ACT Quiz Prep 2

Question 1: You have large, medium, and small books in the ratio of 7:6:3 and you have a total of 32 books. How many small books do you have?

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5
6
7

Question 2: In the standard coordinate plane (x, y), what are the coordinates x₁ and y₁ of A, if A is the point in the first quadrant of the plane that is determined by the intersection of the y = 2x line and the x² + y² = 1 circle?

x₁ = 1/√5 and y₁ = 2/√5
x₁ = 1/√3 and y₁ = 2/√3
x₁ = 1/ and y₁ = 1
x₁ = √5 and y₁ = 2√5
x₁ = 2 and y₁ = 2

Question 3: What is the length of side b in the triangle below?

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5
6

Question 4: Celsius degrees can be transformed into Fahrenheit degrees by using the following formula: °C=(5/9) x (°F-32). What is the number x, if x degrees Celsius is equal to x degrees Fahrenheit?

-40
-60
-44
-32
-20

Question 5: A jar contains a nickel, a dime, and six quarters. Tom draws one coin from the jar, and then Mary draws a coin from those remaining. If the probability that Tom draws the nickel and Mary draws the dime is 1/x, what is the value of x?

50
56
60
1/50
1.56

Question 6: The parabola in the figure below is described by the equation: x² + bx + c = 0. Which of the following inequalities is true?

b > 0 and 4c < b²
b > 0 and 4c < b
b > 0 and 4c > b²
b < 0 and 4c < b²
b < 0 and c > 4b²

Question 7: What is m if the following system of equations has an infinity of solutions?
2x + 6y = 3
4x + 3my = 6

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5

Question 8: sin(x)cos(x)(1 + tan²(x)) =

tan(x) + 1
cos(x)
sin(x)
tan(x)
sin(x) + cos(x)

Question 9: What is the radius of the circle defined by the equation (x - 3)² + (y - 1)² = 81?

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9
12
18

Question 10: Segment DE is parallel to segment BC . AD = 6, AE = 4, BD = 9. What is the length of EC ?

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9

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