# 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).

## 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.

## 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.

## 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.

### 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.

### 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.