Search the California Content Standards

Cluster:
Perform arithmetic operations on polynomials. [Linear and quadratic]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

Standard:
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Cluster:
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

Standard:
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Cluster:
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

Standard:
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *

Cluster:
Perform arithmetic operations on polynomials. [Polynomials that simplify to quadratics]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Prove and apply trigonometric identities.

Standard:
Prove the Pythagorean identity sin^2(θ ) + cos^2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle.

Cluster:
Understand and apply theorems about circles.

Standard:
Prove that all circles are similar.

Cluster:
Understand and apply theorems about circles.

Standard:
Prove that all circles are similar.

Cluster:
Understand and apply theorems about circles.

Standard:
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Cluster:
Understand and apply theorems about circles.

Standard:
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.