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. $\quad (-4,2)$

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. $\quad \dfrac{9}{4}$

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. $\quad 25\%$

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. $\quad \dfrac{5}{2}$

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. $\quad 7$