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

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

Solve a system of linear equations using Gaussian elimination.

Solve a pair of linear equations by writing an equivalent matrix equation.

4 questions on using partial fractions to solve indefinite integrals.

A variety of trigonometric equations which can be solved using inverse operations.

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

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

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

Solve for x and y on a given triangle and calculate the area

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Find angle and side in a right angled triangle.

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Some impossible-looking questions about quadratic equations which can be solved with a bit of thinking.

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 $y$. 

Three forces act on a particle. You're given the magnitude of one, and the directions of all three. Find the magnitudes of the other two forces.

A particle is in equilibrium on an incline. Four forces are acting on it. You're given the angle of the incline and three forces. Resolve the forces to find the angle and magnitude of the other force.

A variety of trigonometric equations which can be solved using inverse operations.

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

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.

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

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

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Indices

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Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

Solve a quadratic equation by completing the square. The roots are not pretty!

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

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Indices

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