Simple Percentages

rebelmaths

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A measurement is performed multiple times for the same object, the student will

• calculate the mean result
• calculate the standard error on the mean 
• write the mean±error to the correct precision as defined by the error written to 1 significant figure 

Advice is provided including on performing the calculations in Python or spreedsheets together with further reading. 

Edit the Python code to make a 3D plot of a surface defined parametrically.

The students should solve a Blakley secret sharing scheme and find the secret.

Tests students' ability to apply the recursive form of the Extended Euclidean Algorithm.  Random four-digit inputs are chosen subject to the condition that the Euclidean Algorithm terminates in seven steps.

Asks students to add and multiply two integers modulo another integer.  The modulus is a random number between 30 and 70, the summands are set to be large enough that modular reduction will be necessary.

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 $3n/4$.

This question tests students' ability to use repeated squaring to perform modular exponentiation.  Moduli are random numbers between 30 and 70, the base is a number between 10 and 29.  To generate questions of approximately uniform difficult the exponent is taken to be 256 plus two smaller powers of 2. 

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-bit message with the Vernam Cipher.  The message and the key are uniform and independently generated eight-bit strings.

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.

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Manipulate surds and rationalise the denominator of a fraction when it is a surd.

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Exercises covering Week 1 material for PHY1030

Python assignment for PHY1030 2023-24

A random dataset given by a linear function with noise (gradient and y-intercept of the linear function are randomised as is distribution of x values).

The purpose of this question is to ask the students to go through one Rijndael round from the AES algorithm.

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.

Dummy question to test random() function when first decimal place of upper limit of range is 4, and test of currency() function.

Part of HELM Book 1.4.2

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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The exercises for HELM Book 1.4.1

The 7th task in HELM book 1.4 section 1.