1.
In the quadrilateral ACGD, DF AC and AG BF. What is the value of d?
2.
For triangle EFG, what is the value of a?
3. A boat is anchored in a small lake with a rope that is 34 feet long. A wind blows the boat until the rope is taut and the water is 16 feet deep. Measuring across the bottom of the lake, how far has the boat moved from the anchor?
4. If a and b are real numbers and , then what must be true of the value of b?
5. In the figure below, 1 is parallel to 2, and 3 is parallel to 4. What is the value of b?
6. If 0° ⤠x ⤠90° and cos x = , then tan x = ?
7. In the figure, AD is a diameter of the circle with center O and AO = 5. What is the measure of arc BCD?
8. If sin θ = and cos θ = , then csc θ = ?
9. Triangle PQR is equilateral. Find the sum of a + b + c + d.
10. If is defined for all positive numbers a and b by ?
11. The measures of the lengths of the 3 sides of a triangle are prime numbers. If 2 of the sides are 5 and 23, how many different lengths are possible for the third side?
12. If a wheel on a stationary bike is 26 inches in diameter, and Mike pedals to make the wheel revolve 50 times, what would be the total distance that the wheel would travel if it weren't stationary?
13. What is the equivalent of (3i + 4)2?
14. Maureen wants to put an exercise wheel in her hamster's cage. The height of the cage is 22 inches, but there must be a 1-inch space above and below the wheel to allow for the wheel frame. What is the radius of the largest wheel that Maureen can place in the cage?
15. What is the sum of the first 15 multiples of 5?