Honors Algebra II |

Math |

Description: |

This course does little review of Algebra I topics so that the year may be spent working on the new topics of Algebra II. Those topics include matrices, quadratics, systems, as well as rational, polynomial, exponential, and logarithmic functions. |

Outcomes: |

Outcomes:
Students should be able to rewrite expressions involving radicals and rational exponents using the properties of exponents.
Students should be able to explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Students should be able to use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
Students should be able to know there is a complex number i^{2} = -1, and every complex number has the form a + bi with a and b real numbers. Students should use the relation i Students should be able to solve quadratic equations with real coefficients that have complex solutions.
Use matrices to represent and manipulate data. Multiply matrices by scalars to produce new matrices. Add, subtract, and multiply matrices of appropriate dimensions.
Students should be able to interpret the expressions that represent a quantity in terms of its context, interpret parts of an expression, such as terms, factors, and coefficients. They should also interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) Students should use the structure of an expression to identify ways to rewrite it. For example, see X
Students should factor a quadratic expression to reveal the zeros of the function it defines.
Students should be able to rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V=IR to highlight resistance R. Students should be able to explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Student should be able to construct a viable argument to justify a solution method.
Students should be able to solve simple rational and radical equations in one variable and give examples showing how extraneous solutions might arise. Students should solve linear equations and inequalities in one letter, including equations with coefficients represented by letters. Students should solve quadratic equations with one variable. Students should solve quadratic equations by inspection (e.g. for X
Students should be able to solve systems consisting of linear equations exactly and approximately (e.g. graphically) focusing on pairs of linear equations in two variable.
Students should understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Students should be able to explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x), find the solutions approximately, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Students should graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Students understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, the f(x) denotes t eh output of f corresponding to the input x. The graph of f is the graph of the equations y=f(x).
Students will use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Students will graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Students will graph linear and quadratic functions and show intercepts, maxima, and minima.
Students will combine standard function types using arithmetic operations. Students will compose functions. |