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# California Academic Content Standards

### Use the links below to find resources that support standards adopted by the California State Board of Education

for English-language arts, mathematics, history-social science, science, and visual and performing arts.

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California Academic Content Standards1641507 9317

Strand Algebra II60 142

- This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system.
- Substrand 1.0Students solve equations and inequalities involving absolute value.1 8
- Substrand 2.0Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.1 23
- Substrand 3.0Students are adept at operations on polynomials, including long division.1
- Substrand 4.0Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.1 1
- Substrand 5.0Students 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.1 4
- Substrand 6.0Students add, subtract, multiply, and divide complex numbers.1 3
- Substrand 7.0Students 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.1 9
- Substrand 8.0Students 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.1 10
- Substrand 9.0Students 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.1 22 - Substrand 10.0Students graph quadratic functions and determine the maxima, minima, and zeros of the function.1 23
- Substrand 11.0Students prove simple laws of logarithms.2 6
- Substrand 12.0Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.1 38
- Substrand 13.0Students use the definition of logarithms to translate between logarithms in any base.1 11
- Substrand 14.0Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.1 9
- Substrand 15.0Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.1 5
- Substrand 16.0Students 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.1 12
- Substrand 17.0Given 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.1 10 - Substrand 18.0Students use fundamental counting principles to compute combinations and permutations.1 12
- Substrand 19.0Students use combinations and permutations to compute probabilities.1 12
- Substrand 20.0Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.1 4
- Substrand 21.0Students apply the method of mathematical induction to prove general statements about the positive integers.1 1
- Substrand 22.0Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.1 15
- Substrand 23.0Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. 15
- Substrand 24.0Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.1 3
- Substrand 25.0Students use properties from number systems to justify steps in combining and simplifying functions.1 2