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This high school math course builds upon advanced algebraic concepts covered in Algebra I and prepares students for advanced-level courses. Students extend their knowledge and understanding by solving open-ended problems and thinking critically. Topics include functions and their graphs; quadratic functions; complex numbers, and advanced polynomial functions. Students are introduced to rational, radical, exponential, and logarithmic functions; sequences and series; probability; statistics; and conic sections. Students work on additional challenging assignments, assessments, and research projects. This is the second semester of MTH304.
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This course builds upon algebraic concepts covered in Algebra I and prepares students for advanced-level courses. Students extend their knowledge and understanding by solving open-ended problems and thinking critically. Topics include functions and their graphs, quadratic functions, inverse functions, advanced polynomial functions, and conic sections. Students are introduced to rational, radical, exponential, and logarithmic functions; sequences and series; data analysis; and matrices. This is the second semester of MTH304.
This course includes all the topics in MTH303, but has more challenging assignments and includes more optional challenge activities. Each semester also includes an independent honors project. This course requires the use of a graphing calculator equivalent to a TI-84 and includes tutorials and activities for using a handheld graphing calculator.
In this unit, students review the order of operations, set definitions, properties of the real number system, and other symbols and terminology. Various strategies for solving linear and absolute value equations are introduced as are strategies for using formulas to solve real-world applications.
Representations and applications of linear relationships are the focus of this unit. Students interpret and create graphs, tables, and equations that represent linear relationships. In addition to simple linear equations, students also use systems of linear equations to solve real-world problems.
Students explore real-world situations regarding input and output, and learn how to graph equations and differentiate between functions and relations. Functions that are covered include some that are continuous, discontinuous, and discrete-valued. Step functions such as the least and greatest integer functions are introduced. Students learn to estimate and calculate domains and ranges of functions and to compose complicated functions from simpler ones. Students learn to express situations in function notation, calculate domains and ranges, and write sums, differences, products, quotients, and compositions of functions.
In this unit, students solve and graph linear inequalities in one variable including conjunctions, disjunctions, and absolute value inequalities. Students also solve and graph inequalities in two variables and systems of inequalities in two variables. They also use linear programming to solve real-world problems.
Students learn to identify, evaluate, graph, and write polynomial functions. They review adding, subtracting, and multiplying polynomials as well as algebraic factoring patterns. Students use these patterns and the zero product property to solve polynomial equations. Additionally, students graph power functions and identify the end behavior of various members of the power function graph family. Students also become familiar with the properties of even and odd functions.
Students learn to add, subtract, multiply, and divide rational expressions. Students learn to simplify compound fractions and solve rational equations. They also explore graphs and end behavior of rational functions including asymptotes and zeros.
Students learn to identify, add, subtract, multiply, and divide radicals, and to factor out perfect squares. Students solve real world problems involving applications of radical equations and convert between rational exponent and radical form of an expression. They learn to identify, graph, find the modulus of, add, subtract, multiply, and divide imaginary and complex numbers.
Students learn how to graph quadratic functions and identify the equations of quadratic functions when given a graph. Students also use the zero product property, completing the square, and the quadratic formula to solve quadratic equations. They explore the Quadratic Formula and how factors of quadratic polynomials relate to x-intercepts of graphs of quadratic functions. Applications include projectile motion, geometry, and other areas.
Students learn polynomial long division and the technique of synthetic division to divide polynomials. Additionally, they learn to apply the remainder theorem and they use the factor and rational roots theorems to factor polynomials over the real and complex numbers. Uses of graphs and technology for factoring polynomials and solving polynomial equations are also covered.
Students discover how exponential functions can be used to describe situations in the real world, such as exponential decay and growth. They define the logarithmic function in terms of its relationship with the exponential function and graph both exponential and logarithmic functions. Students learn to apply multiplication and division laws of exponents to exponential and logarithmic expressions and equations.
Students explore arithmetic and geometric sequences, learning the concept of series as a sum of terms in a sequence and finding sums of finite arithmetic and geometric series. Students also use and interpret sigma notation to describe sums. Throughout the unit, students use sequences and series to solve several types of real-world problems and use spreadsheets to calculate terms of sequences and series.
Students review counting principles including identifying and calculating permutations and combinations. They calculate probabilities of simple, dependent, independent, and binomial events. They also use probability to make predictions and relate the binomial theorem to Pascal's triangle.
Students learn about the measures of center: mode, median, and mean; and the measures of spread: range, variance, and standard deviation. They learn how to produce and interpret bar, box-and-whisker, and scatter plots. Students explore common sampling techniques and learn how to use the properties of normal distributions to compare values.
In this unit, students learn how to add, subtract, multiply, and determinants of matrices. Students also use matrices to solve systems of equations, transform figures, and solve real-world problems.
Students learn about conic sections that are points or lines and curved conic sections, including circles, ellipses, hyperbolas, and parabolas. They learn how to graph conic sections, how to use algebraic reasoning to create equations of conics when given descriptions or graphs, and how to solve real-world problems.
Courses with a teacher have designated start dates throughout Fall, Spring, and Summer. Full-year courses last 10 months and semester courses last 4 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.
To use this course, you'll need a computer with an Internet connection. Some courses require additional free software programs, which you can download from the Internet.
CPU: 1.8 GHz or faster processor (or equivalent)
RAM: 1GB of RAM
Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher
CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor
Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)
It is highly recommended that a broadband connection be used instead of dial up.
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Honors Algebra II, Part 1 (MTH304A)
Algebra II, Core Level, Part 2 (MTH302B)
Algebra II, Comprehensive Level, Part 2 (MTH303B)