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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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Simplify fractions involving the products of factorials.

More work with dividing and multiplying algebraic fractions

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Practice with fractions

Straightforward solving linear equations question

Straightforward solving linear equations question.

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

A simultaneous equations question with integers only

Shows how to define variables to stop degenerate examples.

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

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $0$ and $2 \pi$ and careful with quadrants!

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form  $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$.

Seven standard elementary limits of sequences. 

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \lt 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

$x_n=\frac{an+b}{cn+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \lt 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$.

Given a set in predicate form i.e. $A=\{x|P(x)\}$, find and input the elements of the set.

Given a set $A$, elements of which may also be sets, determine if the given elements or subsets are in $A$.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.