Precalculus Review Units 4-6

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.

Front

How do you identify an ellipse in standard form?

Back

An ellipse in standard form is represented as (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the semi-major axis, and b is the semi-minor axis.

Front

What is the center of a circle given by the equation (x - h)² + (y - k)² = r²?

Back

The center of the circle is the point (h, k).

Front

What defines an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

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

Back

The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

How do you find the magnitude of a vector?

Back

The magnitude of a vector v = is found using the formula: ||v|| = √(x² + y²).

Front

What is the equation of a circle in polar coordinates?

Back

In polar coordinates, the equation of a circle centered at the origin with radius r is r = k, where k is the radius.

Front

What is the difference between a parabola and a hyperbola?

Back

A parabola is a conic section that opens either upward or downward, while a hyperbola consists of two separate curves that open away from each other.