California State Standards for Advanced Algebra

1.0 Students solve equations and inequalities
involving absolute value.

2.0 Students solve systems of
linear equations and inequalities (in two or three variables) by substitution,
with

graphs, or with matrices.

graphs, or with matrices.

3.0 Students are adept at
operations on polynomials, including long division.

4.0 Students factor polynomials
representing the difference of squares, perfect square trinomials, and the
sum

and difference of two cubes.

and difference of two cubes.

5.0 Students demonstrate
knowledge of how real and complex numbers are related both arithmetically
and

graphically. In particular, they can plot complex numbers as points in the plane.

graphically. In particular, they can plot complex numbers as points in the plane.

6.0 Students add, subtract,
multiply, and divide complex numbers.

7.0 Students add, subtract,
multiply, divide, reduce, and evaluate rational expressions with monomial
and

polynomial denominators and simplify complicated rational expressions, including those with negative

exponents in the denominator.

polynomial denominators and simplify complicated rational expressions, including those with negative

exponents in the denominator.

8.0 Students solve and graph
quadratic equations by factoring, completing the square, or using the
quadratic

formula. Students apply these techniques in solving word problems. They also solve quadratic equations in

the complex number system.

formula. Students apply these techniques in solving word problems. They also solve quadratic equations in

the complex number system.

9.0 Students demonstrate and
explain the effect that changing a coefficient has on the graph of
quadratic

functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the

equation y = a (x - b)^2 +c.

functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the

equation y = a (x - b)^2 +c.

10.0 Students graph quadratic
functions and determine the maxima, minima, and zeros of the
function.

11.0 Students prove simple laws
of logarithms.

11.1 Students understand the
inverse relationship between exponents and logarithms and use this relationship
to

solve problems involving logarithms and exponents.

solve problems involving logarithms and exponents.

11.2 Students judge the validity
of an argument according to whether the properties of real numbers,
exponents,

and logarithms have been applied correctly at each step.

and logarithms have been applied correctly at each step.

12.0 Students know the laws of
fractional exponents, understand exponential functions, and use these
functions

in problems involving exponential growth and decay.

in problems involving exponential growth and decay.

13.0 Students use the definition
of logarithms to translate between logarithms in any base.

14.0 Students understand and use
the properties of logarithms to simplify logarithmic numeric expressions and
to

identify their approximate values.

identify their approximate values.

15.0 Students determine whether a
specific algebraic statement involving rational expressions, radical
expression,

or logarithmic or exponential functions is sometimes true, always true, or never true.

or logarithmic or exponential functions is sometimes true, always true, or never true.

16.0 Students demonstrate and
explain how the geometry of the graph of a conic section (e.g., asymptotes,
foci,

eccentricity) depends on the coefficients of the quadratic equation representing it.

eccentricity) depends on the coefficients of the quadratic equation representing it.

17.0 Given a quadratic equation
of the form ax^2 + by^2 + cx + dy + e = 0, students can use the method
for

completing the square to put the equation into standard form and can recognize whether the graph of the

equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.

completing the square to put the equation into standard form and can recognize whether the graph of the

equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.

18.0 Students use fundamental
counting principles to compute combinations and permutations.

19.0 Students use combinations
and permutations to compute probabilities.

20.0 Students know the binomial
theorem and use it the expand binomial expressions that are raised to
positive

integer powers.

integer powers.

21.0 Students apply the method of
mathematical induction to prove general statements about the
positive

integers.

integers.

22.0 Students find the general
term and the sums of arithmetic series and of both finite and infinite
geometric

series.

series.

23.0 Students derive the
summation formulas for arithmetic series and for both finite and infinite
geometric series.

24.0 Students solve problems
involving functional concepts, such as composition, defining the inverse
function

and performing arithmetic operations on functions.

and performing arithmetic operations on functions.

25.0 Students use properties from
number systems to justify steps in combining and simplifying
functions.