High School Math Curriculum

Precalc

Course Description:

This course is an extension of Algebra 2 covering the topics in greater depth.  It also includes different topics to ensure a smooth transition into Calculus.

Units:

  • Functions
  • Polynomials and Rational Functions
  • Exponential and Logarithmic Functions
  • Trigonometric Functions Real Numbers/Angles
  • Analytic Trigonometry
  • Analytic Geometry
  • Polar Coordinates and Vectors
  • Finding Limits

Skills and Understandings:

  • Students will be able to identify functions and their families
  • Students will be able to recognize and follow patterns learned in previous mathematics courses and apply them to more sophisticated problems
  • Students will be able to graph functions and to interpret them by general shape, and their intercepts.
  • Students will be able to analyze rational expressions by looking at their behavior, and finding asymptotes.
  • Students will be able to analyze trigonometry in terms of radians and the last of the 6 trigonometric functions.
  • Students will be able to recognize that logarithms are exponents and behave as such.
  • Students will be able to model real world phenomena using linear, quadratic, or cubic functions.

This course upholds the KAS Mission Statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Allowing students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.

 

Algebra II

Course Description:

This course is an extension of Algebra I with topics reinforced at a greater depth. The goals of this course are to advance students’ understanding of algebraic concepts and to fully prepare them for Pre-Calculus.

Units:

  • Functions – Linear, quadratic, exponential, logarithmic, polynomial, periodic
  • Modeling with functions
  • Trigonometry
  • Linear Systems
  • Complex Numbers
  • Analytic Geometry
  • Limits

Skills and Understandings:

  • Students will understand exponents (fractional, negative)
  • Students will understand equations of lines and how they can be transformed
  • Students will be able to solve equations for the required variable
  • Students will understand functions, what they are and how to transform them.
  • Students will be able to solve quadratic equations by factorizing, completing the square and the quadratic formula
  • Students will understand even and odd functions and their ends
  • Students will be able to find the composition of functions
  • Students will be able to find the inverse of functions
  • Students will be able to divide polynomials and find all the zeros
  • Students will be able to model real life phenomena using linear, quadratic and cubic models

This course upholds the KAS Mission Statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Allowing students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.

 

Geometry

Course Description:

This standard first course in Geometry covers the required concepts of Euclidean Geometry.  Emphasis is on deductive and inductive reasoning, basic right angle trigonometry, realizing that geometry and algebra are not separate courses, and answering the question: “How do you know?”

 

Units:

  • Foundations of Geometry
  • Geometric Reasoning
  • Parallel and Perpendicular Lines
  • Triangle Congruence
  • Properties and Attributes of Triangles including Special Right Triangles
  • Polygons and Quadrilaterals
  • Similarity
  • Right Triangle Trigonometry
  • Transformational Geometry
  • Circles

Skill and Understandings:

  • Students will be able to use deductive reasoning to prove basic theorems
  • Students will learn sever different types of problem solving strategies (including drawing diagrams, looking for patterns, working backwards from conclusion to hypothesis, etc.)
  • Students will be able to define and use parallel lines, angles and angle measures, quadrilaterals, convex polygons.
  • Students will be able to prove triangles congruent
  • Students will be able to use prove similarity/use scale factors and understand proportion/scale drawing.
  • Students will be able to use the Pythagorean theorem to find the lengths of the sides of fight triangles, and carry on to right angle trigonometry.
  • Students will be able to use coordinate geometry to prove diagonals perpendicular, segments equal, and segments parallel.
  • Students will be able to use transformations in the coordinate plane and to describe movement in the plane as transformations.

This course upholds the KAS Mission statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Allowing students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.

 

Business Math

Course Description:

Business Mathematics maximizes student interest through real-world applications. The key concepts covered include bank services, payroll, business discounts and markups, simple and compound interest, stocks and bonds, consumer loans, taxes and insurance, depreciation, financial statements, and business statistics.

