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

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

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

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 $\mod b$.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

Practice calculating concentration of solutions

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

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

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

Calculating the new concentration of a diluted solution.

Example of a dilution calculation involving mass concentration and molarity calculations.

Working backwards from the concentration of a diluted solution to find the concentration of "stock" solution.

Practice at a longer calculation to work out how much glucose is needed to make a solution of a given concentration.

Practice calculating number of moles of a substance given the concentration and volume of a solution.

Quiz covering basic arithmetic with complex numbers and solving roots for a quadratic with complex solutions

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

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

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

A test of basic concepts to do with SI units and concentrations of solutions.

A test of basic concepts to do with SI units and concentrations of solutions.

Multiple solution of sin

Given the original formula the student enters the transformed formula

Find multiple solutions of cos

Working 26_10_16

Given the original formula the student enters the transformed formula

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

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.

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.

A simultaneous equations question with integers only