Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

Using the chain rule with polynomials and negative powers

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.

Work out the volume of a prism with a trapezium cross-section.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Simple probability question. Counting number of occurences of an event in a sample space with given size and finding the probability of the event.

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a rational function with specific features.

Given three vectors with integer components, find the corresponding magnitude and direction.

Replace two parallel forces with an equivalent single force

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Introduction to counting with permutations and combinations

Simple counting exercise, with combinations

Simple counting exercise, with combinations

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

Simple ratio question with custom marking and partial credit possible

A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

Calculate the efficiency and heat from the hot reservoir in a Carnot Cycle (with carnot diagram)

A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

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.