# ACT Math Practice Test Pool 2

#### If Dave drove one-third of the distance of his trip on the first day, and 60 miles on the second day, he figured out that he still had 1/2 of the trip to drive. What was the total length, in miles, of his trip?

We can model this situation by the equation 1/3x + 60 = 1/2x . Solving for x, we get x=360 , which is answer A. a. Correct b. This is the number of miles he drove before he figured out how much of his trip was left. c. This amount is how much he drove the first day. d. This is how much he drove the second day. e. This amount is half of the distance he covered by the end of the second day.

#### 6b²-24b+24=? A) 6 (b-4) B) 6 (b-4) ² C) (6-b) ² D) 6 (b-2) ²

Choice D is correct Factor 6b2-24b+24=6(b2-4b+4) 6(b-2)2

#### If g(x) = 4x - 4x, what is the value of g(3/2)?

Substituting 3/2 into the function, we get 4(3/2) - 4(3/2) = 6 - 4(1/2)3 = 6 - 23 = 6 - 8 = -2. This is response A.

#### What is f(2) for the graph of f(x) below?

Asking for the value of f(2) is just a way of saying “what does y equal when x=2 ?” So you look for when x=2 . On the graph, we have the point (2,1/2) . Note that exact numbers are not provided in the graph, but standard practice indicates that each tick mark is one unit. So we moved 2 tick marks to the right, and then the line crosses through a point on the y axis between 0 and 1. Therefore, f(2) is equal to 1/2 . Choice B is the only possible choice.

#### The diagram below shows the number of people who purchased one, two, or all three of the ice cream flavors shown. If 15 people purchased strawberry ice cream, how many people purchased chocolate ice cream?

Choice (B) is correct. Since x lies within all three circles, x is the number of people who purchased all three flavors. Since 15 people purchased strawberry ice cream, it follows that 6+2+3+x=15 Solving this equation yields x=4. From the diagram, 2+2+4+x people purchased chocolate ice cream. Since x=4 it follows that 2+2+4+4=12 people purchased chocolate ice cream.

#### At Bruno’s Video World, the regular price for a DVD is d dollars. How many DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price?

Since you have x dollars to spend, you must divide x by the sale price of a CD, which is (100%-20%)d or 80%d . 80%d can be written as a fraction in lowest terms as 4/5d . Therefore, you are dividing x/(4/5d) = 5x/4d. This is answer E. a. This is the percent of the original price times x. b. This is the reciprocal of the sale fraction times x. c. This is the fraction of the original price, which represents the sale price. d. This comes from incorrectly handling the fraction in the denominator. e. Correct

#### In the triangle below, find the measure of angle X.

The sum of measures of a triangle is 180 degrees. Therefore, x + 88 + 43 = 180, or x = 49.

#### Which line has a slope of -3?

To find the slope of a line, the equation must be solved for y. The coefficient of x is the slope when the equation is solved for y. The only equation above that gives a coefficient for x of -3 is C.

#### Two sides of a triangle have sides 4 and 8. The length of the third side must be greater than_____ and less than____.

The third side of the triangle must be greater than the smallest side (4) and less than the sum of the two sides (4+8=12)

#### Which of the following is equivalent to x2 < -2x?

x2 < -2x => x2 + 2x < 0 => x(x + 2) < 0 => -2 < x < 0

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