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Algebra II Benchmarks |
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*These Benchmarks were revised in July 2010. References in black are to the 2001 SOL. References in red are to the 2009 SOL. A Guide for Parent Involvement
Note: Chapters referenced are from the adopted text, Glencoe: Algebra 2. These benchmarks apply to both the single and double blocked courses.
1st Nine Weeks Chapter 1: Analyzing Equations and Inequalities (All Sections) Related SOLs: AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices. AII.4 The student will solve absolute value equations and inequalities graphically and algebraically. Graphing calculators will be used both as a primary method of solution and to verify algebraic solutions. AII.10 The student will investigate and describe through the use of graphs the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression. Chapter 2: Graphing Linear Relations and Functions (All Sections) Related SOLs: AII.8 The student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a graph, a table, and symbolic form. A transformational approach to graphing will be employed through the use of graphing calculators. AII.9 The student will find the domain, range, zeros, and inverse of a function; the value of a function for a given element in its domain; and the composition of multiple functions. Functions will include exponential, logarithmic, and those that have domains and ranges that are limited and/or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions. AII.13 The student will solve practical problems, using systems of linear inequalities and linear programming, and describe the results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems. AII.19 The student will collect and analyze data to make predictions and solve practical problems. Graphing calculators will be used to investigate scatterplots to determine the equation for a curve of best fit. Models will include linear, quadratic, exponential, and logarithmic functions. Chapter 3: Solving Systems of Linear Equations and Inequalities (All Sections) Related SOLs: AII.12 The student will represent problem situations with a system of linear equations and solve the system using the inverse matrix method. Graphing calculators or computer programs with matrix capability will be used to perform computations. AII.13 (See above) 2nd Nine Weeks Chapter 4: Using Matrices (All Sections) Related SOLs: AII.1 (See above) AII.11 The student will use matrix multiplication to solve practical problems. Graphing calculators or computer programs with matrix capabilities will be used to find the product. AII.12 (See above) Chapter 5: Exploring Polynomials and Radical Expressions (All Sections) Related SOLs: AII.1 (See above) AII.2 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. AII.3 The student will * add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents; and * write radical expressions as expressions containing rational exponents, and vice versa. AII.5 The student will identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials. AII.7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and confirming algebraic solutions. AII.17 The student will perform operations on complex numbers and express the results in simplest form. Simplifying results will involve using patterns of the powers of i. Chapter 9: Exploring Rational Expressions (All Sections) Related SOLs: AII.7 (See above) AII.20 The student will identify, create, and solve practical problems involving inverse variation and a combination of direct and inverse variations.
3rd Nine Weeks
Chapter 6: Exploring Quadratic Functions and Inequalities (6.1-6.6) Related SOLs: AII.5 (See above) AII.6 The student will select, justify, and apply a technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and confirming algebraic solutions. AII.7,8,9,10,18,19 (See above)
Chapter 7: Exploring Polynomial Functions (All Sections) Related SOLs: AII.5,7,8,9,10 (See above) AII.15 The student will recognize the general shape of polynomial, exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of polynomial functions. Chapter 10: Exploring Exponential and Logarithmic Functions (10.1-10.2) Related SOLs: AII.9,19 (See above)
4th Nine Weeks
Chapter 8: Conic Sections (All Sections) Related SOLs: AII.14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions. AII.18 The student will identify conic sections (circle, ellipse, parabola, and hyperbola) from his/her equations. Given the equations in (h, k) form, students will sketch graphs of conic sections, using transformations. Chapter 11: Investigating Sequences and Series (11.1-11.5, 11.6) Related SOL: AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include sigma and 'a sub n'. Chapter 12: Probability and Statistics (12.2, 12.3, 12.6, 12.7) + supplementary material on standard deviation, mean, and z-scores. Review for SOL Test |