ACT Mathematics OG Test 2 - questions 21-40

Question 7 If 5 times a number n is subtracted from 15, the result is negative. Which of the following gives the possible value(s) for n ?
Question 19 For every pair of natural numbers n and m, to which of the following sets must n + m belong?
Question 18 In the standard (x,y) coordinate plane below, the points (0,0), (10,0), (13,6), and (3,6) are the vertices of a parallelogram. What is the area, in square coordinate units, of the parallelogram?
Question 17 After visiting Florida State University during spring break, Francisco rents a car for 2 days to travel around Florida. He has $255 to spend on car rental for the 2 days. Sea Horse Car Rental charges $50 per day and $0.25 per mile. Ocean Blue Car Rental charges $60 per day and $0.20 per mile. Which company, if either, allows him to travel more miles for the 2 days, and how many miles more? (Note Taxes are already included in the rental charges.)
Question 16 Which of the following equations expresses c in terms of a for all real numbers a, b, and c such that a³ = b and b² = c ?
Question 15 A cargo ship is 4.2 miles from a lighthouse, and a fishing boat is 5.0 miles from the lighthouse, as shown below. The angle between the straight lines from the lighthouse to the 2 vessels is 5°. The approximate distance, in miles, from the cargo ship to the fishing boat is given by which of the following expressions? (Note The law of cosines states that for any triangle with vertices A, B, and C and the sides opposite those vertices with lengths a, b, and c, respectively, c²=a² + b² - 2abcosC. )
Question 11 The sign of a is positive. The sign of b is negative. If it can be determined, what is the sign of the mean of a and b?
Question 1 A park has the shape and dimensions in blocks givenbelow. A water fountain is located halfway between point B and point D. Which of the following is the location of the water fountain from point A ? (Note The park s borders run east-west or north­-south.)
Question 10 The figure below shows 2 tangent circles such that the 10-centimeter diameter of the smaller circle is equal to the radius of the larger circle. What is the area, in square centimeters, of the shaded region?
Question 9 The median of a set of data containing 9 items was found. Four data items were added to the set. Two of these items were greater than the original median, and the other 2 items were less than the original median. Which of the following statements must be true about the median of the new data set?
Question 8 For all x> 21, (x²+8x+7)(x-3)/(x² +4x-21)(x+1) = ?
Question 20 A certain perfect square has exactly 4 digits (that is, it is an integer between 1,000 and 9,999). The positive square root of the perfect square must have how many digits?
Question 3 f(x) = x² + x + 5 and g(x) = √x, then what is the value of g(4)/f(1) ?
Question 5 The scatterplot in the standard (x,y) coordinate plan below contains data points showing a strong linear correlation between the variables x and y. Mia drew the line shown to model the data. One of the following equations represents Mia s line. Which one?
Question 6 The temperature, t, in degrees Fahrenheit, in a certain town on a certain spring day satisfies the inequality |t -24|
Question 2 The braking distance; y feet, for Darnon s car to come to a complete stop . 1s modeled by y= 3(x²+10x)/40 , where x is the speed of the car in miles per hour. According to this model, which of the following is the maximum speed, in miles per hour, Damon can be driving so that the braking distance is less than or equal to 150 feet?
Question 4 At a school picnic, 1 junior and 1 senior will be selected to lead the activities. If there are 125 juniors and 100 seniors at the picnic, how many different 2-person combinations of 1 junior and 1 senior are possible?
Question 12 What is the y-coordinate for the point on the curve with x-coordinate 20 ?
Question 13 The length of this curve is longer than FG. About how many coordinate units long is FG?
Question 14 Tran wants to approximate the area underneath the curve y = 0.005x² - 2x + 200 for 0 <= x <= 200, shown shaded in the graph below.He finds an initial estimate, A, for the shaded area by using FG and computing A= (200 units)(200 units)/2= 20,000 square units The area of the shaded region is