Category Archives: Problem of the Week

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

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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!

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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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SAT/ACT problem of the week, January 26, 2017 solution

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Hint for process of elimination: Taking test values such as $latex a=3 $ and $latex b=5 $ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $latex a $ and $latex b $ do not eliminate all choices, making a second choice (or in very extreme cases even a third choice) will finish off all remaining incorrect answers.

Another hint is, variables are never being multiplied with other variables, this eliminates choices D and E. Also, there is nothing in the original expression which can combine with and eliminate the number 2 from the expression. This eliminates choices A and C, leaving you with the correct answer, B.

Read on for a full solution.

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SAT/ACT problem of the week, January 26, 2017

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Which of the following is equal to $latex 5a + 3b -(5b -2) $?

  1. $latex 5a $ (check answer)
  2. $latex 5a – 2b +2 $ (check answer)
  3. $latex 5a – 10b $ (check answer)
  4. $latex 5a – 15b^2 – 6b $ (check answer)
  5. $latex 8ab – 5b + 2 $ (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on February 1st. If you would like to learn how to enter fancy math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT/ACT problem of the week, January 19, 2017 solution

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Hint for process of elimination: Use the keyword “despite” as a hint that the word in the blank must produce a statement that says that Isiah did the opposite of what might be expected after repeated failure. This should at least eliminate choices A, B, and D, giving you a 50% chance of getting this problem correct. Any time you can eliminate at least one answer, it is most advantageous to guess.

Read on for a full solution.

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SAT/ACT problem of the week, January 19, 2017

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Despite the fact that all his attempts to capture the massive Goliath Tigerfish had failed, Isiah ——— in his attempts to capture the fish during his outing.

  1. failed (check answer)
  2. languished (check answer)
  3. cemented (check answer)
  4. was defeated (check answer)
  5. persevered (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on January 25th.

SAT/ACT problem of the week, January 12, 2017 solution

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Hint for process of elimination: This is considered a difficult problem to solve on the SAT directly, since the test makers don’t necessarily expect you to know logarithms. However, they do expect you to know the equation for percent growth, so you should have an equation to plug into. The equation is described below in the full solution.

Notice that the investment grows from $10,000 to $100,000, which is a tenfold increase in value of the investment. In this case, you might get a hint that the growth rate of the investment is pretty big. If the investment grows at a rate of 20% per year, then it takes less than 5 years for the value of the investment to double. That means it takes less than 15 years for the investment to double three times, which is a factor of $latex 2^3 = 8$. To grow by a factor of 10, it really should not take more than 15 years, at the roughest estimate. This leaves choices A (5 years), B (10 years), and C (12.6 years). Clearly 5 years is too short. After all, an investment that grows at 20% per year cannot grow 1000% in five years. This leaves choice B and C, giving you a 50% chance of getting the answer right. Even if you can’t decide on which answer is correct at this point, you should still give an answer.

Read on for a full solution.

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SAT/ACT problem of the week, January 12, 2017

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A $10 thousand investment in a stock is expected to achieve a rate of return of 20% per year. At this rate, approximately how much time is expected to pass for the investment expected to be valued at $100 thousand?

  1. 5.0 years (check answer)
  2. 10.0 years (check answer)
  3. 12.6 years (check answer)
  4. 16.3 years (check answer)
  5. 50.0 years (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on January 18th. If you would like to learn how to enter fancy math formulas into this blog, visit the WordPress LaTeX tutorial page.

SAT/ACT problem of the week, January 05, 2017 solution

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Hint for process of elimination: The most important thing to recognize is that this problem can EASILY be solved by punching the numbers into the calculator. The second thing to know is the three major easy arithmetic facts and tips that students forget all the time but they shouldn’t live life without knowing:

  • Know that the word “product” implies multiplication.
  • Do not mix up the concepts of multiplication and addition.
  • Know how to multiply negative numbers, including knowing that the product of two negative numbers is positive.

Read on for a full solution.

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SAT/ACT problem of the week, January 05, 2017

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What is the product of -2 and -3? (Seriously, this is a real ACT question.)

  1. -6 (check answer)
  2. -5 (check answer)
  3. -1 (check answer)
  4. 5 (check answer)
  5. 6 (check answer)

Solutions, hints, and questions are welcomed. A full solution will be posted on October 9th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.