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 a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ direction but the positive $y$. 

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

Another example of finding the $x$ and $y$ components when multiple forces are applied at different angles to a particle.

Using e to solve equations involving the natural log

Use Sine rule and Cosine rule to solve a Geometry problem in geology.

Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

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

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. 

set up x- and y axises.

set linear equations and solve the simulatenous equations.

Solve a system of three simultaneous linear equations

Solve a logarithmic equation

Solve an exponential equation

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

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

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

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

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

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.

Solve a random oblique triangle for sides and angles.

Solve a random oblique triangle for sides and angles.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

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Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

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

This exercise will help you solve equations of type ax-b = c.

Some quadratics are to be solved by factorising