Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

Solving a pair of linear simultaneous equations with integer solutions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

No description given

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

Solving binary optimisation problems using Computational Packages

Solving continuous optimisation problems using Computational Packages

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Recovering original function given some information such as derivative and value at some point.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

No description given

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Students are shown a graph with 6 vertices and asked to find the length of the shortest path from A to a random vertex.

There is only one graph, but all of the weights are randomised.

They can find the length any way they wish. In the advice, the steps of Dijkstra's algorithm used in solving this problem are displayed. It is not a complete worked solution but it should be sufficient to figure out the shortest path used to reach each vertex.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years. 

Solving a quadratic equation of the form $ax^2+bx+c=0$.

Some quadratics are to be solved by factorising

Practice solving equations with integer solutions. 

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.

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 is applied in the negative $x$ and negative $y$ direction.

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Solving $\sin(3x)=\sin(x)$ for $x\in \left(0,\frac{\pi}{2}\right)$.

Solving $\sin(2x)-\tan(x)=0$ for $x\in \left(0,\frac{\pi}{2}\right)$.

Solving $\sin(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.