Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Using the chain rule with polynomials and negative powers

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

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

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

Finding probabilities using the binomial distribution.

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

Example showing how to calculate the probability of A or B using the law $p(A \;\textrm{or}\; B)=p(A)+p(B)-p(A\;\textrm{and}\;B)$. 

Also converting percentages to probabilities.

Easily adapted to other applications.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

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Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Using the reduction formulas for products of powers or sin and cosine

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

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

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.