# Hard Math Problem

The bus then stopped for lunch in a suburb before continuing on a 3 hour tour of countryside at a constant speed of 10mph. The ACT will never expect you to do that, so there must be a better way. As soon as we get to √4, we have something that can be simplified to an integer. Something like √5 gets really messy because there are not two equal fractions that can be multiplied together to equal 5.

In other words, x = -2 must be a root of the equation.

If we want polynomial P(x) to be divisible by (x 2), it must be true that P(– 2) = 0.

If you want to refer to sections of Survey of integrating methods while working the exercises, you can click here and it will appear in a separate full-size window.

If you’re wondering why hard ACT Math problems are so difficult, know that it’s not because they test crazy advanced topics like multivariable calculus or anything like that. For the first part of the field trip: 30 miles = 15mph x T, so we know that T = 2 hours. First of all, notice that the angle must be in QIII or QIV, since the sine is negative. The first three choices are all in QI and QII, so the angle can’t possibly be in any of those. As we rise from this bottom, we get negative values of smaller and smaller absolute value, until it equals zero at the positive x-axis.

If the students arrived back at Thomas Jefferson High School two hours later, approximately what was the average speed for the entire field trip? The moment you find an irrational number as you count through the series, you can eliminate answer choice A, for example.

Finally, the bus drove 40 miles straight back to the high school. So we just need to count the perfect squares before 50. So that means out of our 50 numbers, 7 can be reduced to integers (or fractions) and 43 are irrational. Bonus hint: If you come across a problem like this on the ACT, and don’t know how to solve it, make sure you eliminate some answer choices!

This definitely eliminates B, and thinking logically, you could probably take a guess that the overall probability is going to be high. ANSWER: C This question is difficult primarily because you need to have some higher-level knowledge of the equations of circles and ellipses.

You should find that out of the first 11, 8 numbers are irrational.

What would s have to be so that is divisible by (x 2)? If it is taller than it is wide, it looks like the second one.

So let’s get started with the equation for an ellipse: = 1 = 1 If an ellipse is wider than it is tall, our equation looks like the first one.