37 results authored by Ulrich Görtz - search across all users.

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• Question

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• Question

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).

• Question

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).

• Test pause
Draft
Exam (1 question)

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• Question

Some simple multiple choice questions on the field of complex numbers.

• Question

Questions around induction, also illustrating statements where only one of induction start/induction step actually works.

• Question

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.

• Question

Deduce some properties of elements of $\mathbb F_4$, given its multiplication table. (E.g., which element is the zero, the one element, ...)

• Question

Simple direct computations in $\mathbb Z/n$.

• Question

Questions around quadratic equations over finite fields of the form $\mathbb F_p$, $p$ a prime number.

• Question

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.

Translated to German and Part d) added.

• Question

Two slightly more complicated questions on handling fractions.

• Lineare Funktionen
Question

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 $m$, $b$).

• Question

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)

• Question

Some simple abstract questions on injectivity, surjectivity, bijectivity.

• Teilbarkeitsaussage
Question

Guided induction proof of a divisibility statement (with moderate randomization).

• Question

An induction problem concerning the Fibonacci sequence.

• Question

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.

• Question

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.

Question

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)

• Question

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

• Question

Rationalise the denominator with increasingly difficult examples involving compound denominators.

Original: https://numbas.mathcentre.ac.uk/question/22555/rationalising-the-denominator-surds/ by Lauren Richards

• Question

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

• Question

Decide whether statements about square and cube numbers are always true, sometimes true or never true.

German translation of https://numbas.mathcentre.ac.uk/question/22768/always-sometimes-or-never-square-and-cube-numbers/ von Stanislav Duris.

• Question

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

• Bild und Urbild
Question

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

• Question

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.

• Question

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.

• Question

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

https://numbas.mathcentre.ac.uk/question/22784/decimals-to-fractions/ by Lauren Richards

Translated to German.

• Br?che vereinfachen
Schreibe $\displaystyle \frac{a} {b + \frac{c}{d}}$ als einen gekürzten Bruch $\displaystyle \frac{p}{q}$ mit ganzen Zahlen $p$ und $q$.