ACT math question help

Test Preparation ACT Preparation
1

I need help with a circles/trig question. I got a 30 on this practice test (a released crackact test from last year) and I’m trying to bring math up to a 33 before june 11.

the question is number 58 of math test on the link.

https://drive.google.com/file/d/0B-SjC2QWxqXRdzBDNE5yZkZaUlk/view?pref=2&pli=1

2

@markj4994 first you need to find the measure of angle ADC. By definition, sin ∠ADC = 1/4, so ∠ADC = sin^(-1) (1/4) (this is roughly 14.5°).

The circumference of the circle is 8π. Then the length of arc AC is 8π*(∠ADC / 2π) = 4 sin^(-1) (1/4) ≈ 1.01.

This is correct, although that ACT test seems to be created by tricksters who like degrees (radians are much better), so it turns out that sin^(-1) (1/4) should return 14.5°, not 0.2527. To convert to the correct answer whose units are centimeters, we have to multiply by π/180°, giving us (π/45)*sin^(-1) (1/4) (choice F).

3

Thanks u helped a lot! Do u think if I study and review and take a couple more practice Tests I could move up from a 30 to a 33? @MITer94

4

@markj4994 Probably - although I am not very familiar with ACT practice materials (I took it once w/out prep). Generally if you’re pushing for high scores such as a 33 or 36, it comes down to making sure you don’t make silly mistakes during the test.

5

@MITer94 sorry to bother you again but could u help with number 48 and 54 of another test (math section)

https://drive.google.com/file/d/0B-SjC2QWxqXRRjZFRzlSY3VnNWc/view?pref=2&pli=1

thank you so much!

6

@markj4994 Sure no problem.

  1. is a fairly straightforward trigonometry question and all you need to know are the definitions of sine, cosine, and tangent. Note that the lower-right angle is also 53° (using parallel lines). Make sure you are comfortable with these definitions, then 48. should be very easy. I don't want to spoil the answer here.
  2. Here we can use the fact that the sum of two interior angles of a triangle equals the exterior angle of the third angle. In this case, α+β = 60°, so what we really want to find is cos 60°. Now what is cos 60°?