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You are here: Home / Archives for ACT Practice Questions

Reflection of points in the coordinate plane: ACT Math Practice Question

May 8, 2023 Leave a Comment

 

Try the following ACT math practice question that tests your understanding of reflection of points across the vertical axis and straight lines in the coordinate plane.

In the $xy$-coordinate plane, point $A$ is the reflection of the point with coordinates $(4, 2)$ across the straight line $y = x$. If point $B$ is the reflection of point $A$ across the $y$-axis, what are the coordinates of point $B$?

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

Choice C

Video Explanation

 

Filed Under: ACT Practice Questions

Finding area of a quadrilateral: ACT Math Practice Question

April 20, 2023 Leave a Comment

 

Try the following ACT math practice question that tests your understanding of finding areas of unusually shaped quadrilaterals.

In the figure shown above, $ABCD$ is a $2 \times 2$ square, $E$ is the midpoint of $\overline{AD}$, and $F$ is on $\overline{BE}$. If $\overline{CF}$ is perpendicular to $\overline{BE}$, then the area of quadrilateral $CDEF$ is

  1. $\quad 2$
  2. $\quad 3-\dfrac{\sqrt{3}}{2}$
  3. $\quad \dfrac{11}{5}$
  4. $\quad \sqrt{5}$
  5. $\quad \dfrac{9}{4}$

Choice C

Video Explanation

 

Filed Under: ACT Practice Questions

Percent change and area: ACT Math Practice Question

April 10, 2023 Leave a Comment

 

Try the following ACT math practice question that tests your understanding of computing percent changes in the context of geometric shapes.

If the length of a rectangle is increased by $20\%$ and the area is unchanged, then the width is decreased by:

  1. $\quad 15 \frac{1}{3}\%$
  2. $\quad 16 \frac{2}{3}\%$
  3. $\quad 18\%$
  4. $\quad 20\%$
  5. $\quad 25\%$

Choice B

Video Explanation

 

Filed Under: ACT Practice Questions

Logarithms: ACT Math Practice Question

March 15, 2023 Leave a Comment

 

Try the following ACT math practice question that tests your understanding of logarithmic operations.

If $3 = k\cdot 2^r$ and $15 = k\cdot 4^r$, then $r =$

  1. $\quad -\log_{2}5$
  2. $\quad \log_{5}2$
  3. $\quad \log_{10}5$
  4. $\quad \log_{2}5$
  5. $\quad \dfrac{5}{2}$

Choice D

Video Explanation

 

Filed Under: ACT Practice Questions

Counting handshakes: ACT Math Practice Question

March 2, 2023 Leave a Comment

 

Try the following ACT math practice question that tests your understanding of principles of counting when applied to the number of handshakes at a gathering.

A total of $28$ handshakes was exchanged at the conclusion of a gathering. Assuming that each participant shook hands with every other participant, the number of people present was:

  1. $\quad 56$
  2. $\quad 28$
  3. $\quad 14$
  4. $\quad 8$
  5. $\quad 7$

Choice D

Video Explanation

 

Filed Under: ACT Practice Questions

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