Solutions

Question 1

1. Use the REPL (read eval print loop) to carry out the following calculations:

1. \(3 + 8\)

2. \(3 / 7\)

3. \(456 / 21\)

4. \(\frac{4 ^ 3 + 2}{2\times 5} - 5 ^ {\frac{1}{2}}\)

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Question 2

2.. Install the Python plugin for VScode.

The How to install VScode plugins section describes how to do this and includes an animation with a demonstration.

Question 3

3. Use the command line and a python script written in VScode to solve the following problems:

1. Find the solutions to the following equation: \(x ^ 2 - 3 x + 2 = 1\).

The code to do this:

import sympy as sym

x = sym.Symbol("x")
equation = sym.Eq(x ** 2 - 3 * x + 2, 1)
print(sym.solveset(equation))

{3/2 - sqrt(5)/2, sqrt(5)/2 + 3/2}

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2. Differentiate the following function: \(f(x) = \cos(x) / 4\)

import sympy as sym

x = sym.Symbol("x")
f = sym.cos(x) / 4
print(sym.diff(f, x))

-sin(x)/4

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3. Find the determinant of \(A = \begin{pmatrix} 1 / 5 & 1\\1 & 1\end{pmatrix}\).

import sympy as sym

A = sym.Matrix([[sym.S(1) / 5, 1], [1, 1]])
print(sym.det(A))

-4/5

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4. Count the number of ways of picking 2 letters from “ABCD” where order

  does not matter.

import itertools

combinations = tuple(itertools.combinations("ABCD", r=2))
print(len(combinations))

6

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5. Simulate the probability of picking a red token from a bag with 3 red

  rokens, 5 blue tokens and a yellow token.

import random


def pick_token():
    """
    Pick a token from a bag with 3 red and 5 blue and a yellow

    Returns
    -------
    str
        Either "Red", "Blue" or "Yellow"
    """
    bag = ["Red"] * 3 + ["Blue"] * 5 + ["Yellow"]
    return random.choice(bag)


number_of_repetitions = 10000
random.seed(0)
selections_with_red = [
    pick_token() == "Red" for repetition in range(number_of_repetitions)
]
print(sum(selections_with_red) / number_of_repetitions)

0.3349

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6. Obtain the first 5 terms of the sequence defined by:

$$

    \left\{
        \begin{array}{l}
          a_0 = 0,\\
          a_1 = 2,\\
          a_n = 3 a_{n - 1} + a_{n - 2}, n \geq 2
        \end{array}
    \right.
  $$

def get_sequence(n):
    """
    A function to give the nth term of the sequence using the recursive
    definition.

    Parameters
    ----------
    n: int
        The index of the number

    Returns
    -------
    int
        The nth term of the sequence number
    """
    if n == 0:
        return 0
    if n == 1:
        return 2
    return 3 * get_sequence(n - 1) + get_sequence(n - 2)


for n in range(5):
    print(get_sequence(n=n))

0
2
6
20
66

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Question 4

4. Install the Markdown all in one plugin for markdown in VScode and then:

1. Create a new file main.md.

2. Write some basic markdown in it.

3. Use the plugin to preview the rendered markdown.

• Go to Code > Preferences > Extensions.

• Search for Markdown and click Install on Markdown all in one.

• Create a new file, write some markdown and click on save to save it as main.md

• Click on the Open Preview to the Side icon in the top right.

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