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Academic Team Math Questions 1. Of 45, 60, 75, or 90 degrees, which one is a solution of the equation 2 sine 2x = 1? 2. The square of negative 3 is how much larger than the cube of negative 3? 3. What is the probability that a number chosen at random between 100 and 110 is a prime number? 4. Using the formula for the cosine of the sum of two angles, express cosine (90 + x) in simplified form. 5. If a = -2 and b = -3, find the numerical value of the sum of a squared and b all divided by b. 6. Find the sum of the roots for the following quadratic equation: 5x2 – 15x + 24 = 0 7. Solve the following equation for x: the square root of the quantity 3x plus 1 equals 1 plus square root of x. 8. Find the sine of the angle 3,660 9. What is the length of the longest chord of a circle whose area is 121PI square meters? 10. Find the quadratic equation whose roots are 5/2 and 5. 11. What is the distance between the x-intercept and the y-intercept of the equation 3x – 5y = 15? 12. A man standing 50 times the square root of 3 feet from the base of a building is looking at an angle of elevation 30 to the top of a 20-foot tower atop the building. How tall is the building? 13. If the radius of a circle is 6 centimeters and a sector of this circle has a central angle of 60, what is the perimeter of the sector? 14. If the y part of the solution to the system of equations 4x + 5y = 7 and –3x + 2y = 35 is 7, what is the sum of x and y? 15. If 2 complementary angles are in a 4 to 11 ratio, what is the degree measure of the larger angle? 16. If 100 percent of D is 40 percent of E, what percent of D is E? 17. What is 140 degrees expressed in radians? 18. Of the integers 2, 3, 5, and 7, which one NEVER divides the sum of 2 consecutive positive integers? 19. The curved shape of a rainbow is a subset of the graph of which one of the trigonometric functions? 20. Give the derivative with respect to x of sine x. 21. If f of x equals x3 – 6x + 1, what is f of 2? 22. What is the maximum possible area of a rectangle whose perimeter is 36 inches? 23. What is the quadratic equation in the form x2 + bx + c = 0 whose solutions are –3 and 8? 24. If the population of a city increases by 1% each year, how many years will it take for the population to double assuming that there is no decrease? 25. If you know that x = 1 + i times the square root of three is one of the complex roots of the equation x3 + 8 = 0, then what is the other complex root of this equation? Academic Team Math Answers 1. 75 degrees 2. 36 3. 4/9 4. Negative sine x 5. –1/3 6. 3 7. 0, 1 8. Square root of 3 over 2 9. 22 meters 10. 2x2 – 15x + 25 = 0 11. The square root of 34 12. 30 feet 13. 12 + 2PI centimeters 14. 0 66 16. 250 percent 17. 7/9 PI, or 7 PI/9 18. 2 19. sine 20. cosine x 21. –3 22. 81 square inches 23. x2 – 5x – 24 = 0 24. Approximately 70 years 25. 1 – i times the square root of three