%

PV

No description given

Gleichungen lösen nach dem ägyptischen Stile

Wirzelziehen nach der baylonischen Methode.

Fragen zum Abbildungsbegriff / Questions regarding the notion of map between two sets.

Asks the student to give the images/preimages of subsets of the domain/range of a map.

No description given

A set of Numbas exercises for students transitioning from school to University. Designed to help students gain familiarity with using Numbas to enter mathematics, and as revision for algebra, geometry and calculus. 

No description given

Suche von den fünf gegebenen Bruchzahlen diejenige aus, die nicht denselben Wert hat wie alle anderen.

Quelle: Angepasste und übersetzte Version von https://numbas.mathcentre.ac.uk/question/23233/select-the-fraction-not-equivalent-to-the-others-small-denominators/ von Christian Lawson-Perfect.

Multiples, factors, lowest common multiples and highest common factors.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Given $\rho(t)=\rho_0e^{kt}$, and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$, find $k$. (Two examples).

Apply and combine logarithm laws in a given equation to find the value of $x$.

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $\log(ax+b)-\log(cx+d)=s$

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.

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

Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

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

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

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Solve exponential equation of the form \[ a^{kx}=b^{kx+m}. \]

Solve exponential equation of the form \[ a^{kx}=a^{m}. \]

Using the IF to find the General Solution.

Separable 1st order ODE with exponentials

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other.