Some examples of interactive plots illustrating mathematical concepts, supported by Python exercises.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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A set of practice questions for primary teaching students studying Mathematical Patterns and Relationships

Area and Perimeter of Rectangles

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

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This question shows how to generate a random set of $(x,y)$ samples, where $y = mx + c + \mathrm{noise}$.

The JSXGraph extension is used to show a scatter plot of the data. This isn't necessary if you just want to generate the data.

A mathematical expression part with a pattern restriction to ensure that the student has extracted the highest common factor of two terms.

The answer must be of the form $a(b+cx)$, where $b$ and $c$ are coprime.

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This question shows a JSXGraph diagram above a mathematical expression input, containing a plot of the expression the student enters.

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Exam for Maths 4, Review week 2023

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

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Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

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First assessment in 2021/22 for Foundation Mathematics, counts 5% towards the module total.

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Decimal Places and Significant Figures

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Simple Percentages

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Asks students to compute the multiplicative inverse of $a$ in $\mathbb{Z}_n$ where $n$ is an odd number between 31 and 61 and $a$ is an integer coprime to $n$ that lies between $n/4$ and $3n/4$.

A straightforward test of encrypting and decrypting an eight-letter message with the Vigenère Cipher using a four-letter key.  Message letters are generated uniformly at random from the English alphabet, as are the key letters.  Students are expected to be able to map English letters onto elements of $\mathbb{Z}_{26}$ in the usual order.

A straightforward test of encrypting and decrypting an eight-letter message with the Substitution Cipher.  Message letters are generated uniformly at random from the English alphabet and the key is a uniformly chosen random permutation of the alphabet.  Students are expected to be able to map English letters onto elements of $\mathbb{Z}_{26}$ in the usual order.

A straightforward test of encrypting and decrypting an eight-letter message with the Caesar Cipher.  Message letters are generated uniformly at random from the English alphabet, as is the key.  Students are expected to be able to map English letters onto elements of $\mathbb{Z}_{26}$ in the usual order.