School Year 2008-2009

Instructor: Mrs. Armstrong

Room: 130

Course Syllabus

Prerequisite: Successful completion of Geometry-234 and/or Informal Geometry-233. Permission of the Department Chairperson and/or instructor required. Signature required.

Textbook: Holliday, Marks, Cuevas, Casey, Moore-Harris, Day, Carter, Hayek.

Algebra 1. Columbus, Ohio: Glencoe/McGraw-Hill. 2005.

Course Description: This course is a continuation of Algebra I including trigonometry and applications in science using numerical, graphical and analytical approach. The emphasis is on relationships among quantities, ways of representing mathematical relationships, and the analysis of change. Students will concentrate on understanding relations and functions, selecting, converting flexibly among, and using various representations. Students will enlarge their repertoire of functions and learn about the characteristics of classes of functions; they will identify essential quantitative relationships in a situation and determine the class of functions that might model the relationships. Students will become proficient in performing manipulation of symbols in expressions, equations, and inequalities as well as the algebraic properties that underlie the symbol manipulation. Students are evaluated and assessed on individual performance in the following areas: assignments, quizzes, projects and tests. Students will be using a TI-83 plus or TI-84 plus graphing calculator.

Format: Class meetings will include lectures, projects, critical-thinking writing assignments, class work, homework, and calculator/computer activities.

Evaluation and Assessment: Grades are computed based on the following ratio:

Points earned / Total points possible

Students are expected to review material daily.
Students are expected to do their homework but will not be collected. We will go over the homework daily.
Students are expected to do their assignments by themselves unless otherwise indicated by Mrs. Armstrong.
Students are expected to participate either through volunteering or being called upon by Mrs. Armstrong.
Quizzes may or may not be announced.
Assessment will be any of the following formats: short answer, multiple choice, essays, true/false, matching, and/or problem solving.
Students are expected to show their work. Without showing proper work, full credit will not be given.
Students may be asked to orally present a problem, a topic or a chapter.
Class work will be graded.

Standard: Number, Number Sense and Operations Standard

Benchmark:

Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative.
Determine what properties hold for vector addition and multiplication, and for scalar multiplication.
Represent complex numbers on the complex plane.
Use matrices to represent given information in a problem situation.
Model, using the coordinate plane, vector addition and scalar multiplication.
Compute sums, differences and products of matrices using paper and pencil calculations for simple cases, and technology for more complicated cases.
Compute sums, differences, products and quotients of complex numbers.
Use fractional and negative exponents as optional ways of representing and finding solutions for problem situations; e.g., 272/3 _ (271/3)2 _ 9.
Use vector addition and scalar multiplication to solve problems.

Standard: Measurement Standard

Benchmark:

Determine the number of significant digits in a measurement.
Use radian and degree angle measures to solve problems and perform

conversions as needed.

Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base.
Calculate distances, areas, surface areas and volumes of composites three-dimensional objects
Solve real-world problems involving area, surface area, volume and density to a specified degree of precision.

Standard: Geometry and Spatial Sense Standard

Benchmark:

Use polar coordinates to specify locations on a plane.
Represent translations using vectors.
Describe multiplication of a vector and a scalar graphically and algebraically, and apply to problem situations.
Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines.
Identify, sketch and classify the cross sections of three-dimensional objects.

Standard: Patterns, Functions and Algebra Standard

Benchmark:

Identify and describe problem situations involving an iterative process that can be represented as a recursive function; e.g., compound interest.
Translate a recursive function into a closed form expression or formula for the nth term to solve a problem situation involving an iterative process; e.g., find the value of an annuity after 7 years.
Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior.
Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology.
Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y =x.
Represent the inverse of a function symbolically and graphically as a reflection about y = x.
Model and solve problems with matrices and vectors.
Solve equations involving radical expressions and complex roots.
Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution).
Describe the characteristics of the graphs of conic sections.
Describe how a change in the value of a constant in an exponential, logarithmic or radical equation affects the graph of the equation.

Standard: Data Analysis and Probability Standard

Benchmark:

Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation.
Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each.
Describe how a linear transformation of univariate data affects range, mean, mode and median.
Create a scatter plot of bivariate data, identify trends, and find a function to model the data.
Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation.
Use technology to compute the standard deviation for a set of data, and interpret standard deviation in relation to the context or problem situation.
Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal.
Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions.
Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques.
Understand and use the concept of random variable, and compute and interpret the expected value for a random variable in simple cases.
Examine statements and decisions involving risk; e.g., insurance rates and medical decisions

The following topics will be covered in Algebra II Trig but not limited to the following: Please note that this is a tentative schedule.

Quarter 1:

Expressions and formulas, properties of Real Numbers, solve equations: including Absolute value and Compound and inequalities, relations and functions, linear equations, slope write linear equations, model Real-World data: scatter plots, special functions, graph inequalities, systems of equations, introduction to matrices, operations with matrices

Quarter 2:

Multiply matrices, transform matrices, determinants, Cramer’s rule, Identity and Inverse Matrices, solve system using matrices, monomials, polynomials, dividing polynomials, factoring, roots, radical expressions and equations, rational exponents, complex numbers, quadratics

Quarter 3:

Polynomial functions, solve equations, remainder and factor theorem, roots and zeros, rational root theorem, operations and functions, inverse functions and relations, square root functions, conics, distance and midpoint, operations on rational expressions, direct/joint/inverse variation

Quarter 4:

Exponential functions, log, properties of log, log base e, natural log, exponential growth and decay, sequences and series, binomial theorem, right triangle trig, trig functions, law of sine and cosine, circular functions, inverse trig functions, graph trig functions, trig identities, sum and difference formulas, double and half angle formulas, solve trig equations