## Mathematics Department Courses

**Algebra I – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Pre-Algebra or consent of instructor

Prerequisite: Pre-Algebra or consent of instructor

This course is designed as a college preparatory course to continue studies in mathematics and science. Areas of study include solving linear equations and inequalities, quadratic equations and systems of equations using the real numbers. Also included is graphing (both on a number line and in a coordinate plane), factoring, and working with functions. Problem solving will occur with all the above topics.

The student will:

- Use order of operations to evaluate phrases and perform the four basic operations with rational numbers
- Solve, graph and write linear equations and inequalities
- Translate verbal sentences and apply the problem- solving techniques to solve real life problems
- Perform the four basic operations and factor polynomials and solve quadratic equations
- Use proportions and systems of equations to solve word and numeric problems

**Math Concepts II
Offered to grades: 10, 11, 12
**

**Length: 2 Terms**

**Category: Elective**

Prerequisite: None

Prerequisite: None

Math Concepts II is designed as a prerequisite course for Algebra I and Consumer Math. Math Concepts II improves a student’s foundational skills and prepares them for Algebra I or Consumer Math. It is for the student who needs additional work on basic mathematical concepts and fundamental algebraic ideas.

The student will:

- Use order of operations to evaluate expressions and perform four basic operations with rational numbers
- Write, compare, and solve ratios and proportions
- Solve one- and two-step equations
- Identify and graph points in the coordinate plane
- Use equations, tables, and graphs to solve problems

**Basic Geometry
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Algebra I

Prerequisite: Algebra I

Several mathematical concepts are learned by experimentation and construction.

The student will:

- Know the terms and symbols used in geometry
- Learn the logical organization of inductive and deductive reasoning to prove congruence and/or similarity of geometric figures
- Know and be able to use formulas to find the distance between two points and perimeters and areas of two-dimensional figures
- Know how to set up and solve a proportion
- Learn techniques for drawing realistic looking geometric figures
- Know the names and measures of angles formed by a transversal cutting parallel lines
- Know how to find lengths of sides and measures of angles of right triangles
- Know how to use a straightedge and compass to construct various geometric figures

**Formal Geometry – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Algebra I

Prerequisite: Algebra I

This course is designed for college-bound students who intend to enroll in Algebra II. It uses both plane and spatial objects to accomplish a sound development of logic. Students are given frequent opportunities to use definitions, postulates and theorems to formulate proofs. A deep study of triangles and other polygons is included. A short time is spent on straight-edge and compass constructions.

The student will:

- Use coordinate geometry to find midpoints and lengths of segments and slopes of lines
- Recognize and apply the postulates, theorems, definitions and algebraic techniques to find segment length and angle measurements in congruent triangles, similar triangles, and quadrilaterals
- Find measures of angles, arcs and segments involving circles
- Find the areas, circumferences and perimeters of various plane figures
- Organize theorems, postulates and definitions into logical sequential two-column proofs

**Algebra II – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Formal Geometry

Prerequisite: Formal Geometry

Algebra II enhances the problem-solving process started in Algebra I by continuing to develop the basic and advanced properties of functions and algebra. Algebra II gives students the opportunity to model real data by understanding and applying the algebraic concepts of equations and inequalities, basic relations and functions, polynomials, and exponential functions. Students in Algebra II are able to describe the world around them by utilizing estimation, technology, and graphing techniques. Algebra II is designed to meet part of the three-year entrance requirements for mathematics to most colleges. Algebra II provides a valuable background for those entering technical fields and also serves as a useful course for other college-bound students.

The student will:

- Solve linear equations and inequalities
- Graph and evaluate linear equations and functions
- Use systems of linear equations and inequalities to solve problems
- Solve and graph quadratic functions
- Evaluate, graph, and solve polynomial equations and functions
- Simplify radical expressions and solve equations involving radicals
- Graph and solve exponential and logarithmic equations
- Simplify rational expressions and graph and solve rational functions and equations
- Evaluate trigonometric functions and inverse trigonometric functions

**Foundations of Algebra II, Part 1 and Part 2 – RAI
Offered to grades: 10, 11, 12
**

**Length: 4 TERMS**

**Category: Elective**

This course is designed to cover some topics found in the 2-term algebra II curriculum with opportunities for additional review and practice built into the daily lessons. It is for the student who needs self-confidence in mathematics and more emphasis on fundamental algebraic ideas. It is intended to be equivalent to the standard second-year algebra course. Meets the same requirements for college acceptance.

