Timur Zaripov

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

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

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

Finding the value of a variable

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

Solve for $x$: $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Cofactors Determinant and inverse of a 3x3 matrix.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Dealing with expressions in online tests and in Matlab.

What is the value of the expression given a choice of n?

Find the determinant of a $3 \times 3$ matrix.

Multiplication of  matrices of different sizes.

Multiplication of  matrices of different sizes.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Solve for $x$: $\displaystyle ax+b = cx+d$

This question tests students knowledge of basic matrix arithmetic.

Multiplication of $2 \times 2$ matrices.

Exercises in multiplying matrices. 

aij  notation and definition of the order of a matrix.

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

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

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

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Polar form of a complex number.

Calculate the principal value of a complex number.

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.