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ACT Math Practice Question: Coordinate plane, mid-point, and line intersections

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Try this ACT math practice question that relies on finding the mid-point of the line segment connecting vertices of a triangle in the coordinate plane.

If $2x-3y=1$, $x+2y=4$, and $y=-2$ are equations that represent sides $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$ of triangle $ABC$ in the coordinate plane, what are the coordinates of the mid-point of side $\overline{BC}$?

  1. $\quad (4, 0)$

  2. $\quad (4, -1)$

  3. $\quad \left(\dfrac{9}{2}, -\dfrac{1}{4}\right)$

  4. $\quad \left(5, -\dfrac{1}{2}\right)$

  5. $\quad (5, -1)$

Official ACT Prep Guide 2018: Almost identical to last year

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officialACTguide2018

The new Official ACT Prep Guide, 2018 1st Edition has been released in May 2017. This guide is almost identical to last year’s version. All three of the practice tests are identical. The only change has been the replacement of Question 59 in Practice Test 1. The question on the left in the images shown below has been replaced by the question on the right in the 2018 ACT Guide. There was an error in the original question which I discussed in an earlier blog post: Error in Q59 of 2016 Official ACT Guide.

OldACTGuide-Q59NewACT-Q59
 

Apart from this minor change, the rest of my comments listed below are the same as I made last year in the review of 2016 Official ACT Guide.

  • The practice tests are a patchwork of questions from the the 5 tests in the Real ACT Guide and recently released ACT tests from 2015.

  • First Practice Test: The math section in the first practice test in the guide has around 40 questions from the June 2015 ACT test (Form 73C), and the remainder are a combination of new questions and questions from the five tests in the Real ACT Guide.

  • Second Practice Test: Half of the math questions are from the Test#2 from Real ACT guide and the remainder are either new or from the other tests in the Real ACT guide.

  • Third Practice Test: Half of the math questions are from April 2015 ACT test (Form 73G) and the rest are from Test#4 from the Real ACT Guide.

  • Because they have reused part of the tests that are in the older Real ACT guide, this makes the practice tests in the older guide useless. I don’t know if this was done deliberately to ensure “planned obsolescence” of the older guide.

My final recommendation would be to use the April and June 2015 ACT tests on their own, and use the five practice tests in the Real ACT Guide, 3rd Edition for additional practice. I do not recommend buying this guide.

As I have said before, this analysis is based on the math section only, but I am pretty certain it will be mirrored in the remaining sections of the tests as well. I will leave it to others to analyze those sections.