ACT Math Practice Test Pool 2

Question 1

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?

Accepted Answer

12

Answer

The Venn diagram shows the number of people who purchased different ice cream flavors. To find how many people purchased chocolate ice cream, sum the numbers within the chocolate circle. These are 1 (chocolate only), 4 (strawberry and chocolate), 6 (all three), and 1 (chocolate and vanilla). Adding these values gives 1 + 4 + 6 + 1 = 12 people who purchased chocolate ice cream.

Question 2

Which line has a slope of -3?

Accepted Answer

3x + y = 2

Answer

The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope. To find the slope of the given equations, rearrange them into this form. For option C, 3x + y = 2, subtract 3x from both sides to get y = -3x + 2. In this equation, the coefficient of x is -3, which is the slope. Therefore, the line 3x + y = 2 has a slope of -3.

Question 3

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

Accepted Answer

-2

Answer

The function is given as g(x) = 4x - 4^x. To find the value of g(3/2), substitute x = 3/2 into the function. This gives g(3/2) = 4(3/2) - 4^(3/2). First, calculate 4(3/2) = 6. Next, calculate 4^(3/2) = (√4)^3 = 2^3 = 8. Finally, subtract the second value from the first: 6 - 8 = -2.

Question 4

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?

Accepted Answer

5x/4d

Answer

The regular price for a DVD is 'd' dollars. With a 20% discount, the sale price per DVD is d - 0.20d = 0.80d. To find how many DVDs can be purchased for 'x' dollars, divide the total money 'x' by the sale price per DVD: x / (0.80d). Since 0.80 is equivalent to 4/5, this expression becomes x / (4/5 d). Dividing by a fraction is the same as multiplying by its reciprocal, so x * (5 / 4d) = 5x / 4d.

Question 5

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

Accepted Answer

49

Answer

The sum of the interior angles in any triangle is always 180 degrees. The diagram shows a triangle with two known angles: 88 degrees and 43 degrees. To find the measure of angle X, subtract the sum of these two angles from 180 degrees. First, add the known angles: 88 + 43 = 131 degrees. Then, subtract this sum from 180: X = 180 - 131 = 49 degrees.

ACT Practice Test

ACT Practice Test

ACT Math Practice Test Pool 2