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CalcMe exercises solutions

Becoming familiar with the interface and basic commands

Write a CalcMe algorithm that does the following actions in the order they appear:

  • Define the variable y as the quotient of 39 divided by 7 and the variable z as the remainder of 63 divided by 11.

  • Specify the variable y as a prime number and factor the variable z.

  • Define p as a 2nd degree polynomial in x with roots y and z.

  • Evaluate p in 0 and -3 and save the results in two variables, then find the greater common divisor of these results.

  • Illustrate the graph of p and cos(y·x+z).

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Introduction to randomization

Write a CalcMe algorithm that does the following actions in the order they appear:

  • Define a list L of 4 random numbers between –10 and 10, excluding 0.

  • Find the least common multiple of two different random numbers of the list.

  • Define a random number x as a decimal number (to the second decimal place) between 7 and 15 that is not an integer number.

  • Define a random number y as a rational number (to the first decimal place) between 3.2 and 6.8 that is not an integer number.

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Commands sections

Write a CalcMe algorithm that does the following actions in the order they appear:

  • Define a list L of random coefficients between -5 and 5, excluding 0 of random length between 5 and 10 (creating a user function for the randomness).

  • Define a polynomial p(x) of degree 2 with random coefficients from the list L and find its roots.

  • Plot the graph of p(x) in green, draw the minimum or maximum of the function and write the point coordinates on the plotter.

  • Create a list K whose elements are the quotient of L's elements and its position if, and only if, its greatest common denominator is 1.

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Programming methods

Exercise 1

Write a CalcMe algorithm that generates order 3 random matrices until you find one with the determinant 1. Besides, this algorithm should count how many matrices are generated until finding the required one.

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Exercise 2

Write a CalcMe algorithm that does the following actions in the order they appear:

  • Create two lists, L1 and L2, that contain the first ten multiples of two different random numbers between 3 and 9.

  • Merge the two lists into one ordered list L3.

  • Create a new list L that only saves the numbers appearing on both lists L1 and L2 using programming tools.

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Exercise 3

Write a CalcMe algorithm that does the following actions in the order they appear:

  • If the matrix is square and invertible, calculate its inverse.

  • If the matrix is square but not invertible, calculate its nucleus.

  • If the matrix is not square, call the function again with the matrix multiplied by its transpose.

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