Content created by Newcastle University

Use the product rule to differentiate various functions.

Elementary examples of multiplication and addition of complex numbers. Four parts.

Composite multiplication and division of complex numbers. Two parts.

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Determine the long-term behaviour of 1D dynamical systems.

Fixed points of 2D dynamical systems.

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

Fixed points of a 1D dynamical system.

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

No description given

No description given

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

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

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.

No description given

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.

No description given

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.