Search the California Content Standards

Cluster:
Investigate patterns of association in bivariate data.

Standard:
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Cluster:
Interpret the structure of expressions. [Quadratic and exponential]

Standard:
Interpret expressions that represent a quantity in terms of its context. * Interpret parts of an expression, such as terms, factors, and coefficients. *

Cluster:
Interpret the structure of expressions. [Quadratic and exponential]

Standard:
Interpret expressions that represent a quantity in terms of its context. * Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and a factor not depending on P. *

Cluster:
Interpret the structure of expressions. [Quadratic and exponential]

Standard:
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).

Cluster:
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines.*

Cluster:
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*

Cluster:
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.*

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:
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.