ACT Math April_2012

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ACT Math April_2012

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What is the value of x when 3 (x/2) + 16 = 10?

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A bowl contains 100 jelly beans, of which 42 are red, 36 are blue, and 22 are green. What is the probability that a jelly bean picked at random from the bowl will NOT be red?

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For what value of x is the equation 3.6x + 7.99 = 1.03 - 2.4x true?

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In the figure below, the measure of

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Which of the following numbers is a solution to x^2 -16=6x?

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|6-4| - |3-7| =?

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Dakota bought a pair of shoes that had an original price of $70.00. The store offered a 20% discount on the original price of the shoes, and Dakota paid 6% sales tax on the discounted price of the shoes. How much did Dakota pay for the shoes, including tax?

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What is the value of x^2 y^3 - xy^2 +x when x =-3 and y=2?

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A toy car travels at a constant rate of 11 inches every 5 seconds. At this rate, which of the following is closest : . to the number of feet the car travels in 2 minutes ?

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Dalia is taking inventory of cases of soda cans. There are 24 cans in a full case, and Dalia has 4 partially filled cases: 1 case is 1/2 full, 1 case is 2/3 full, and 2 cases are each 5/6 full. How many soda cans are in the 4 partially filled cases?

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Each side of a square is 3 cm long. One vertex of the square is at (6,4) on a square coordinate grid marked in centimeter units. Which of the following points on the grid could be another vertex of the square?

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Eduardo is making a cake with frosting. The recipe calls for 1/8 teaspoon of vanilla extract for the cake and 3/4 teaspoon of vanilla extract for the frosting. To make ‘2 cakes with frosting by doubling this recipe, how ; many teaspoons of vanilla extract does Eduardo need?

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In the standard (x,y) coordinate plane, what is the midpoint ofthe line segment with endpoints (1,9) and. (7,-3) ?

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In the plane shown in the figure below, lines m and n are cut by transversal line t. The 8 angles at the intersections of these lines are labeled. Which of the following statements, when it is true, CANNOT i always be used to prove that lines m and n are parallel?

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The dimensions of the right triangle shown below are in feet. What is the area, in square feet, of the triangle?

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If f(x) = x^2 - x + 1, what is f(-3) ?

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What is the length, in feet, of the side of a square whose area, in square feet, is equal to the area of a 25-foot-by-16-foot rectangle?

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The graph below shows the number of ski boats sold each month by Martin’s Marine Supply. The number near each point is the actual number of ski boats sold for the month corresponding with the point. The curve represents a model equation that comes close to fitting the actual numbers sold by month. One of the following is the value for September 2005 on the model curve. Which one?

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The graph below shows the number of ski boats sold each month by Martin’s Marine Supply. The number near each point is the actual number of ski boats sold for the month corresponding with the point. The curve represents a model ; equation that comes close to fitting the actual numbers sold by month. What is the average number of ski boats actually sold per month between and including the months of January 2006 and April 2006 ?

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The graph below shows the number of ski boats sold each month by Martin’s Marine Supply. The number near each point is the actual number of ski boats sold for the month corresponding with the point. The curve represents a model ; equation that comes close to fitting the actual numbers sold by month. During the period shown in the graph, each ski boat sold for exactly $30,000 before sales tax. On January 1, 2006, the sales tax was increased from 6% to 7%. How i much more was the total sales tax on the actual number | of ski boats sold in July 2006 than on the actual number sold in July 2005 ?

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For nonzero real numbers a, b, and c, the expression (a^5 b^3 c^4) / (5 a^2 b^7 c) is equivalent to:

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Akiko’s average heart rate is 70 beats per minute. In scientific notation, how many times would her heart beat in 24 hours?

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The lengths of the 3 sides of a triangle are in the ratio 5:6:9. The perimeter of the triangle is 100 inches. What is the length, in inches, of the longest side of the | triangle?

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Given that sin A = 20/25, which of the following values DO YOUR FIGURING HERE. could tan A equal?

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Which of the following sets of 3 numbers could be the i side lengths, in meters, of a right triangle?

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When graphed in the standard (x,y) coordinate plane, the line 2x + 3y - 1 = 0 has a slope of:

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Which of the following expressions is equivalent to (2x^2 + x43) + (2x + 1) + (3x - 1) - (2x + 2x + 2x)?

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Jason will have a rectangular concrete patio constructed f beside his house, as shown below. The patio will have a 4 length of 18 feet, and the top surface of the patio will have an area of 270 square feet. The patio will be constructed so that one side of the patio is against a side of Jason’s house. The patio will have a thickness of 6 inches. The patio will consist of how many cubic feet of concrete?

