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.
California Standards for Algebra ll | Omega Math's Alignment to California Standards |
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1.0 Students solve equations and inequalities involving absolute value. | Algebra ll - 6.3 |
2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. | Algebra ll - Chapter 9 |
3.0 Students are adept at operations on polynomials, including long division. | Algebra ll - 2.2, 2.4, 2.5, 2.7 |
4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. | Algebra ll - Chapter 3 |
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. | Algebra ll - 6.2, 6.7 |
6.0 Students add, subtract, multiply, and divide complex numbers. | Algebra ll - 6.2 |
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. | Algebra ll - Chapter 4 |
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. | Algebra ll - 6.4 - 6.7, 8.5, 3.6 |
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. | Algebra ll - 8.5 |
10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. | Algebra ll - 8.5 |
11.0 Students prove simple laws of logarithms. | Algebra ll - 11.5 |
11.1Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. | Algebra ll - 11.1, 11.6 |
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. | Algebra ll - 11.6 |
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. | Algebra ll - 2.3, 5.4, Chapter 11 |
13.0 Students use the definition of logarithms to translate between logarithms in any base. | Algebra ll - 11.5 |
14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. | Algebra ll - 11.3 |
15.0 Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true. | Algebra ll - 4.1, 5.1, 11.6 |
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. | Algebra ll - 8.5(quadratic) |
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. | Chapter 8 |
18.0 Students use fundamental counting principles to compute combinations and permutations. | Algebra ll - 12.1, 12.2 |
19.0 Students use combinations and permutations to compute probabilities. | Algebra ll - 12.4, 12.5, 12.6 |
20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. | Algebra ll - 12.2 |
21.0 Students apply the method of mathematical induction to prove general statements about the positive integers. | Algebra ll - 12.2 |
22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. | Algebra ll - 12.2 |
23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. | Algebra ll - 12.2 |
24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. | Algebra ll - Chapter 10 |
25.0 Students use properties from number systems to justify steps in combining and simplifying functions. | Algebra ll - 10.3 |