Essay about Algebra: Real Number and Equations

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2012 Curricula Scope & Sequence

dition n er sio CCSS e v CC S S
Carnegie Learning® algebra ii promotes the understanding of both linear and non-linear functional forms, as well as the relationships between text, equations, graphs, and tables through the mathematical modeling of realistic situations. Our program motivates students to talk about mathematical functions, tackle real-world problems, strengthen their conceptual foundations, and understand algebra’s relevance in everyday life.
Textbook Chapter Cognitive Tutor® Software Unit
1. Linear Models and Four Quadrant Graphs 2. Linear Models in General Form 3. Graphs of Linear Equations in Two Variables 4. Absolute Value Equation and Inequalities 5. Relations and Functions 6. Linear Function Operations and Composition 7. Graphs of Functions 8. Inverses of Functions 9. Systems of Linear Equations Modeling, Part 2 10. Systems of Linear Equations 11. Graphs of Linear Inequalities in Two Variables 12. Systems of Linear Inequalities 13. 14. 15. 16. 3. Quadratic Functions
17. 18.

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Traditional Pathway: Algebra II

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Skills Covered
• • • • • • • • • • Solve linear equations in one variable. Solve linear inequalities in one variable and graph the solution on a number line. Represent linear functions using equations, tables, and graphs. Write an equation of a line in slope-intercept form, general form, and point-slope form. Transform a linear function. Solve absolute value equations and inequalities in one variable. Graph absolute value functions in two variables. Use function notation. Find the inverse of a linear function. Represent a piecewise function using equations, tables, and graphs.

1. Linear Functions, Equations and Functions

2. Systems of Linear Equations and Inequalities

• Determine the number of solutions of a linear system. • Solve linear systems graphically, using the substitution method, using the elimination method, and using Cramer’s Rule. • Determine consistency and dependence of linear systems. • Write and graph an inequality in two variables. • Write and graph a system of linear inequalities. • Solve a system of three linear equations in three unknowns. • Represent quadratic functions using equations, tables, and graphs. • Determine the key characteristics of the graph of a quadratic function including: domain, range, intercepts, vertex, line of symmetry, maximum or minimum, and concavity. • Solve quadratic equations using factoring method and the Quadratic Formula. • Transform a quadratic function. • Write an equation of a quadratic function in general form, vertex form, and factored form. • Multiply and factor polynomials. • Complete the square. • Use the discriminant to determine the number and type of roots. • Classify numbers as counting numbers, whole numbers, integers, rational numbers and irrational numbers. • Convert a repeating decimal to a fraction. • Identify and use properties of real numbers. • Convert between radical form and exponential form. • Simplify radicals using imaginary numbers. • Solve quadratic equations with complex solutions. • Add, subtract, multiply, and divide complex numbers. • Represent polynomial functions using equations, tables, and graphs. • Determine the key characteristics of the graph of a polynomial function including: domain, range, intercepts, extrema, intervals of increase and decrease, and end behavior. • Solve polynomial equations and inequalities graphically and by factoring. • Use the Fundamental Theorem of Algebra. • Add, subtract, and multiply polynomials. • Divide polynomials using long division and synthetic division. • Use the Remainder and Factor Theorems.

19. 20.

Quadratic Models in Factored Form Linear and Quadratic Transformations Quadratic Expression Factoring Quadratic Equation Solving using Factoring Forms of Quadratics Graphs and Equations of Quadratic Functions Quadratic Equation Solving Quadratic Models in General Form

4. The Real Number System
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