52 results authored by Ulrich Görtz - search across all users.
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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.
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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
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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.
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Quadratwurzeln vereinfachen, Nenner rational machen
Deutsche Übersetzung von https://numbas.mathcentre.ac.uk/question/22587/using-surds-rationalising-the-denominator/ von Elliott Fletcher
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No description given
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Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).
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Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).
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Questions around induction, also illustrating statements where only one of induction start/induction step actually works.
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Questions on the construction $t+U$ where $K$ is a field, $t\in K^n$, $U\subseteq K^n$ (in parts a) - d), $K=\mathbb R$ and $n=2$ so that we can draw pictures). Part e) is a bit more abstract and probably more difficult.
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Deduce some properties of elements of $\mathbb F_4$, given its multiplication table. (E.g., which element is the zero, the one element, ...)
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Simple direct computations in $\mathbb Z/n$.
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Two slightly more complicated questions on handling fractions.
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Some simple questions around injectivity, surjectivity, bijectivity (and the inverse function) of linear functions $\mathbb R\to \mathbb R$ (i.e., $x\mapsto mx+b$ for some real numbers $m$, $b$).
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Questions around the notion of map, with underlying topic the statement of Goldbach's conjecture. The student has to write the conjecture (by filling in some gaps) as a surjectivity statement for a map, and compute some preimages of elements.
(In German)
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Some simple abstract questions on injectivity, surjectivity, bijectivity.
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An induction problem concerning the Fibonacci sequence.
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Prove (by induction) that every value $\ge$ 44ct can be combined by using 5ct and 12ct stamps.
Idea seen in collection of exercises for preparing for the Putnam contest.
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Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.
Original: https://numbas.mathcentre.ac.uk/question/11698/equation-of-a-straight-line/ by Newcastle University Mathematics and Statistics,
translated to German, added Parts b), c), d), e)
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Rationalise the denominator with increasingly difficult examples involving compound denominators.
Translated to German, made some minor changes to Advice section.
Original: https://numbas.mathcentre.ac.uk/question/22555/rationalising-the-denominator-surds/ by Lauren Richards
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Fragen zum Abbildungsbegriff / Questions regarding the notion of map between two sets.
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Asks the student to give the images/preimages of subsets of the domain/range of a map.
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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.
