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

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

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

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

An introduction to using the quotient rule

An introduction to using the quotient rule

An introduction to using the quotient rule

An introduction to using the quotient rule

This quiz asks questions on basic techniques of differentation and some introductory applications.

5 questions on finding local and global maxima and minima on compact intervals and on the real line for differentiable functions.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

First- and second order recurrence equations, homogenous and nonhomogenous

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Solving three simultaneous congruences using the Chinese Remainder Theorem:

\[\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*} \] where $\operatorname{gcd}(n_1,n_2,n_3)=1$

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 $\mod b$.

Chemistry Calculations for Fourth Year Proect. 

Differentiate $\displaystyle \frac{ax+b}{cx+d}$.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.

Simplify logarithmic expressions using rules on logarithms.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Simplifying indices.

This quiz asks questions on basic techniques of differentation and some introductory applications.

Identifying the correct rule to use

More work on differentiation with fractional coefficients.

Differentiate $ \sin(ax+b) e ^ {nx}$.

Differentiate $x^m\cos(ax+b)$