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.

Given sequences with missing terms, find the common difference between terms.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

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.

Fill in a frequency table for grouped data, then estimate the mean and identify the modal class.

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

Apply and combine logarithm laws in a given equation to find the value of $x$.

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 find remainders using the remainder theorem. 

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

Find the sum of the first n terms of a Geometric progression

Find the nth term of a Geometric progression

Find the sum of the first n terms of an arithmetic progression

Find the nth term of an Arithmetic progression

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

Given a table of data, calculate the mean, mode and median, and complete a frequency table.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

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

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Find roots and the area under a parabola

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Find the nth term of an Arithmetic progression

Find the solution of a first order separable differential equation of the form $(a+y)y'=b+x$.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the mean.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.