**Part 1**

Prerequisites: Algebra I, Basic Geometry or Formal Geometry

The student will:

- Solve linear and absolute value equations and inequalities
- Graph and evaluate linear equations and functions
- Use systems of linear equations and inequalities to solve problems
- Use matrices to organize numerical data
- Solve and graph quadratic functions and inequalities
- Evaluate, graph, and solve polynomial equations and functions

**Part 2**

Prerequisites: Foundations of Algebra II (part 1)

The student will:

- Simplify radical expressions and solve equations involving radicals
- Graph and solve exponential and logarithmic equations
- Simplify rational expressions and graph and solve rational functions and equations
- Evaluate trigonometric functions and inverse trigonometric functions

**Consumer Math
Offered to grades: 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Math Concepts or Algebra

Prerequisite: Math Concepts or Algebra

This course focuses on the basic skills necessary to function in everyday life situations. This course will familiarize the student by applying math skills to personal finances.

The student will:

- Know how to compute issues dealing with wages and the deductions that are included
- Know how to perform all aspects associated with checking and savings accounts
- Know how to perform all aspects associated with credit cards, personal loans and buying a house
- Know how to compute the costs associated with buying, leasing or renting an automobile.
- Know how to compute sales and income taxes.
- Know how the cost associated with insurance impacts your personal finances.
- Know how to create and evaluate a personal budget.

**Finite Math – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Algebra II

Prerequisite: Algebra II

*Dual Credit DMACC Course*

This is a general education course in practical mathematics for those students not majoring in mathematics or science. This course will include such topics as set operations and applications, methods of counting, probability, systems of linear equations, matrices, geometric linear programming and an introduction to Markov chains. The use of a graphing calculator is required.

The student will:

- Slopes and Equations of Lines
- Linear Functions and Applications
- The Least Squares Line
- Solution of Linear Systems by the Echelon Method
- Solution of Linear Systems by the Gauss-Jordan Method
- Addition and Subtraction of Matrices
- Multiplication of Matrices
- Matrix Inverses
- Graphing Linear Inequalities
- Solving Linear Programming Problems Graphically
- Applications of Linear Programming
- Slack Variables and the Pivot
- Maximization Problems
- Minimization Problems; Duality
- Simple and Compound Interest
- Future Value of an Annuity
- Present Value of an Annuity; Amortization Sets
- Applications of Venn Diagrams
- Introduction to Probability
- Basic Concepts of Probability
- Conditional Probability; Independent Events
- Bayes’ Theorem
- The Multiplication Principle; Permutations Combinations
- Probability Applications of Counting Principles
- Binomial Probability
- Probability Distributions; Expected Value
- Basic Properties of Markov Chains
- Absorbing Markov Chains
- Strictly Determined Games
- Mixed Strategies
- Game Theory and Linear Programming

**Trigonometry – RAI
Offered to grades: 10, 11, 12
**

**Length: 1 Term**

**Category: Elective**

Prerequisite: Algebra II (B or higher recommended)

Prerequisite: Algebra II (B or higher recommended)

This course would explore in-depth applications of trigonometry in numerous chosen fields of study. Students will become more aware of the uses of trigonometry as they relate to the fields of astronomy, surveying, navigation, construction, geography, physics, engineering, chemistry, and calculus.

The student will:

- Measure angles in radians and degrees
- Evaluate trigonometric functions
- Solve triangles and find the area of triangles
- Graph trigonometric functions
- Determine the amplitude, period, and phase shift for a graph
- Evaluate inverse trigonometric functions
- Verify trigonometric identities
- Solve trigonometric equations

**Pre-Calculus – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Trigonometry – Recommended C or higher in Trigonometry

Prerequisite: Trigonometry – Recommended C or higher in Trigonometry

This course is a culmination in the process of acquiring the fundamental skills of algebra, geometry and trigonometry and is designed to meet the needs of the college-bound student. General areas of study include functions, graphs, and their applications. Most of the time is spent on the polynomial, exponential, logarithmic, and trigonometric functions. Equations and graphs of the conic sections are also included. Some time is spent studying vectors, matrices, and limits.

