A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always obtuse. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

A question testing the application of the Sine Rule when given two sides and an angle.  In this question the triangle is obtuse and the first angle to be found is obtuse.

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

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Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct,  but the feedback indicates that the third was wrong.

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

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

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

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 binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

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

Finding probabilities using the Poisson distribution.

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

Finding probabilities using the binomial distribution.

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

$f(X)$ and $g(X)$ as polynomials over the rational numbers $\mathbb{Q}$.

Find their greatest common divisor (GCD) and enter as a normalized polynomial.

Modular arithmetic. Find the following numbers modulo the given number $n$. Three examples to do.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

This is a simple question testing the student on their ability to calculate the lowest common multiple of two integers which are: 

Part a) - coprime;

Part b) - where the greatest common divisor between the two integers is greater than one and not equal to either given number; and

Part c) - where one of the integer is a multiple of the other. 

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

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

This question tests the student's ability to find remainders using the remainder theorem. 

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

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A fill-in-the-blank style question to test vocabulary within the topic of Algebra.