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ACT Math Practice Question: Trigonometric Identities

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Try this ACT math practice question on trigonometric identities:

For all $\theta$, the expression $\csc^{2} \theta \tan^{2} \theta – 1 $ is equivalent to:

  1. $\quad \cot^{2} \theta$

  2. $\quad \tan^{2} \theta$

  3. $\quad \csc^{2} \theta$

  4. $\quad \sec^{2} \theta$

  5. $\quad \cos^{2} \theta$

ACT Math Practice Question: Exponents and Scientific Notation

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Try this ACT math practice question on exponents and scientific notation:

Given $a$ and $b$ are positive integers, what is $\dfrac{60 \times 10^a}{3 \times 10^b}$ expressed
in scientific notation?

  1. $\quad 2 \times 10^{a-b-1}$

  2. $\quad 2 \times 10^{a-b+1}$

  3. $\quad 2 \times 10^{(\frac{a}{b}-1)}$

  4. $\quad 20 \times 10^{a-b-1}$

  5. $\quad 20 \times 10^{a-b+1}$

Error in Math Question 59 Practice Test 1 Official ACT Prep Guide 2016

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Both choices (C) and (E) are correct answers to question 59 (page 70) in the Math section of the first practice test in the newly published Official ACT Prep Guide 2016. I have reproduced the entire question along with my video explanation that clarifies this mistake.

Practice Test #1: Question 59 Mathematics

In scalene triangle $\triangle GHI$ shown below, point $J$ lies on side $\overline{HI}$, $\overrightarrow{GJ}$ bisects $\angle HGI$ such that $\angle HGJ$ and $\angle IGJ$ each measure $\theta$, and the given lengths $a$, $b$, $c$, $d$, and $e$ are in inches and are distinct. For all possible values of $\theta$, the area of $\triangle GHJ$ is what fraction of the area of $\triangle GHI$ ?
Q59ACTTest1

  1. $\dfrac{1}{2}$

  2. $\dfrac{a}{b}$

  3. $\dfrac{d}{d+e}$

  4. $\dfrac{ad \sin{\theta}}{b(d+e)\sin{2\theta}}$

  5. $\dfrac{c \sin{\theta}}{b \sin{2 \theta}}$