Newcastle University Mathematics and Statistics

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

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Given a generating matrix for a linear code, give a parity check matrix

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Rolling a pair of dice. Find probability that at least one die shows a given number.

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

English sentences which are propositions are given and for each the appropriate proposition  involving quantifiers is to be chosen. 

Write down the lexicographic parity check matrix and generator matrix for a Hamming code, which is the dual of a Simplex code, then determine if a given word is a codeword of the corresponding Simplex code.

Compute tables of Hamming distances in given codes, then determine which codes are equivalent.

Given a generating matrix for a binary linear code, construct a parity check matrix, list all the codewords, list all the words in a given coset, give coset leaders, calculate syndromes for each coset, correct a codeword with one error.

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

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Given normal distribution $\operatorname{N}(m,\sigma^2)$ find $P(a \lt X \lt b),\; a \lt m,\;b \gt m$ and also find the value of $X$ corresponding to a given percentile $p$%. 

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

This is out of date. There is a new "getting statrted" exam at https://numbas.mathcentre.ac.uk/exam/21108/getting-started/

6 questions which introduce the user to the Numbas system.

Questions testing understanding of the index laws.

Questions testing rather basic understanding of the index laws.

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).

Add/subtract fractions and reduce to lowest form.

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

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Inverse and division of complex numbers.  Four parts.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.