ACT Math Prep

Elem.Algebra

100

Solve for x when 2x + 3 = 3x – 4? 

A. –7 B. - 1/5 C. 1 D. 1/5 E. 7

What is "E" 7?

200

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? A. l = w + 3 B. l = w – 3 C. l = 2w + 3 D. l = 2w – 3

What is D? (l=2w -3)

300

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

A. $ 44.44 B. $109.08 C. $118.80 D. $408.04 E. $444.40

What is "D" $408.04?

400

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

F. 4 G. 14 H. 16 J. 20 K. 50

What is "G" 14?

500

A DVD player with a list price of $100 is marked down 30%. If John gets an employee discount of 20% off the sale price, this is how much John pays for the DVD player. 

A. $86.00 B. $77.60 C. $56.00 D. $50.00 E. $44.00

What is "C", $56.00?

Pre-Algebra

100

The greatest common factor of 42, 126, and 210 ? F. 2 G. 6 H. 14 J. 21 K. 42

What is "K" 42?

200

The number of irrational numbers between 1 and 6 ? F. 1 G. 3 H. 4 J. 10 K. Infinitely many

What is "F" infinitely many?

300

An industrial cleaner is manufactured using only the 3 secret ingredients A, B, and C, which are mixed in the ratio of 2:3:5, respectively, by weight. This is how many pounds of secret ingredient B are in a 42-pound (net weight) bucket of this cleaner. A. 4.2 B. 12.6 C. 14.0 D. 18.0 E. 21.0

What is "B", 12.6?

400

This is the x-intercept of the graph of y = x2 – 4x + 4 . A. –2 B. –1 C. 0 D. 1 E. 2

What is "E", 2?

500

If h(x) = x³ + x and g(x) = 2x + 3, then g(h(2)) = ? F. 7 G. 10 H. 17 J. 19 K. 23

What is "K", 23?

Int. Algebra

100

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? A. 16 B. 17.5 C. 20.5 D. 22 E. 35

What is "A" 16?

200

This is a factor of the polynomial 2x2 – 3x – 5 . F. x – 1 G. 2x – 3 H. 2x – 5 J. 2x + 5 K. 3x + 5

What is "H", 2x - 5?

300

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, this is the maximum number of pounds of sugar to be consumed by each track team member in the coming year. A. 14 B. 44 C. 48 D. 54 E. 66

What is 54?

400

If xy = 144, x + y = 30, and x > y, this is the value of x – y ? F. 4 G. 6 H. 18 J. 22 K. 24

What is "H", 18?

500

The following statements must be true whenever n, a, b, and c are positive integers such that n < a, c > a, and b > c . A. a < n B. b – n > a – n C. b < n D. n + b = a + c E. 2n > a + b

What is "B", b - n > a - n?

Geometry

100

This is the degree measure of the acute angle formed by the hands of a 12-hour clock that reads exactly 1 o’clock. A. 15° B. 30° C. 45° D. 60° E. 72°

What is "B", 30 degrees?

200

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. This is the number of miles that the oil rig is from the departure point. F. 3 G. square root of 63 H. 15 J. 21 K. 225

What is "H", 15?

300

3.A circle has a circumference of 16 pi feet. What is the radius of the circle, in feet? A. square root of 8 B. 4 C. 8 D. 16 E. 32

What is "C", 8?

400

This is the sine of 90 degrees. A. 0 B. -1 C. 1 D. undefined.

What is "C", 1?

500

After arranging the flower bed, Taher decides that the flower bed would look more attractive if 1 of the angles in the triangle were a right angle. He decides to place the right angle at vertex A and to leave the lengths of AB and AC as 4 and 5 feet, respectively. To the nearest 0.1 foot, this is how long of a piece of lumber he would need to replace the 6-foot piece represented by BC . A. 3.0 B. 3.3 C. 6.0 D. 6.4 E. 7.8

What is "D", 6.4?

Coord. Geometry

100

This is the quadrant that the point (1,2) is located in. A. I B. II C. III D. IV

What is "A", I?

200

In the standard (x,y) coordinate plane, these are the coordinates of the midpoint of a line segment whose endpoints are (–3,0) and (7,4) . A. (2,2) B. (2,4) C. (5,2) D. (5,4) E. (5,5)

What is "A", (2,2)?

300

The following is an equation of the circle with its center at (0,0) that passes through (3,4) in the standard (x,y) coordinate plane? F. x – y = 1 G. x + y = 25 H. x2 + y = 25 J. x2 + y2 = 5 K. x2 + y2 = 25

What is "K", x2 + y2 = 25?

400

This is the distance from the origin to the coordinate point (1,1). A. 1 B. square root of 2 C. 2 D. square root of 3

What is "B", square root of 2?

500

Points A, B, C, and D are on a line such that B is between A and C, and C is between B and D. The distance from A to B is 6 units. The distance from B to C is twice the distance from A to B, and the distance from C to D is twice the distance from B to C. This is the distance, in units, from the midpoint of BC to the midpoint of CD . F. 18 G. 14 H. 12 J. 9 K. 6

What is "F", 18?