Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.

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Addition and Subtraction by hand questions, whole numbers and decimals. Fully worked solutions in feedback.

Addition calculations to be carried out by hand, full worked solutions in feedback.

Demonstration of adaptive marking: the student must first add up the number of apples to buy, then work out how much that would cost. Adaptive marking carries an incorrect number of apples into the cost calculation.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Round random numbers to the closest whole number, 1 to 3 decimals places. Also rounding that could show common misunderstandings.

Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.

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

Finding probabilities using the Poisson distribution.

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$.

There is a video included explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.

Find a regression equation.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$. Find $g(x)$.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

Elementary examples of multiplication and powers of complex numbers. Four parts.

Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

Product of one of 2, 3, 5, 9, or 10 by a number up to 10. With hints to learn calculation rather than memorisation.