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# Tutor profile: Miguel P.

Miguel P.
Doctor in STEM Education with a strong background in mathematics and mathematics education.

## Questions

### Subject:Pre-Calculus

TutorMe
Question:

Use the Pythagorean theorem to prove that $$sin^2(x)+cos^2(x)=1$$.

Miguel P.

This question will not challenge students' understanding of the Pythagorean theorem as much as their understanding of the unit circle. To illustrate it, they will draw the unit circle and plot an angle x, sin(x), and cos(x). Then, they will just need to apply the Pythagorean theorem to prove the equality.

### Subject:Pre-Algebra

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Question:

a) Solve $$7-x<10$$. b) Solve $$3\le7-x$$. c) Solve $$3\le7-x<10$$.

Miguel P.

Many students struggle with inequalities; especially with double inequalities. Although compound inequalities might be an Algebra 1 question depending on where students are or their levels, the concept of solving inequalities is the same whether you have one or two. We can solve the problem one side at a time (following the same steps on both sides), or work on both inequalities at the same time. Students will be asked to solve both simple inequalities first and then predict what the answer to the compound inequality would be by making sense of their answers to parts a) and b), allowing them to make connections between problems with one inequality and problems with two. Then, they will solve the compound inequality and notice that they used the same steps for solving all three problems. Step by step, a solution to the compound inequality would be: $$3\le7-x<10$$ $$-7 +3\le-7+7-x<-7+10$$ $$-4\le -x<3$$ Multiply everything by -1: $$4\ge x>-3$$ The solution interval for the problem can then be rewritten as: $$x\in(-3,4]$$

### Subject:Statistics

TutorMe
Question:

Exploring data with CODAP (free online data exploration tool available at https://codap.concord.org/): 1. First, open a new document on CODAP and drag the Energy.csv file (provided by me) onto the workspace to import the data. 2. Use the tools necessary to answer the following questions: a. Which is the most used source of energy throughout the year? And the least? b. How common is the use of renewable energies compared to non-renewable? Is there a trend throughout the years? c. At what times of the year are the different types of energy more prominent? Can you explain the phenomena you observe? d. Pose one question of your own for these data and find an answer with CODAP.

Miguel P.

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