Pre-ACT Mathematics Practice Test

A consultant charges $45 for each hour she works on a consultation, plus a flat $30 consulting fee. How many hours of work are included in a $210 bill for a consultation?

Vehicle A averages 14 miles per gallon of gasoline, and Vehicle B averages 36 miles per gallon of gasoline. At these rates, how many more gallons of gasoline does Vehicle A need than Vehicle B to make a 1,008-mile trip?

The expression (4z + 3)(z − 2) is equivalent to:

The figure below is composed of square BCDE and equilateral triangle ΔABE. The length of CD is 6 inches. What is the perimeter of ABCDE, in inches?

If 40% of a given number is 8, then what is 15% of the given number?

The 6 consecutive integers below add up to 447.

What is the value of x ?

In the standard (x, y) coordinate plane, point M with coordinates (5, 4) is the midpoint of AB , and B has coordinates (7,3). What are the coordinates of A ?

Given the triangle shown below with exterior angles that measure x°, y°, and z° as shown, what is the sum of x, y, and z ?

Which of the following is the slope of a line parallel to the line in the standard (x,y) coordinate plane?

The shipping rate for customers of Ship Quick consists of a fee per box and a price per pound for each box. The table below gives the fee and the price per pound for customers shipping boxes of various weights. Gregg wants Ship Quick to ship 1 box that weighs 15 pounds. What is the shipping rate for this box?

A computer chip 0.32 cm thick is made up of layers of silicon. If the top and bottom layers are each 0.03 cm thick and the inner layers are each 0.02 cm thick, how many inner layers are there?

The length of a rectangle with area 54 square centimeters is 9 centimeters. What is the perimeter of the rectangle, in centimeters?

This month, Kami sold 70 figurines in 2 sizes. The large figurines sold for $12 each, and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines.  How many large figurines did Kami sell this month?

To get a driver’s license, an applicant must pass a written test and a driving test. Past records show that 80% of the applicants pass the written test and 60% of those who have passed the written test pass the driving test. Based on these figures, how many applicants in a random group of 1,000 applicants would you expect to get driver’s licenses?

Last month, Lucie had total expenditures of $900. The pie chart below breaks down these expenditures by category. The category in which Lucie’s expenditures were greatest is what percent of her total expenditures, to the nearest 1% ?

What is the product of the complex numbers (−3i + 4) and (3i + 4) ?

The radius of the base of the right circular cone shown below is 5 inches, and the height of the cone is 7 inches. Solving which of the following equations gives the measure, θ, of the angle formed by a slant height of the cone and a radius?

A formula to estimate the monthly payment, p dollars, on a short-term loan is

where a dollars is the amount of the loan, r is the annual interest rate expressed as a decimal, and y years is the length of the loan. When a is multiplied by 2, what is the effect on ?

Marcus’s favorite casserole recipe requires 3 eggs and makes 6 servings. Marcus will modify the recipe by using 5 eggs and increasing all other ingredients in the recipe proportionally. What is the total number of servings the modified recipe will make?

The ABC Book Club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal?

In parallelogram ABCD below, AC is a diagonal, the measure of ∠ABC is 40°, and the measure of ∠ACD is 57°. What is the measure of ∠CAD?

In Cherokee County, the fine for speeding is $17 for each mile per hour the driver is traveling over the posted speed limit. In Cherokee County, Kirk was fined $221 for speeding on a roadwith a posted speed limit of 30 mph. Kirk wasfined for traveling at what speed, in miles per hour?

In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoints (3,8) and (1,−4) ?

The average of 5 distinct scores has the same value as the median of the 5 scores. The sum of the 5 scores is 420. What is the sum of the 4 scores that are NOT the median?

The fluctuation of water depth at a pier is shown in the figure below. One of the following values gives the positive difference, in feet, between the greatest water depth and the least water depth shown in this graph. Which value is it?

For which of the following conditions will the sum of integers m and n always be an odd integer?

A line through the origin and (10, 4) is shown in the standard (x, y) coordinate plane below. The acute angle between the line and the positive x-axis has measure θ. What is the value of tan θ ?

The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the value of the greater number minus the lesser number?

Two enterprising college students decide to start a business. They will make up and deliver helium balloon bouquets for special occasions. It will cost them $39.99 to buy a machine to fill the balloons with helium. They estimate that it will cost them $2.00 to buy the balloons, helium, and ribbons needed to make each balloon bouquet. Which of the following expressions could be used to model the total cost for producing b balloon bouquets?

Hexagon ABCDEF shown below was drawn on a grid with unit squares. Each vertex is at the intersection of 2 grid lines. What is the area of the hexagon, in square units?

What is the slope of the line through (–5, 2) and (6, 7) in the standard (x, y) coordinate plane?

Ms. Lewis plans to drive 900 miles to her vacation destination, driving an average of 50 miles per hour. How many miles per hour faster must she average, while driving, to reduce her total driving time by 3 hours?

Minh cuts a board in the shape of a regular hexagon and pounds in a nail at an equal distance from each vertex, as shown in the figure below. How many rubber bands will she need in order to stretch a different rubber band across every possible pair of nails?

A plastic cover is made for the pool. The cover will rest on the top of the pool and will include a wedge-shaped flap that forms a 45° angle at the center of the cover, as shown in the figure below. A zipper will go along 1 side of the wedge-shaped flap and around the arc. Which of the following is closest to the length, in feet, of the zipper?

The edges of a cube are each 3 inches long. What is the surface area, in square inches, of this cube?

For a project in Home Economics class, Kirk is making a tablecloth for a circular table 3 feet in diameter. The finished tablecloth needs to hang down 5 inches over the edge of the table all the way around. To finish the edge of the tablecloth, Kirk will fold under and sew down 1 inch of the material all around the edge. Kirk is going to use a single piece of rectangular fabric that is 60 inches wide. What is the shortest length of fabric, in inches, Kirk could use to make the tablecloth without putting any separate pieces of fabric together?