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You are here: Home / Archives for ACT Practice Questions

Simplifying fractional exponents and roots: ACT Math Practice Question

April 2, 2021 Leave a Comment

 

Try this ACT math practice question that tests your ability to simplify expressions that contain roots and fractional exponents.

For $x \gt 0$, which of the following expressions is equivalent to $(\sqrt[4]{x^3})(\sqrt{x})^3$?

  1. $\quad x$
  2. $\quad x^2$
  3. $\quad x(\sqrt[4]{x})$
  4. $\quad x^2(\sqrt[4]{x})$
  5. $\quad x^3(\sqrt[4]{x})$

Choice D


Video explanation

Filed Under: ACT Practice Questions

Right triangles and trigonometric expressions: ACT Math Practice Question

January 6, 2021 Leave a Comment

 

Try the following ACT math practice question that tests your understanding of evaluating trigonometric expressions in the context of right triangles.

In the right triangle $ABC$ shown below, what is the value of $1 – \cos^2{A} – \cos^2{B}$ ?

  1. $\quad -1$
  2. $\quad \displaystyle -\frac{1}{2}$
  3. $\quad \displaystyle \hskip 0.8em 0$
  4. $\quad \displaystyle \hskip 0.8em 1$
  5. $\quad \displaystyle \hskip 0.6em \frac{1}{2}$

Choice C


Video explanation

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Circles and intersections with x-axis: ACT Math Practice Question

December 16, 2020 Leave a Comment

 

Try this ACT math practice question that tests your ability to find the x-intercepts of circles.

The circle $(x+1)^2+(y-2)^2=29$ intersects the $x-$axis in two points, one of which is $(4,0)$. What are the coordinates of the other point where the circle intersects the $x-$axis?

  1. $\quad (-7, 0)$
  2. $\quad (-6, 0)$
  3. $\quad (-\sqrt{29}, 0)$
  4. $\quad (-5, 0)$
  5. $\quad (-4, 0)$

Choice B


Video explanation

Filed Under: ACT Practice Questions

Simplifying a hard trigonometric expression: ACT Math Practice Question

December 5, 2020 Leave a Comment

 

Try this ACT math practice question that tests your ability to algebraically simplify a trigonometric expression using trigonometric identities.

$$\dfrac{\cos \theta}{1 – \sin \theta} \quad – \quad \dfrac{\sin \theta}{\cos \theta}$$

When $\cos \theta \neq 0$ and $\sin \theta \neq 1$, which of the following is equivalent to the expression above?

  1. $\quad \sec \theta$
  2. $\quad \csc \theta$
  3. $\quad \cos \theta$
  4. $\quad \cos^{2} \theta$
  5. $\quad \dfrac{\cos \theta – \sin \theta}{(\cos \theta)(1 – \sin \theta)}$

Choice A

Video explanation

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Right triangles and algebra: ACT Math Practice Question

July 2, 2020 Leave a Comment

 

Try this ACT math practice question on the topics of right triangles, algebraic translation and manipulation.

The perimeter of a right triangle is $18$ inches, and one of the legs of the triangle is $6$ inches long. How many inches longer is the hypotenuse than the length of the shortest leg ?

  1. $\quad 1.5$
  2. $\quad 2$
  3. $\quad 3$
  4. $\quad 3.5$
  5. $\quad 4$

Choice C

Video explanation

Filed Under: ACT Practice Questions

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