ACT Math Domain 2: Integrating Essential Skills

If the perimeter of a rectangular garden is 60 feet and the length is twice the width, what is the area of the garden?

A train travels from Station A to Station B at 60 mph and returns at 40 mph. What is the average speed for the round trip if both segments are the same distance?

A rectangle is three times as long as it is wide. If the length and width are both increased by 5 feet, the area becomes 100 square feet. What were the original dimensions?

If \(f(x) = 2x^2 - 3x + 5\) and \(g(x) = x - 2\), what is \(f(g(3))\)?

A cylindrical tank has a radius of 5 feet and is filled with water to a height of 12 feet. If the water is drained until the height of the water is 4 feet, what is the volume of water remaining in the tank?

A circular park with a radius of 30 feet is surrounded by a walkway of uniform width. If the total area of the park and walkway is four times the area of the park alone, what is the width of the walkway?

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the base of the wall, how high on the wall does the ladder reach?

If 8 workers can complete 6 tasks in 3 hours, how many hours would it take 4 workers to complete 9 tasks?

A square and a rectangle have the same perimeter. The rectangle's length is twice its width. If the side of the square is 10 units, what is the area of the rectangle?

A train leaves from City A to City B at a speed of 80 km/h. Two hours later, another train leaves from City B to City A on a parallel track at a speed of 100 km/h. If the distance between City A and City B is 720 km, how far from City A do the trains meet?

A rectangular field is three times as long as it is wide. If decreasing the width by 10 meters and increasing the length by 30 meters doubles the area, what was the original width?

If \(5^x \times 5^{x+2} = 5^{11}\), what is the value of \(x\)?

Two angles are supplementary. If one angle is 30 degrees less than four times the other, what is the measure of the larger angle?

A clock shows the time as 3:15. What is the angle between the hour and the minute hands?

A square and a circle have the same perimeter. If the side of the square is 10 units, what is the area of the circle?

A sequence is defined as \(a_n = n^2 + n - 1\). What is the fifth term of the sequence?

A cube has a volume of 64 cubic units. What is the surface area of the cube?

A train leaves from City A to City B at a speed of 80 km/h. Two hours later, another train leaves from City B to City A on a parallel track at a speed of 100 km/h. If the distance between City A and City B is 720 km, how far from City A do the trains meet?

Three numbers are in the ratio 3:4:5 and their sum is 60. What is the largest number?

In a right triangle, the lengths of the legs are 7 units and 24 units. What is the length of the hypotenuse?

If \(x\) and \(y\) are numbers such that \(x + y = 10\) and \(xy = 16\), what is \(x^2 + y^2\)?

A square and a rectangle have the same area. The rectangle's length is twice its width. If the side of the square is 12 units, what is the perimeter of the rectangle?

A container initially holds 10 gallons of water. Water is added at a rate of 2 gallons per minute, and at the same time, water leaks out at a rate of 0.5 gallons per minute. After 10 minutes, how many gallons of water are in the container?

A rectangle's length is decreased by 4 units and its width is increased by 3 units, resulting in no change to the area. If the original dimensions of the rectangle were 12 units by 5 units, what is the new length and width?

A clock shows the time as 8:20. What is the exact angle between the hour and the minute hands?

If a number is tripled and then decreased by 14, the result is 50. What was the original number?

The sum of three consecutive even numbers is 54. What are the numbers?

In a right triangle, one angle measures \(29^\circ\). What is the measure of the other non-right angle?

If a number is tripled and then decreased by 14, the result is 50. What was the original number?

A sequence is defined as \(a_n = n^2 + n - 1\). What is the fifth term of the sequence?