Units:

  • Whole Numbers and Decimals
  • Fractions
  • Percent
  • Bank Services
  • Payroll
  • Mathematics of Buying
  • Mathematics of Selling
  • Simple Interest
  • Compound Interest
  • Annuities, Stocks, and Bonds
  • Business and Consumer Loans
  • Taxes and Insurance
  • Depreciation
  • Financial Statements and Ratios
  • Business Statistics

Skill and Understandings:

  • Students will understand and recall skills for whole numbers and decimals.
  • Students will understand the use and the relationship between whole numbers, decimals, fractions, and percent.
  • Students will understand bank services and payroll
  • Students will understand the mathematical concepts of buying and selling.
  • Students will understand simple and compound interest.
  • Students will understand the basics of the stock market and bonds.
  • Students will understand the basics of statistics.

This course upholds the KAS Mission statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Awarding students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations.
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.

 

Consumer Math

Course Description:

This course provides students with key math concepts essential for successful adult living. From buying groceries to budgeting for housing, education, and travel. Students gain practical math competence through real-world examples in the areas of money management, banking, credit-card math, career choices, consumerism, jobs, and everyday living.

Units:

  • On Your Own
  • Making and Changing Your Budget
  • Banking and Saving
  • Cash or Credit
  • Selecting Housing
  • Buying and Preparing Food
  • Buying Personal Items
  • Owning a Vehicle
  • Recreation, Travel, and Entertainment

Skill and Understandings:

  • Students will understand and recall skills and concepts used to distinguish the importance between wants and needs.
  • Students will understand methods used to make and maintain a budget.
  • Students will understand the needs and requirements of a savings account.
  • Students will understand the uses and benefits of using cash and credit.
  • Students will understand the importance of selecting housing.

This course upholds the KAS Mission statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Awarding students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations.
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.

 

Statistics

Course Description:

The goals of this course are to advance students’ understanding of the concepts of Statistics. The topics to be covered will include: graphing, distributions, statistical relationships, probability, random variables, and testing a claim. The required text is The Practice of Statistics (3rd Edition) by Yates, Moore, and Starnes.  Students are expected to come to class prepared with a notebook, pencil, eraser and a TI83 or TI84 calculator.

Units:

  • Exploring Data
  • Describing location in a distribution
  • Relationships between two variables.
  • Producing data
  • Least-Square Regression Lines
  • Statistical Probability
  • Sampling distributions
  • Transforming to Achieve Linearity

Skill and Understandings:

  • Students will be able to display distributions with graphs.
  • Students will understand normal distributions.
  • Students will understand and use standard deviations.
  • Students will be able to use mean, median, and mode.
  • Students will be able to use least-square regression lines.
  • Students will be able to standardize data into Z-scores.
  • Students will be able to analyze scatterplots and correlations
  • Students will be able to design samples from statistical data.

This course upholds the KAS Mission statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Allowing students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.

 

Advanced Placement Calculus

Course Description:

This course covers each topic in the Calculus AB topic outline as it appears in the AP® Calculus Course Descriptions. The objective of this course is to give students the understanding of calculus concepts, related mathematical skills and appropriate technology necessary for success in collegiate mathematics and also prepare students for success on the Advanced Placement Exam. Students will have the opportunity to work problems verbally, graphically, numerically, and analytically. Students will establish a strong foundation and understanding in Calculus by practical application, which cannot simply be accomplished by the memorization of rules, but rather through understanding each concept.

Units:

  • Pre-Calculus Topics
  • Rates of Change and Limits
  • Derivatives
  • Differentiation rules
  • Applications of Differentiation
  • Integrals
  • Differential Equations
  • Application of Integration

Skill and Understandings:

  • Students will understand and recall skills and concepts used in Pre-Calculus class.
  • Students will understand Rates of Change and Limits and how to evaluate them.
  • Students will be able to derive equations and understand the basic derivative rules.
  • Students will derive the different differentiation rules and understand how to apply them.

This course upholds the KAS Mission statement by:

  • Allowing students to explore through the means of technology (graphical calculators and computers) the world of mathematics.
  • Awarding students the opportunity to explore and experiment with mathematical concepts in order to develop solutions and generalizations.
  • Teaching students that mathematical rigor is global and that mathematical communication is universal.
  • Encouraging students to develop a commitment to their own learning though mathematics.