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Jason will have a rectangular concrete patio constructed f beside his house, as shown below. The patio will have a 4 length of 18 feet, and the top surface of the patio will have an area of 270 square feet. The patio will be constructed so that one side of the patio is against a side of Jason’s house. ason chooses Tully’s Concrete Finishing to seal his patio. Tully’s Concrete Finishing uses the formula C =3.5A + 120 to calculate the charge, C dollars, to a seal a patio, where A square feet is the area of the top surface of the patio. What will be the charge for sealing Jason’s patio?

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Jason will have a rectangular concrete patio constructed f beside his house, as shown below. The patio will have a 4 length of 18 feet, and the top surface of the patio will have an area of 270 square feet. The patio will be constructed so that one side of the patio is against a side of Jason’s house. Jason will plant shrubs along the portion of the Hy perimeter of the patio that is NOT against his house. y What is the length, in feet, of that portion?

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An airplane taking off from an airport climbs at a constant angle of ascent so that it will reach an altitude of 10,000 feet when the airplane has flown 8 miles, as illustrated in the figure below. Which of the following expressions gives the angle of ascent? (Note: 1 mile = 5,280 feet)

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Which of the following inequalities orders the 4 numbers √3, 1 (5/6), 1.6, and 5/3 from largest to smallest?

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What is the 7th term of the geometric sequence 1, -2, 4,-8, .... ?

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The hypotenuse of POM is PM. Which of the : following statements could be true about POM ?

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Let ABC and DFF be similar triangles such that the scale factor of ABC to DFF is = The perimeter of ABC is 20 inches. What is the perimeter of DEF, in inches?

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Planter’s Greenhouse estimates its profit by subtracting its overhead costs from 40% of its net sales. Which of the following equations represents this relationship between estimated profit (P), net sales (S), and overhead costs (C) of Planter’s Greenhouse?

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In right triangle POR shown below, OR is 450 feet long and the measure of

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Which of the following is equivalent to ((5+3x) / 2) - 3 > 0 ?

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Sofia and Lance are contributing a total of $2,500 per year to help their nephew pay for college. Each year, Lance contributes 1 (1/2) times the amount Sofia contributes. What is the amount, in dollars, Lance will contribute over a period of 4 years?

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Which of the following is the least common denominator for (1/(x^2 - 4)) + (1/(4x -8)) ?

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The circle shown below has a diameter of 6 cm, What is the area, in square centimeters, of the circle?

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Which of the following is an equation of the line that passes through (10,-2) and (-2,-5) in the standard (x,y) coordinate plane?

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A health club surveyed 175 members about which types of equipment they had used in the past month. Of the 175 members, 117 had used treadmills, 89 had used stationary bikes, and 53 had used both types of equipment, Some members had used neither type of equipment. Of the 175 members, how many had used treadmills, stationary bikes, or both?

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What is the largest 2-digit integer that is divisible by 7 and is a multiple of 3 ?

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In the standard (x,y) coordinate plane, the line y=1/4 x + 6 is perpendicular to the line:

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An emergency helicopter is located 2 miles north and 4 miles east of City Center. There is an emergency . 22 miles south and 6 miles west of City Center. Which of the following is the distance, in miles, between the helicopter and the emergency?

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The 3 statements given below are all true about certain positive integers x, y, and z. (1). x is an even prime number (2). 6

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The shaded region in the standard (x,y) coordinate DO YOUR FIGURING HERE. plane below is bounded by a parabola and a line. The shaded region and its boundary is the solution set of ; which of the following systems of inequalities?

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What is the value of y in the solution of the system of equations below? x+y=-a, x-y= b

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In the circle shown below, central angle

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The solution to ax=b is x=3. The solution to ax - 2 = b is x = 8. What is the value of a?

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Consider the equation x^2 - 6x + k = 0. When solved for x, this equation will have exactly one real solution for which of the following values of k ?

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In the distance that Molly pushed the wheelbarrow . shown below, the wheel rotated 3π/2 radians, The distance that Molly pushed the wheelbarrow is what fraction of the circumference of the wheel?

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The domain of the function f(x) = 1 / (100 - |x| ) contains all real values of x EXCEPT:

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In the figure below, E lies 3/5 of the way from B to C on rectangle ABCD. The area of AED is what fraction of the area of rectangle ABCD ?

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A right square pyramid with equilateral triangular faces is shown in the figure below. The slant height of the pyramid is 3√3 inches. What is the total length, in inches, of all 8 edges of the pyramid?

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A circle in the standard (x,y) coordinate plane intersects the x-axis at (-7,0) and (1,0). The radius of the circle is 5 coordinate units. Which of the following could be the center of the circle?

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What percent of the even numbers from 2 to 50, inclusive, have a units digit that is twice the tens digit?

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The graphs of f(x) and g(x) are shown in the standard (x,y) coordinate planes below. One of the following : expressions represents g(x) in terms of f(x), Which one?

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A news anchor made the true statement below. If it is raining, then the parade is canceled. Which of the following statements is logically equivalent to the news anchor’s statement?

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