This shows how to use captured groups in a mathematical expression part's pattern restriction to mark an answer involving multiple occurrences of an undefined function.

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

rebelmaths

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

rebelmaths

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

rebelmaths

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

rebelmaths

This question uses the linear algebra extension to generate a system of linear equations which can be solved.

We want to produce an equation of the form $\mathrm{A}\mathbf{x} = \mathbf{y}$, where $\mathrm{A}$ and $\mathbf{y}$ are given, and $\mathbf{x}$ is to be found by the student.

First, we generate a linearly independent set of vectors to form $\mathrm{A}$, then freely pick the value of $\mathbf{x}$, and calculate the corresponding $\mathbf{y}$.

To generate $\mathrm{A}$, we generate more vectors we need, then pick a linearly independent subset of those using the subset_with_dimension function.

Differentiation questions (mostly partial differentiation) with customised feedback, with the intention of catching common errors.

Einfache Matheprüfung mit 4 Fragen.

Modifiziert (dynamische Zahlenwerte) nach: Berggren, J. L. & Schmidl, P. G. (2011). Mathematik im mittelalterlichen Islam. Springer, S. 73, Aufgabe 12.

Indefinite Integrals

rebel

rebelmaths

Adaptiert von: Katz, V. J. (2009). A history of mathematics: An introduction (3. ed.). Boston: Addison-Wesley, S. 418.

Indische & arabische Mathematik

Indische & arabische Mathematik

Aus der indischen Mathematik

Chinesische Mathematik

Aufgabe zum Chinesischen Wurzelziehen, inspiriert von: Katz, V. J. (2009). A history of mathematics: An introduction (3. ed.). Boston: Addison-Wesley (pp. 199/200).

Aufgabe zum Chinesischen Wurzelziehen, inspiriert von: Katz, V. J. (2009). A history of mathematics: An introduction (3. ed.). Boston: Addison-Wesley (pp. 199/200).

Practice on the differentiation questions of SFY0018 CBA1 (basic maths questions practised elsewhere)

No description given

Ein paar Beispiele zum Arbeiten mit mathematischen Ausdrücken

Übungen zur Ethnomathematik

A resource for Business students to practise calculating Normal probabilities and finding $Z$-values. 

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.

https://numbas.mathcentre.ac.uk/question/22664/addition-and-subtraction-of-fractions/ by Lauren Richards

Translated to German and Part d) added.

Finde die Bruchzahl, deren Wert sich von den anderen unterscheidet. Die Nenner sind meistens zwei- oder dreistellig.

Angepasste und übersetzte Version von https://numbas.mathcentre.ac.uk/question/23234/select-the-fraction-not-equivalent-to-the-others-large-denominators/ von Christian Lawson-Perfect.

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

German translation of https://numbas.mathcentre.ac.uk/question/12012/solve-an-equation-in-algebraic-fractions/ by Newcastle University Mathematics and Statistics

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Translated to German, minor changes to advice section.

Original: https://numbas.mathcentre.ac.uk/question/22497/surds-simplification/ by Lauren Richards.

Quadratwurzeln vereinfachen, Nenner rational machen

Deutsche Übersetzung von https://numbas.mathcentre.ac.uk/question/22587/using-surds-rationalising-the-denominator/ von Elliott Fletcher