Please help - Practice ACT Math Questions

Test Preparation ACT Preparation
1

Hello!

I have been preparing for the September 12th ACT, and can’t seem to get past the following math questions. Any help would be hugely appreciated!

  • #58 from Princeton Review "Cracking the ACT" 2015 Edition (I can't upload a picture, but if someone else wants to follow along in their book...): An angle with vertex at the origin and measure θ is shown in the standard (x,y) plane. If one side of the angle includes the positive x-axis and the other side passes through (-12, -5), then what is the sine of θ?

    –> For this one, the answer is -5/13. I can find the other side of the triangle (13), but I struggle with visualizing/ drawing the triangle formed by the angle. Any advice on this would be wonderful!

  • #54 from Princeton Review: A particular linear equation includes the (x,y) pairs below. What is the value of b? x y 1 1 2 b 3 3 3 9

Answer choices:
F -8
G -5
H -1
J 0
K 7

Part of the explanation provided doesn’t make sense to me: “For the (x,y) pair (-2,b), b must be a positive value, which eliminates all answers except choice (K) - 7.” Where do they get the -2? I thought it could be a typo, but I’m honestly not sure…

  • Actual Question #51 from April 2015 ACT (I think this one is conceptually similar to #58 above): What are the values of θ, between 0 and 2pi, when tan θ = -1?

Thank you so much to anyone who answers! Good luck to everyone taking the test on Saturday! :slight_smile:

2

PR is notorious for having math sections that are harder than the real ACT. And it also contains a lot of typos from my experiences. And for #54, how can there be two x’s with same values?

3

I’m not sure on #54… I think it might be a typo like you just mentioned, but that’s how it’s typed in the book. Thank you for your input - I’m hoping it’s harder than the actual test!!

4
  1. I assume they're referring to the obtuse angle, by standard convention. Draw the points (0,0) and (-12,-5). Also label (-12,0) and connect to make a triangle. Sine is negative in quadrant III, and sin theta = -5/13.
  2. Yeah there's a typo.
  3. 3pi/4 and 7pi/4. Are you familiar with trig functions and the unit circle? (I was able to get the answer by visualizing a unit circle and the line y = -x).
5

Thank you!! I meant to say thanks earlier, but was in the middle of studying… glad to be done with it!