ACT Math practice test

The whole numbers 1 through 25 were each written on separate cards and placed in a box. One card will be drawn at random. What is the probability that the number on the card is a perfect square?

The table gives values of the polynomial functions $f$ and $g$. For which value of $x$ in the table is $f(x)-g(x)$ the greatest?

At a performance, the ratio of child tickets to adult tickets sold was $3{:}5$. If 320 tickets were sold in all, how many adult tickets were sold?

Which of the following expressions is equivalent to $(3m^2-n^2)-(5m^2-2mn+n^2)$?

A survey asked 20 families how many pets they own. The table shows the number of pets and how many families reported each amount. Based on the table, what is the range of the number of pets owned?

The graph of $y=f(x)$ is shown in the standard $(x,y)$ coordinate plane. What is the maximum value of $f$?

A certain quadrilateral has angle measures of $72^\circ$, $95^\circ$, $108^\circ$, and $x^\circ$. What is the value of $x$?

The graph of a linear inequality is shown in the standard $(x,y)$ coordinate plane. Which of the following points is in the solution set of the inequality?

What is the value of $\dfrac{\dfrac{3}{4}+\dfrac{1}{6}}{\dfrac{2}{3}-\dfrac{1}{4}}$?

Priya can rent equipment under either of 2 plans. For $d$ rental days, Plan A costs $38+7d$ dollars and Plan B costs $14+11d$ dollars. For which of the following ordered pairs $(d,c)$ do the 2 plans charge the same total cost of $c$ dollars?

An isosceles triangle has two sides that are each 8 centimeters long and a third side that is 5 centimeters long. What is the perimeter, in centimeters, of the triangle?

Given that $i$ is the imaginary unit, what is $i^{2}+i^{3}$?

Which of the following labeled points is closest to the length, in centimeters, of a cable measuring $\sqrt{5}$ meters? (Note: 1 meter equals 100 centimeters.)

A circular patio has a radius of 5 meters. Sealing the patio costs 4 dollars per square meter. Using 3.14 for $\pi$, what is the total cost, in dollars, to seal the patio?

Let $a=-7$ and $b=10$. If $2a+b=22-2m$, what is the value of $m$?

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 table shows the height of a young plant, in centimeters, several weeks after planting, where $x$ is the number of weeks and $y$ is the height in centimeters.

Which of the following equations represents the relationship between $x$ and $y$?

What is the value of $\log_2(128)$?

A red light flashes every 12 minutes and a blue light flashes every 18 minutes. If both flash at the same time, after how many minutes do they next flash at the same time?

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?

Water enters a tank at a constant rate of 9 liters per minute, and no water leaves during the measurement. After 4 minutes, the tank holds 58 liters. Let $V(t)$ be its volume after $t$ minutes. Which equation models $V(t)$?

The table shows several values of a quadratic function $k$.

Which of the following is a factored form of $k(x)$?

Which of the following expressions is equivalent to $3x^3-27x$?

A workshop uses $C(q)$ to represent the total cost, in dollars, of producing $q$ wooden trays. What does $\dfrac{C(40)}{40}$ represent?

On a scale drawing, 4 centimeters represents 7 meters. Under the same scale, a segment measuring $x-3$ centimeters represents 14 meters. What is the value of $x$?

The North route had 3 deliveries with an average delivery time of 18 minutes. The South route had 2 deliveries with an average delivery time of 28 minutes. What was the mean delivery time, in minutes, for all 5 deliveries?

In the standard $(x,y)$ coordinate plane, which of the following is the vector from $A(2,-1)$ to $B(7,3)$?

The endpoints of a diameter of a circle are $A(-4,1)$ and $B(2,5)$, as shown below. Which of the following is an equation of the circle?

The function $p$ is defined by $p(x)=8x^2$. A second function is formed so that $q(x)=p(x-9)$. Compared with the graph of $y=p(x)$, the graph of $y=q(x)$ is:

A ball’s height, in meters, $t$ seconds after launch is $h(t)=-5t^2+20t+25$. How many seconds after launch does the ball reach the ground?

The table below classifies 140 commuters by travel method and arrival time. What is the probability that a randomly selected commuter traveled by train, given that the commuter arrived before 8 a.m.?

A vial has a capacity of $\dfrac{14}{15}$ liter and contains $\dfrac{7}{12}$ liter of solution. What fraction of the vial’s capacity is filled?

A 17-meter support cable runs from an anchor on level ground 8 meters from the base of a vertical wall to a point on the wall. What is the height, in meters, of that point above the ground?

Service A charges a $20 fee plus $4 per hour. Service B charges a $6 fee plus $6 per hour. After the same number of hours, the 2 services charge the same total amount. What is that total amount, in dollars?

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

How many lines of symmetry does a kite that is not a rhombus have?

In the standard $(x,y)$ coordinate plane, a point is at $(4,-1)$. The point is translated 6 coordinate units left and 3 coordinate units up, and the image is then reflected across the $y$-axis. What are the coordinates of the final image?

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 $\angle PQR$?

If $i=\sqrt{-1}$, which of the following is equivalent to $(4+2i)^2$?

The number line below shows the interval from 4 to 5 split into four equal parts by points $J$, $K$, and $L$. Which statement about $\sqrt{20}$ is true?

The 20 students in a class had a mean test score of 82. The 8 students in the morning section had a mean score of 88. What was the mean score of the other 12 students?

A sound wave travels at a speed of 1,100 feet per second. What is that speed, in miles per hour? (Note: 1 mile $=5{,}280$ feet)

When $x^3 - 2x^2 - 5x + 6$ is divided by $x - 1$, the quotient is:

The table gives values of $f(x)$, $g(x)$, and $h(x)$ for every $x$ in the domain $\{2,4,6,7,9\}$. If $a$ is in this domain and $h(f(g(a)))=2$, what is the value of $a$?

A trapezoid with parallel bases 6 and $x$ and height 10 is shaded inside a rectangle that is 14 units wide and 10 units high. A point is selected at random from the rectangle. The probability that the point is in the shaded region is $\dfrac{1}{2}$. What is the value of $x$?