Officer Aptitude Rating (OAR) Domain 1: Math Skills Test (MST) Welcome to your Officer Aptitude Rating (OAR) Domain 1: Math Skills Test (MST) 1. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If the sum of the interior angles of a polygon is four times the sum of its exterior angles, how many sides does the polygon have? A. 6 B. 8 C. 10 D. 12 None 2. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A cylindrical tank with a radius of 4 feet is filled with water to a depth of 3 feet. What is the volume of the water in the tank in cubic feet? A. 48 B. 64 C. 96 D. 128 None 3. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If the ratio of the speeds of two trains is 3:4 and the slower train travels at 90 mph, what is the speed of the faster train? A. 100 mph B. 110 mph C. 120 mph D. 130 mph None 4. Officer Aptitude Rating (OAR): Math Skills Test (MST)} Solve for \( x \) in the equation \( 2^{2x-3} = 32 \). A. 3 B. 4 C. 5 D. 6 None 5. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A circle is inscribed in a square. If the area of the square is 100 square units, what is the area of the circle? A. 50$\pi$ B. 64$\pi$ C. 75$\pi$ D. 78.5$\pi$ None 6. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If \( \log_a(5) = 0.5 \) and \( \log_a(7) = 0.7 \), what is \( \log_a(35) \)? A. 1 B. 1.2 C. 1.4 D. 1.5 None 7. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A train travels 60 miles in 2 hours and then 90 miles in 3 hours. What is its average speed for the entire journey? A. 30 mph B. 40 mph C. 50 mph D. 60 mph None 8. Officer Aptitude Rating (OAR): Math Skills Test (MST)} In a right triangle, if one angle measures 30 degrees and the hypotenuse is 10 units, what is the length of the side opposite the 30-degree angle? A. 5 B. 5$\sqrt{2}$ C. 5$\sqrt{3}$ D. 10 None 9. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If a rectangular prism has a length of 8 units, width of 5 units, and height of 4 units, what is the longest possible straight-line distance inside the prism? A. 9 units B. 10 units C. 11 units D. 17 units None 10. Officer Aptitude Rating (OAR): Math Skills Test (MST)} What is the sum of the series \( 4 + 12 + 20 + \ldots + 100 \)? A. 252 B. 504 C. 756 D. 1004 None 11. Officer Aptitude Rating (OAR): Math Skills Test (MST)} What is the remainder when \(2^{20}\) is divided by 17? A. 1 B. 2 C. 4 D. 16 None 12. Officer Aptitude Rating (OAR): Math Skills Test (MST)} In a sequence, each term after the first is obtained by adding 2 to the reciprocal of the preceding term. If the first term is 1, what is the third term? A. \( \frac{5}{3} \) B. \( \frac{7}{5} \) C. \( \frac{8}{5} \) D. \( \frac{11}{7} \) None 13. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If \(x\) is inversely proportional to \(y\), and \(x = 5\) when \(y = 3\), what is the value of \(x\) when \(y = 9\)? A. \( \frac{5}{3} \) B. \( \frac{3}{5} \) C. \( \frac{15}{9} \) D. \( \frac{9}{5} \) None 14. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A triangle has sides of length 7, 24, and 25. What is the radius of its inscribed circle? A. 3 B. 4 C. 5 D. 6 None 15. Officer Aptitude Rating (OAR): Math Skills Test (MST)} The function \(f(x) = x^2 - 4x + 3\) reaches its minimum value at \(x = k\). What is the value of \(k\)? A. 1 B. 2 C. 3 D. 4 None 16. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If \(3x - 2y = 12\) and \(4x + 3y = -9\), what is the value of \(x\)? A. -3 B. -1 C. 1 D. 3 None 17. Officer Aptitude Rating (OAR): Math Skills Test (MST)} In a geometric sequence, the first term is 3, and the fourth term is 24. What is the common ratio? A. 2 B. 3 C. 4 D. 5 None 18. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If \(x\) and \(y\) are integers such that \(x^2 - y^2 = 40\), what is the smallest possible value of \(x\)? A. 5 B. 6 C. 7 D. 8 None 19. Officer Aptitude Rating (OAR): Math Skills Test (MST)} What is the area of a trapezoid with bases of length 8 and 14 and height 6? A. 66 B. 72 C. 84 D. 132 None 20. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A clock shows a time of 3:15. What is the angle between the hour and the minute hands? A. 0 degrees B. 7.5 degrees C. 15 degrees D. 22.5 degrees None 21. Officer Aptitude Rating (OAR): Math Skills Test (MST)} What is the sum of all prime numbers less than 20? A. 41 B. 58 C. 77 D. 82 None 22. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A rectangle has a length that is twice its width. If the diagonal measures \(10\sqrt{2}\) units, what is the area of the rectangle? A. 50 units\(^2\) B. 100 units\(^2\) C. 150 units\(^2\) D. 200 units\(^2\) None 23. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If \(x\) satisfies the equation \(3^x + 3^{x+1} = 4 \times 3^x\), what is the value of \(x\)? A. 0 B. 1 C. 2 D. 3 None 24. Officer Aptitude Rating (OAR): Math Skills Test (MST)} What is the 15th term of the arithmetic sequence 3, 7, 11, ...? A. 57 B. 59 C. 61 D. 63 None 25. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A circle has a circumference of 31.4 units. What is the approximate area of the circle? A. 50 units\(^2\) B. 78 units\(^2\) C. 100 units\(^2\) D. 314 units\(^2\) None 26. Officer Aptitude Rating (OAR): Math Skills Test (MST)} In an isosceles triangle, the base angles are \(45^\circ\) each. What is the length of the base if the equal sides are 10 units each? A. 5 units B. \(5\sqrt{2}\) units C. 10 units D. \(10\sqrt{2}\) units None 27. Officer Aptitude Rating (OAR): Math Skills Test (MST)} What is the coefficient of \(x^2\) in the expansion of \((3x - 4)^3\)? A. -72 B. -36 C. 36 D. 72 None 28. Officer Aptitude Rating (OAR): Math Skills Test (MST)} If the probability of an event not occurring is 0.7, what is the probability of the event occurring? A. 0.1 B. 0.3 C. 0.5 D. 0.7 None 29. Officer Aptitude Rating (OAR): Math Skills Test (MST)} A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 8? A. \( \frac{1}{6} \) B. \( \frac{5}{36} \) C. \( \frac{1}{12} \) D. \( \frac{1}{9} \) None 30. Officer Aptitude Rating (OAR): Math Skills Test (MST)} In a sequence, each term after the first is obtained by adding 2 to the reciprocal of the preceding term. If the first term is 1, what is the third term? A. \( \frac{5}{3} \) B. \( \frac{7}{5} \) C. \( \frac{8}{5} \) D. \( \frac{11}{7} \) None 1 out of 30 Time is Up! Time's up
