ACT Math practice test

At a school fair, the probability that a player wins a prize is 0.35, the probability that a player wins a coupon is 0.20, and the probability that a player wins both is 0.08. What is the probability that a player wins a prize or a coupon?

The temperature of a greenhouse, in degrees Fahrenheit, after $h$ hours is modeled by $T(h)=72-5h$. What temperature does the model predict after 4 hours?

Which of the following is equivalent to $(7m+4n)-(n-3m)$?

The quantity $y$ varies directly with $x$. When $x=4$, $y=12$. What is $y$ when $x=10$?

The mean mass of grain in 4 storage bins is 20 kilograms. What is the total mass of grain in the 4 bins, in kilograms?

Triangles $ABC$ and $DEF$ are congruent, with $A$ corresponding to $D$, $B$ to $E$, and $C$ to $F$. If $AB=2x+3$ and $DE=5x-12$, what is the value of $x$?

Given that $i$ is the imaginary unit, which of the following numbers is equal to $(3+2i)(4-i)$?

Which of the following lists the numbers $-{\displaystyle \frac{5}{2}}$, $-\sqrt{5}$, and $-2$ in order from least to greatest?

In right triangle $ABC$ shown below, $\mathrm{\angle }C=90^{\circ }$, $\mathrm{\angle }A=45^{\circ }$, and leg $AC$ has length $9\sqrt{2}$ centimeters. What is the length, in centimeters, of hypotenuse $AB$?

In the circle with center $O$ shown, $\overline{PR}$ is a diameter and $Q$ is a point on the circle. What is the measure of $\mathrm{\angle }PQR$?

In the standard $(x,y)$ coordinate plane, what is the distance, in coordinate units, from $(2,-9)$ to $(9,15)$?

An isosceles triangle has a vertex angle measuring $46^{\circ }$. What is the measure of each base angle?

In the standard $(x,y)$ coordinate plane, the graphs of $y=2x-1$ and $y=-x+8$ intersect at the point $(a,b)$. What is the value of $a+b$?

Which of the following is equivalent to ${\displaystyle \frac{10}{\sqrt{5}}}$?

The graph of $y=x^2+x-20$ intersects the $x$-axis at two points. What are the $x$-coordinates of those points?

An integer is chosen at random from the integers 20 through 50, inclusive. What is the probability that the integer is not divisible by 3?

Three security guards start together at a museum’s front desk. Guard A returns to the desk every 8 minutes, Guard B every 12 minutes, and Guard C every 18 minutes. How many minutes after the start will all three next return to the desk at the same time?

The quadratic function $f$ is defined by $f(x)=2x^2-12x+5$. What is the equation of the axis of symmetry of the graph of $y=f(x)$?

At a performing arts program with 70 students, 34 study orchestra, 29 study choir, and 12 study both. How many students study neither orchestra nor choir?

The ellipse shown below has center $(1,-2)$, horizontal vertices $(-3,-2)$ and $(5,-2)$, and vertical co-vertices $(1,-4)$ and $(1,0)$. Which of the following equations represents the ellipse?

The function $f$ is defined by $f(x)=x^2+3$. Let $g(x)=f(x)-8$. What is the minimum value of $g$?

A neighborhood association budgeted $8,600 for tree care in the first year of a program. The budget increased by the same dollar amount each year and was $11,800 in the fifth year. What was the budget in the third year?

A transit survey recorded 14 one-way commute distances. The table shows each distance and how often it occurred. What is the median one-way commute distance, in miles?

The function $W(h)$ gives the total number of liters of water used by a gardener’s 12 plants over $h$ days. The gardener finds that $W(5)=90$. Which of the following statements correctly interprets this equation?

A pump moves water at 18 gallons per minute. How many seconds will it take the pump to move 205.2 liters of water?

(Note: 1 gallon $=3.8$ liters)

Which of the following expressions is equivalent to $2w^3+w^2-2w+8$?

A high school surveyed 160 juniors about taking AP Chemistry and AP Biology. The table shows the results.

To the nearest $1\mathrm{\%}$, what percent of the juniors take at least one of the two AP science courses?

What is $\left[\begin{array}{cc}1& 2\\ 3& 0\end{array}\right]\left[\begin{array}{cc}2& -1\\ 1& 4\end{array}\right]$?

A group bought 24 museum tickets. Adult tickets cost $13 each, child tickets cost $8 each, and the group paid $252 in all. How many adult tickets did the group buy?

Which of the following is equivalent to ${\log }_b\text{\hspace{0.17em}⁣}\left({\displaystyle \frac{a^2}{c}}\right)$ for $a>0$, $b>0$, $b\mathrm{\ne }1$, and $c>0$?

A class has 10 students, and 4 of them have taken calculus. Two students are selected at random without replacement. What is the probability that both selected students have taken calculus?

Given that $2\le a\le 5$, $6\le b\le 9$, and $3\le c\le 7$, what is the greatest possible value for $\left({\displaystyle \frac{a}{b}}\right)\left({\displaystyle \frac{c}{4}}\right)$?

In the circle shown, radius $OA$ is 13 centimeters. Segment $OM$ is perpendicular to chord $AB$, and $OM=5$ centimeters. What is the length, in centimeters, of chord $AB$?

A kayaker on a lake looks up at the top of a cliff-side lighthouse. The angle of elevation from the kayaker to the top of the lighthouse is $55^{\circ }$, and the lighthouse stands 120 feet above the water, as shown below. Which of the following expressions gives $d$, the horizontal distance in feet from the kayaker to the base of the lighthouse?

In the standard $(x,y)$ coordinate plane, a polygon has vertices $(-4,-2)$, $(1,-2)$, $(1,2)$, $(4,2)$, $(4,5)$, and $(-4,5)$. What is the area, in square units, of the polygon?

Given that $i$ is the imaginary unit, which of the following is equal to ${\displaystyle \frac{7+i}{2-i}}$?

In the standard $(x,y)$ coordinate plane, how many points are both 2 coordinate units from $(-1,4)$ and also 6 coordinate units from the line $x=7$?

As shown, points $W$, $X$, $Y$, and $Z$ lie on the number line. Which of these points is closest to $\sqrt{7}+\sqrt{5}$?

The graphs of $y=3x+2$ and $y=2x^2-6x+6$ intersect at 2 points in the standard $(x,y)$ coordinate plane. What is the sum of the $y$-coordinates of those 2 points?

In circle $O$ shown, segment $\overline{PR}$ is a diameter. Starting at $P$ and moving clockwise, $Q$ is the midpoint of semicircle $PR$, and $S$ is the midpoint of arc $QR$. What percent of the area enclosed by circle $O$ is the region bounded by $\overline{OQ}$, $\overline{OS}$, and the minor arc $QS$?

A function, $f$, is defined by $f(x)=2x^2-5x+11$. What is $f(4)$?

Priya asked 16 classmates how many miles each biked last week. The table shows the results. What is the median number of miles biked?

When a polynomial $P(x)$ is divided by $x-1$, the remainder is 20. When it is divided by $x+1$, the remainder is 18. The remainder when $P(x)$ is divided by $(x-1)(x+1)$ has the form $ax+b$. Which of the following is that remainder?

Two positive numbers are in the ratio $5:9$. When 4 is subtracted from each number, the resulting numbers are in the ratio $1:2$. What is the larger of the two original numbers?

A circular disk has radius 12. Two nonoverlapping sectors sharing the disk’s center are painted on it: one with central angle $90^{\circ }$ and radius 12, and one with central angle $120^{\circ }$ and radius 6. A point is selected at random from the disk. What is the probability that the point is in a painted sector?