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Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

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.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

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

Rearrange equations to make $x$ the subject. 

Provided via mathcentre.ac.uk

rearranging the Michelas-Menten equation to make the substrate the subject.

rebelmaths

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

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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.

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve a system of three simultaneous linear equations

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

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. 

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.