ACT Math Prep

What is the largest value of x that solves the equation x ² - 4x +3 = 0

3

The largest value of x is found by factoring the quadratic equation, which gives the solutions x = 1 and x = 3. Therefore, the largest value is 3.

If the area of circle A is 16π then what is the circumference of circle B if its radius is ½ that of circle A ?

4π

The circumference of circle B is 4π

C = 2π r = 2π r(2) = 4π

In the word HAWKS, how many ways is it possible to rearrange the letters if none repeat and the letter W must go last?

24

There are 24 ways to rearrange the letters, as the first four letters can be arranged in 4! (24) ways while keeping W fixed at the end.

What is the slope of the line represented by the equation 10 x + 2 x = y + 6 ?

12

In triangle ABC below, the tan of the marked angle equals

¹² ⁄ ₅

Use the equation tangent = opposite / adjacent. Your first impulse here may be to solve for the unknown side, but take a close look at where the marked angle is. Its adjacent side is 5, meaning the tangent of that angle must have a denominator of 5. Only (D) has it, so it's the only answer that can work. If you do solve for the unknown side, remember your Pythagorean triples: this is a 5:12:13 triangle, so the unknown side must be 12.

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

$408.04

When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y ?

14

What is the value of x when 2x + 3 = 3x – 4 ?

7

What is the greatest common factor of 42, 126, and 210 ?

42

Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

16

In the figure below, ray EF was constructed starting from rays ED and EG. By using a compass D and G were marked equidistant from E on rays ED and EG. The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:

1. are equal.

2. are NOT equal.

3. sum to 30°.

4. sum to 45°.

5. sum to 60°.

are equal

Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of D²/25 + 4D – 250 gallons per minute, pumping out a mine that is 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?

1,250

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?

l = 2w – 3

In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?

110

How many irrational numbers are there between 1 and 6 ?

Infinitely Many

A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year. Assuming each track member had consumed sugar at the level of a typical high school student and will adhere to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track team member in the coming year?

54

In the standard (x,y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

(3,–7)

The lead of a screw is the distance that the screw advances in a straight line when the screw is turned 1 complete turn. If a screw is 2 inches long and has a lead of inch, how many complete turns would get it all the way into a piece of wood?

If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

Which of the following is the sine of angle A in the right triangle below?

The volume, V, of the right circular cone with radius r and height h, shown below, can be found using the formula V =  r ²h. A cone-shaped paper cup has a volume of 142 cubic centimeters and a height of 8.5 centimeters. What is the radius, to the nearest centimeter, of the paper cup?

A boat departs Port Isabelle, Texas, traveling to an oil rig. The oil rig is located 9 miles east and 12 miles north of the boat’s departure point. About how many miles is the oil rig from the departure point?

In the figure below, ∠ ABC ≅ ∠ DFE, ∠ BAC ≅ ∠ FDE, D and F are on AB, AD ≅ FB, and distances in centimeters are as shown. What is the length of AD, in centimeters?

Which of the following is a factor of the polynomial 2x2 – 3x – 5 ?