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. 

Finding the distance between two complex numbers using the modulus of their difference. Three parts.

Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient.

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

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.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

Finding the value of a variable

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

Finding probabilities using the binomial distribution.

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

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

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

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

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

Finding unknown sides/angles in right-angled triangles.  6 different combinations of unknowns are included in this single question. Makes my previous questions redundant

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

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Solve a quadratic equation by completing the square. The roots are not pretty!

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

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Using differentiation to find the tangent and normal to a line at a given point

Finding the stationary points of a cubic with two turning points

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