ACT Exams- Math Easy 2 By Jane Eastwood | 1. If tan(x) = 5/13, then sin(x) = ? A) 5/29 B) 13/29 C) 5/13 D) 13/5 Answer: B Explanation: Use trig identity relationship between tan, sin and the given angle value. 2. An isosceles triangle has an area of 24 square units. If one of the angles is 60°, what is the length of one of the two congruent sides? A) 6 B) 8 C) 12 D) 4√3 Correct Answer: D Explanation: Use the formula for area of an equilateral triangle to back-solve for the side length. 3. Evaluate: lim_{x→0} (arcsin(3x) – 3x)/x A) 0 B) 1 C) 3 D) The limit does not exist. Correct Answer: B Explanation: Apply L’Hopital’s rule to evaluate the indeterminate form limit. 4. A bag contains 5 red balls and x blue balls. If selecting a ball at random, the probability of selecting a red ball is 2/7, what is the value of x? A) 7 B) 12 C) 14 D) 21 Correct Answer: D Explanation: Set up and solve the probability equation to find the value of x. 5. If (x+1)/(x-3) = (y-2)/(y+4), and x=1, then y= ? A) -3 B) -7 C) 3 D) 7 Correct Answer: A Explanation: Substitute x=1 into the equation and solve for y. 6. Evaluate the triple integral ∫∫∫_R xyz dV where R is the region bounded by the parabolic cylinder z = x^2 + y^2 and the planes z = 0 and z = 1. A) π/10 B) π/15 C) π/30 D) π/60 Correct Answer: C Explanation: Set up and evaluate the triple integral in cylindrical coordinates. 7. A circle is inscribed in an equilateral triangle with side length 8. What is the area of the circle? A) 8π B) 4√3π C) 12π/3 D) 12π Correct Answer: B Explanation: Use properties of an equilateral triangle and inscribed circle to relate the triangle altitude to the circle radius and find the area. Loading … Posted in Other