

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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.

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Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation.

Link to use of t tables and p-values in Show steps.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

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

Finding probabilities using the binomial distribution.

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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

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

Choosing whether given random variables are qualitiative or quantitative.