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