ParaPro Domain 2: Mathematics Welcome to your ParaPro Domain 2: Mathematics 1. ParaPro: Mathematics If \(x\) and \(y\) are integers such that \(2x + 3y = 12\) and \(x - y = 4\), what is the value of \(x\)? A. 2 B. 3 C. 6 D. 8 None 2. ParaPro: Mathematics A circle is inscribed in a square. The total area of the square that is not covered by the circle is 42 square units. What is the radius of the circle? A. 3.5 units B. 4.5 units C. 5.5 units D. 6.5 units None 3. ParaPro: Mathematics What is the sum of the interior angles of a polygon with 20 sides? A. 3240 degrees B. 3060 degrees C. 2880 degrees D. 3180 degrees None 4. ParaPro: Mathematics If the sequence \(a_n = 3^n - n^2\) for \(n \ge 1\), what is \(a_5\)? A. 212 B. 200 C. 243 D. 184 None 5. ParaPro: Mathematics What is the least common multiple (LCM) of 24, 36, and 48? A. 144 B. 288 C. 72 D. 432 None 6. ParaPro: Mathematics In a right triangle, one angle measures 25 degrees. What is the measure of the other non-right angle? A. 155 degrees B. 65 degrees C. 90 degrees D. 115 degrees None 7. ParaPro: Mathematics If the volume of a sphere is \(288\pi\) cubic units, what is the radius of the sphere? A. 6 units B. 4 units C. 8 units D. 12 units None 8. ParaPro: Mathematics A function \(f(x) = ax^2 + bx + c\) has a vertex at \((2, -3)\). If \(a = 1\), what is \(c\) when \(b = -4\)? A. -7 B. 1 C. -1 D. 5 None 9. ParaPro: Mathematics What is the coefficient of \(x^2\) in the expansion of \((x - 2)^4\)? A. -8 B. 6 C. -6 D. 8 None 10. ParaPro: Mathematics A ladder leans against a wall, reaching a height of 15 feet. If the bottom of the ladder is 5 feet from the wall, what is the length of the ladder? A. 15.81 feet B. 16 feet C. 17 feet D. 15 feet None 11. ParaPro: Mathematics What is the inverse function of \(f(x) = 3x - 7\)? A. \(f^{-1}(x) = \frac{x + 7}{3}\) B. \(f^{-1}(x) = \frac{x - 7}{3}\) C. \(f^{-1}(x) = 3x + 7\) D. \(f^{-1}(x) = \frac{3x - 7}{x}\) None 12. ParaPro: Mathematics If the prime factors of a number \(N\) are 2, 3, and 7, what is the smallest possible value of \(N\)? A. 42 B. 12 C. 21 D. 14 None 13. ParaPro: Mathematics A rectangular prism has a volume of 448 cubic units. If its length and width are in the ratio of 4:7 and its height is 8 units, what is the length of the prism? A. 8 units B. 14 units C. 4 units D. 7 units None 14. ParaPro: Mathematics If the ratio of the exterior angle to the interior angle of a regular polygon is 1:5, how many sides does the polygon have? A. 12 B. 6 C. 8 D. 10 None 15. ParaPro: Mathematics A complex number is given by \(3 + 4i\). What is the magnitude of this complex number? A. 5 B. 7 C. 9 D. 12 None 16. ParaPro: Mathematics What is the equation of the line perpendicular to \(y = \frac{1}{3}x - 7\) that passes through the point \((3, -4)\)? A. \(y = -3x + 5\) B. \(y = 3x - 13\) C. \(y = -3x - 5\) D. \(y = -3x + 1\) None 17. ParaPro: Mathematics If a binomial \(a + b\) is raised to the 5th power, what is the coefficient of the \(ab^4\) term in its expansion? A. 5 B. 10 C. 20 D. 40 None 18. ParaPro: Mathematics What is the range of the function \(f(x) = \frac{1}{x-2}\)? A. All real numbers except 0 B. All real numbers C. All real numbers except 2 D. All real numbers except 1 None 19. ParaPro: Mathematics The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure of the largest angle? A. 144 degrees B. 108 degrees C. 72 degrees D. 36 degrees None 20. ParaPro: Mathematics A sequence is defined by \(a_n = 2^n + n^2\). What is the 4th term of the sequence? A. 24 B. 20 C. 28 D. 32 None 21. ParaPro: Mathematics In the coordinate plane, what is the area of a triangle with vertices at \((1, 1)\), \((4, 1)\), and \((1, 4)\)? A. 4.5 square units B. 9 square units C. 6 square units D. 3 square units None 22. ParaPro: Mathematics A cylinder has a radius of 3 units and a height of 4 units. What is the volume of the cylinder? A. \(36\pi\) cubic units B. \(12\pi\) cubic units C. \(24\pi\) cubic units D. \(48\pi\) cubic units None 23. ParaPro: Mathematics The sum of an infinite geometric series is 20, and the first term is 12. What is the common ratio? A. 3-Jan B. 3-Feb C. -0.5 D. 2-Jan None 24. ParaPro: Mathematics A set of data has a mean of 50 and a standard deviation of 5. If one data point at 65 is removed, what is the new mean of the set? A. It remains 50 B. It decreases but cannot be determined exactly C. It increases but cannot be determined exactly D. It becomes 45 None 25. ParaPro: Mathematics If the ratio of the exterior angle to the interior angle of a regular polygon is 1:5, how many sides does the polygon have? A. 12 B. 6 C. 8 D. 10 None 26. ParaPro: Mathematics A complex number is given by \(3 + 4i\). What is the magnitude of this complex number? A. 5 B. 7 C. 9 D. 12 None 27. ParaPro: Mathematics If a binomial \(a + b\) is raised to the 5th power, what is the coefficient of the \(ab^4\) term in its expansion? A. 5 B. 10 C. 20 D. 40 None 28. ParaPro: Mathematics The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure of the largest angle? A. 144 degrees B. 108 degrees C. 72 degrees D. 36 degrees None 29. ParaPro: Mathematics A cylinder has a radius of 3 units and a height of 4 units. What is the volume of the cylinder? A. \(36\pi\) cubic units B. \(12\pi\) cubic units C. \(24\pi\) cubic units D. \(48\pi\) cubic units None 30. ParaPro: Mathematics The sum of an infinite geometric series is 20, and the first term is 12. What is the common ratio? A. 3-Jan B. 3-Feb C. -0.5 D. 2-Jan None 1 out of 30 Time is Up! Time's up
