Circles of Confusion
If the diameter of a circle is √8, what is its area in simplest radical form?
2*[pai]
If sin θ = -3/5 and θ is in Quadrant III, what is the value of tan θ?
3/4
What is the axis of symmetry of the parabola y = -2x² + 8x - 5?
x = 2
If 2^x = 8, what is the value of x?
3
A chord of length 6 cm is 4 cm from the center of a circle. What is the radius of the circle?
5 cm
If cos θ = 1/3 and θ is in Quadrant IV, what is the exact value of sin(θ + π/2)?
-√8/3
Find the vertex of the parabola y = x² - 6x + 13.
(3, 4)
Solve for x: 3^(2x-1) = 27
2
The equation of a circle is x² + y² - 6x + 4y - 12 = 0. What is the radius of the circle?
4
In a right triangle, the hypotenuse is 10 and one angle is 30 degrees. What is the length of the side opposite the 30-degree angle?
5
The discriminant of a quadratic equation is -4. How many real roots does the equation have?
No real roots
If P(t) = 1000e^(0.05t) models a population after t years, what is the population after 10 years (rounded to the nearest whole number)?
Approximately 1284
A tangent line to a circle intersects the circle at point P. If the radius drawn to P has length 5 and the tangent segment has length 12, what is the distance from the center of the circle to the point of intersection of the tangent line and the radius extended?
13
If sin θ = 2/3, what is the value of cos 2θ?
-1/9
Find the sum of the roots of the equation 3x² - 5x + 2 = 0.
5/3
The half-life of a radioactive substance is 20 years. If you start with 100 grams, how many grams will remain after 40 years?
25 grams
Two circles intersect at points A and B. The radii of the circles are 5 and 8, respectively. The distance between the centers of the circles is 7. What is the length of the common chord AB?
6
Find the exact value of sin(7π/12).
(√6 + √2)/4
A rectangular garden is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. If 800 meters of fencing is available, what dimensions will maximize the garden's area?
100 meters by 200 meters
Solve the equation 4^x - 2^(x+2) + 3 = 0.
1