The student will:

- Graph linear, polynomial, radical, trigonometric, logarithmic, and exponential functions
- Study the nature of graphs and various transformations
- Solve systems of equations and inequalities by utilizing algebraic algorithms, matrices, and graphing
- Study trigonometric identities before applying them to solve trigonometric equations
- Transfer the concepts of the rectangular coordinate system to the polar coordinate plane

**AP Calculus AB – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Pre-Calculus (B or higher recommended)

Prerequisite: Pre-Calculus (B or higher recommended)

*Daul Credit DMACC Course*

This course contains coverage of all topics required for the AP Calculus AB exam, and is designed for prospective mathematics majors as well as for students whose primary interests are in engineering, physics, business or the life sciences. Applications include approximations by differentials, work, max./min. and solids of revolution problems. Techniques of differentiation and integrations are studied throughout the course.

The student will:

- Recognize functions when described graphically, numerically, in tables and in words
- Know how to graph elementary functions, including algebraic, exponential, logarithmic and trigonometric functions
- Know the relationship of the graphs of functions, their first derivatives and their second derivatives
- Know the procedures for finding derivatives and antiderivatives of algebraic and transcendental functions
- Know how to find maximum and minimum functional values of a given domain
- Know how to determine limits, continuity and differentiability of functions
- Know how to interpret the meaning of the integral
- Know how to apply the fundamental theorem of integral calculus to evaluate integrals
- Know how to apply integration and differentiation techniques to solve real world problems

**AP Calculus BC (Calculus II) – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: AP Calculus AB

Prerequisite: AP Calculus AB

*Dual Credit (DMACC) Course*

The course contains coverage of all topics required for the AP Calculus BC exam, and is designed for students whose primary interests are mathematics, engineering, physics, business or life sciences. The course will include all topics from AP Calculus AB, as well as additional topics listed below:

The student will:

- Analyze planar curves including those given in parametric form, polar form, and vector form, including velocity and acceleration
- Find numerical solution of differential equations using Euler’s method
- Use L’Hospital’s Rule, including its use in determining limits and convergence of improper integrals and series
- Compute derivatives of parametric, polar, and vector functions
- Study a variety of applications of integrals
- Take antiderivatives by substitution, parts, and simple partial fractions (non repeating linear factors only)
- Find improper integrals (as limits of definite integrals), as well as study applications of antidifferentiation
- Solve logistic differential equations and using the in modeling
- Find numerical approximations to definite integrals
- Use of Riemann sums (using left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values
- Study series of constants, including decimal expansion, geometric series with applications, harmonic series, alternating series with error bound
- Apply the ratio test for convergence and divergence
- Compare series to test for convergence or divergence
- Know how to use Taylor polynomial approximation, Malaurin series and the general Taylor series centered at x=a, Maclaurin series for the functions e^x, sin x, cos x, and 1/(1-x)
- Be comfortable using formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series
- Use functions defined by power series, as well as study radius and interval of convergence of power series
- Apply Lagrange error bound for Taylor polynomials

**Probability and Statistics – RAI
Offered to grades: 10, 11, 12
**

**Length: 1 Term**

**Category: Elective**

Prerequisite: Algebra II or Foundations of Algebra II (C or higher recommeded)

Prerequisite: Algebra II or Foundations of Algebra II (C or higher recommeded)

This course will provide an introduction to statistics and probability, and how they are applied to the real world. The general areas of study will include analyzing data, graphic displays, probability rules, counting principles, simulations, random variables, normal distributions, and regression analysis. The intent of this course is to help prepare the student for college and for further study in mathematics.

The student will:

- Represent data in graphical displays
- Calculate central measures and measures of position
- Use counting principles
- Perform probability simulations
- Perform random sampling
- Know how to use statistical inference to make decisions
- Calculate probabilities using binomial or normal distributions

**AP Statistics – RAI
Offered to grades: 10, 11, 12
**

**Length: 2 TERMS**

**Category: Elective**

Prerequisite: Algebra II

Prerequisite: Algebra II

*Dual Credit (DMACC) Course*

This course is a college freshman level course offered at Waukee High School. This course offers students an opportunity to earn college math credit in addition to or instead of taking AP Calculus.

- AP Statistics will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to four broad conceptual themes:
- Exploring Data: Describing patterns in data and departures from patterns
- Sampling and Experimentation: Planning, designing, and conducting a study or experiment
- Anticipating Patterns: Exploring random phenomena using probability and simulation
- Statistical Inference: Estimating population parameters and testing hypotheses

Students who successfully complete the course may receive college credit through the AP Statistics examination or directly from DMACC as a concurrent credit course. AP Statistics corresponds to MAT 157 Elementary Statistics at DMACC. Students may earn 4 credits upon successful completion of both terms.