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

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

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

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

Integers in bases from 2 to 9 and converting them to base 10.

Looking at gradients and values for x and y for straight-line graphs

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

This question tests to see if students can recognise a $p$-series and based on its $p$-value determine if it is convergent or divergent.

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

This question tests a student's ability to raise a positive base to a negative exponent and then take the negative. The base and the exponent have the same absolute value.

Given a graph of a straight line, the student is asked various questions about it, e.g. values of $f$, of $f$ inverse, about its gradient, about intercepts.

Calculate the net present value for the following property assets:

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 values which satisfy an inequality.

This question tests a student's ability to raise a positive base to a negative exponent and then take the negative. The base and the exponent have the same absolute value.

These questions are asking you to use a non-calculator method to work out a percentage amount of a value.

This question asks you to work out one value as a percentage of another.  You are expected to do these without the help of a calculator.

These questions are asking you to use a non-calculator method to work out a percentage amount of a value.

Useful for a review of the base 10 number system before introducing different bases and also just ensuring students understand how the base 10 system works.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Solving linear equations to find the value of x.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

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.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.