All posts by Juan Rodriguez

Juan Tutors has a Patreon! (New tutoring clients should read this post)

JuanTutors.com has a new Patreon page! To celebrate this new initiative, Juan and any willing tutor is matching new monthly donations up to $25 with an equal discount per tutoring session while the donation is still active. Please speak with Juan about the full details of this deal.

So excited about what’s to come!

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January 2019 Algebra I Regents, THE WHOLE TEST SOLUTIONS, Premiering now!

Check it out! In the description I have a link to a review packet, which is currently discounted at 20% for a limited time!

Is 16/7 rational or irrational? THE ANSWER MIGHT SURPRISE YOU!

Is 16/7 irrational? The answer might seem obvious to you, but in fact the vast majority of students get this wrong!

I’ve even spoken to adults, and adults who know the difference between rational and irrational numbers get this question wrong.

What is it about this number that tricks so many people? I discuss the cause in this video. By the end of this video, you’ll end up a little bit smarter, and a little bit more ready for the ACT and every other test that your school throws at you, so that you can get into the college of your choice and achieve the career you deserve.

Is the product of the square root of 16 and the fraction 4/7 rational or irrational?

A. Yes, because the product of two rational numbers is always rational.
B. Yes, because the product of two irrational numbers is rational.
C. No, because the product of a rational number and an irrational number is irrational.
D. No, because the product of two irrational numbers is irrational.
E. Yes, because the product is both rational and irrational.

Get better math grades TODAY by fixing these five simple errors!

This video goes through the five most common mistakes that students make, and how to fix them! Avoid these mistakes and your grades will improve right away.

Not showing work: If you don’t show work, your MATH IS SLOWED DOWN, and your MATH IS LESS ACCURATE! Instead, show work to raise your grade, speed up, and be more accurate.

USE IT OR KEEP IT: I use the expression “use it or keep it” because, when solving math problems, all operations have to be either used or kept. Nothing becomes something else. Nothing disappears. If you are doing a math problem, and you think something should disappear, figure out how to use it, or you have to keep it.

The distributive property: The distributive property is the bane of your existence! I know. But if you follow the basic rules of the distributive property like I show you in the video, you’ll get more problems right than your friends do.

And don’t forget to do the operation you wrote down! Many problems end up being wrong because the student wrote down the correct operation, but combined things incorrectly. Use your calculator if you need to, and make sure that the math that you write down or the math that is written down for you is what you do.

Finally, check your answers! You might feel like checking your answers is a waste of your time, but the students who improve the most are the students who check their answers. The reason for this is, if you do math problems and you make a mistake, you’ll never catch the mistake, and you’ll lose the opportunity to find a pattern in the kinds of errors that you make.

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I STILL STRUGGLE with SOLVING FOR X!!! HELP!!!

I know it’s hard sometimes to find the answer to basic equations. It’s also embarrassing to ask the teacher how to solve super easy algebra problems when they have already jumped ahead to other topics! “Basic algebra mistakes get in my way”.

This video shows you how to solve basic equations in a way that you can apply to more complicated equations.

I solve one step equations, two step equations, and multistep equations in a way that will leave you understanding how to solve future equations. Hopefully this video will help you solve for x in a way you will remember! Take notes, pause the video to try problems, and you’ll be well on your way to becoming an ACT math expert!

Leave any questions in the comments and I will answer them as soon as I get them!

SAT/ACT problem of the week, December 29, 2016 solution

Hint for process of elimination: The largest part of the student body population consists of girls. Therefore, the population of girls is greater than \dfrac{1}{3} , or 33.3%, of the total population. This at least eliminating choice A. But the ratio of girls to girls plus boys is \dfrac{150\%}{150\%+100\%}=3/5, or 60%. Therefore the population of girls is under 60%. That at least eliminates both D and E. Answer C is too nice for this particular complex situation, and is also meant to draw your eye since the number 50\% appears twice in the problem, so I lean towards B.

Read on for a full solution.

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SAT/ACT problem of the week, December 22, 2016

Set A is 20% of set B, and set B is 20% of set C. What percent of set C is set A?

  1. 4% (check answer)
  2. 5% (check answer)
  3. 10% (check answer)
  4. 40% (check answer)
  5. 96% (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on December 30th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT/ACT problem of the week, December 15, 2016 solution

Hint for process of elimination: It can help you to draw boxes, where each box represents \dfrac{1}{2} hour. Write the number 20 in each box until you get to 150 pictures. Then just count boxes.

It will also help you to think intuitively about this problem. You know how time works, and you know what twenty doggy pictures looks like. Approximate. How many half hour time slots will it take to draw 150 doggies?

Read on for a full solution.

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