ACT: MATH

Pre-Algebra

100

A radio station offers free competitions. Normally, one in every twenty contestants wins the free competition. What is the probability of losing the free competition? A. 1/20 B. 1/19 C. 19/20 D. 19/1 E. 20/19

C. 19/20

200

A flight with a low-cost airline travels 9 ´ 103 miles per hour for 3 ´ 10-2 hours. How far has this cheap flight traveled? F. 135 miles G. 270 miles H. 900 miles J. 1350 miles K. 2700 miles

G. 270 miles

300

A company purchases cell phones at a cost of x and sells the cell phones at four times the cost. What equation below represents the profit made on each sell phone? A. x B. 3x C. 4x D. 3 - x E. 4 - x

B. 3x

400

| √4 - 12 | = ? F. -8 G. -10 H. 8 J. 10 K. 12

J. 10

500

In a shipment of 100 mp3 players, 1% are faulty. What is the ratio of non-faulty mp3 players to faulty mp3 players? A. 1: 100 B. 99: 100 C. 1: 99 D. 99: 1 E. 1: 499

D. 99: 1

Elementary Algebra

100

How many real solutions exist for the following equation: x2 + 8 = 0 (the 2 is squared) A. 0 B. 1 C. 2 D. 4 E. 8

A. 0

200

Which of the following equations is equal to √45? A. 1 ÷ 45 B. 5√9 C. 9√5 D. 3√5 E. 5√3

D. 3√5

300

An internet provider sells internet packages based on low monthly rates. The price for the internet service depends on the speed of the internet connection. The chart below indicates the prices of the various internet packages: Price in dollars (P) 10 20 30 40 Gigabyte speed (S) 2 4 6 8 Which equation represents the prices of these internet packages? A. P = (S - 5) ´ 5 B. P = (S + 5) x 5 C. P = 5 ÷ S D. P = S x 5 E. P = S ÷ 5

D. P = S x 5

400

Consider a class which has n students. In this class, t% of the students subscribe to digital TV packages. Which of the following equations represents the number of students who do NOT subscribe to any digital TV package? F. 100(n - t) G. (100 - t)n ÷ 100 H. (100 - t)n x 100 J. (1 - t)n K. n - t

G. (100 - t)n ÷ 100

500

What is the largest possible product of 2 even integers whose sum is 22? F. 11 G. 44 H. 100 J. 120 K. 144

J. 120

Intermediate Algebra

100

Consider the following matrices: A -1 4  3 -2 B -3 2 -2 8 What is A + B? F. 2 2 -10 10 G. 2 -2 10 -10 H. -4 6 1 6 I. 4 -6 1 -6 J. 4 6 1 6

H. -4 6 1 6

200

x and y are real numbers. ai and bi are imaginary numbers. When does ai + x = bi + y ? A. When a = b B. When x = y C. When a = x and b = y D. When a = y and b = x E. When a = b and x = y

E. When a = b and x = y

300

If f(x) = 5x-2 and g(x) = x^2 +3x, then what is the value of g(f(-3)) ? A. -340 B. -17 C. -2 D. 0 E. 238

E. 238

400

A company sells jeans and T-shirts. J represents jeans and T represents T-shirts in the equations below: 2J + T = $50 J + 2T = $40 Sarah buys one pair of jeans and one T-shirt. How much does she pay for her entire purchase? F. $10 G. $20 H. $30 J. $70 K. $90

H. $30

500

In the equations below, x represents the cost of one video game when renting video games online and y reporesents the cost of one movie ticket when purchasing discounted movie tickets online. If x - 2 > 5 and y = x - 2 Then the cost of 2 discounted movie tickets is greater than which one of the following? A. x - 2 B. x - 5 C. y + 5 D. 5 E. 10

E. 10

Coordinate Geometry

100

If a circle has a diameter of 12, what is the circumference of the circle? A. 6pi B. 12pi C. 24pi D. 36pi E. 144pi

B. 12pi

200

Consider a cone with a height of 12 inches and a radius at its base of 3 inches. What is the volume of this cone? F. 3pi G. 12pi H. 36pi J. 72pi K. 108pi

H. 36pi

300

Consider two stores in a town. The first store is a DVD rentals store. The second is a pizza place where customers collect their pizzas after they order pizza online. The DVD rentals store is represented by the coordinates (-4, 2) and the online pizza place is represented by the coordinates (2,-4). If the DVD rental store and the online pizza place are connected by a line segment, what is the midpoint of this line? F. (1, 1) G. (-1,-1) H. (2, 2) J. (-2,-2) K. (-3,-3)

G. (-1,-1)

400

If a circle with center (-6, 6) is tangent to the x axis in the standard (x, y) coordinate plane, what is the diameter of the circle? A. -6 B. -12 C. 6 D. 12 E. 36

D. 12

500

Marta has just bought a new pair of tennis shoes. She wants to wear the new running shoes to run up and down a hill near her house. The measurements of the hill can be placed on a two dimensional linear graph on which x = 5 and y = 165. If the line crosses the y axis at 15, what is the slope of this hill? A. 10 B. 20 C. 30 D. 36 E. 75

C. 30

Plane Geometry

100

A football field is 100 yards long and 30 yards wide. What is the area of the football field in square yards? F. 130 G. 150 H. 300 J. 1500 K. 3000

K. 3,000

200

A box is manufactured to contain either laptop computers or notebook computers. When the computer systems are removed from the box, it is reused to hold other items. If the length of the box is 20cm, the width is 15cm, and the height is 25cm, what is the volume of the box? A. 150 B. 300 C. 750 D. 7500 E. 15000

D. 7500

300

If one leg of a triangle is 5cm and the other leg is 12cm, what is the measurement of the hypotenuese of the triangle? A. 5√12cm B. 12√5cm C. √17cm D. 13cm E. 17cm

D. 13cm

400

A right triangle has a leg that is 4in long and the hypotenuse is 5in long. What is the area of the triangle? F. 4 G. 5 H. 6 J. 12 K. 20

H. 6

500

In an isosceles triangle, the vertex angle is 36°. What is the measure of one of its base angles? A. 36° B. 45° C. 72° D. 144° E. Cannot be determined from the information provided.

C. 72°