Search the California Content Standards

Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]

Standard:
Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Cluster:
Solve systems of equations. [Linear-quadratic systems]

Standard:
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.

Cluster:
Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

Standard:
Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.

Cluster:
Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

Standard:
Use the relation i^2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Cluster:
Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

Standard:
Solve quadratic equations with real coefficients that have complex solutions.

Cluster:
Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

Standard:
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

Cluster:
Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

Standard:
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. *