Final exam review

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

How do you determine if a hyperbola is vertical or horizontal?

Back

A hyperbola is vertical if its equation is of the form (y-k)²/a² - (x-h)²/b² = 1. It is horizontal if it is of the form (x-h)²/a² - (y-k)²/b² = 1.

Front

What are the characteristics of an ellipse?

Back

An ellipse has two foci, a major axis, a minor axis, and the sum of the distances from any point on the ellipse to the two foci is constant.

Front

What is the sine of 7π/6?

Back

-1/2

Front

What defines a hyperbola?

Back

A hyperbola is defined as the set of all points where the absolute difference of the distances to two fixed points (foci) is constant.

Front

What is the general form of a conic section?

Back

The general form is Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, and C are not all zero.

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the two foci coincide, and the distance from the center to any point on the circle is constant.

Front

What is the formula for the area of an ellipse?

Back

Area = π * a * b, where a is the semi-major axis and b is the semi-minor axis.

Front

How do you find the vertex of a parabola given its equation?

Back

For a parabola in the form y = ax² + bx + c, the vertex can be found at x = -b/(2a).

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, the sum of the angles is 180 degrees, and one angle is always 90 degrees.