# Mathematics

## GENERAL OBJECTIVES OF THE MATHEMATICS DEPARTMENT

- The student will learn to realize and appreciate the mathematical aspects found in God's

creation and how they contribute to man's way of life. - The student will become confident in his or her ability in the area of mathematics.
- The student will become a problem solver, learning to plan and think logically to reach a

solution. - The student will learn to communicate the mathematics he or she learns both verbally and

in written form. - The student will gain a background of understanding from each mathematics class,

preparing the student more fully for more advanced classes in mathematics and science.

**Pre-Algebra**

This course is designed to develop the student's skill in the fundamental operations of mathematics and to prepare them for further instruction in mathematics and science.

**Course Objectives**

- To help the student recognize that in math, the order of God’s creation is very evident.
- To help the student understand the language and symbols of Algebra.
- To develop the student’s skills in the fundamental operations of math, which are essential in everyday life.
- To improve the student’s ability to problem solve by using logical thought patterns.
- To prepare the student for further math and science courses: Algebra 1, Geometry, Chemistry, Physics, and Algebra 2.

**Algebra 1**

Algebra 1 is a branch of mathematics whose foundation is crucial for success in higher level courses. Given the technological prevalence in today’s workplace it is important that Algebra 1 lends itself to be useful. This course will sharpen a student’s aptitude for number sense, sound reasoning, and logical thought patterns by unwrapping algebraic concepts in a problem solving and systematic way. Unknown quantities will be represented by letters and they will be solved for through both algebraic and graphical methods. The topics in Algebra 1 include a review of basic algebraic concepts and functions, properties of real numbers, finding and using linear equations and inequalities to write equations and to solve problems, graphs of equations, solving systems of equations and inequalities, rules of radicals and exponents, finding and using exponential equations to solve problems, polynomials and factoring, finding and using quadratic equations to solve problems and probability and data analysis.

**Course Objectives**

The student will:

- Evaluate and write algebraic expressions
- Perform operations on the real numbers
- Solve one-step and multi-step equations and inequalities
- Graph linear and quadratic functions and inequalities
- Write linear functions in slope-intercept, point-slope, and standard forms
- Solve linear systems of equations and inequalities by graphing, substitution, and elimination
- Apply exponent properties to solve growth and decay problems
- Perform operations on and factor polynomials
- Solve quadratic equations by graphing, completing the square, and by using the quadratic formula
- Solve radical equations in applications such as the Distance Formula
- Simplify and perform operations on rational expressions
- Calculate the probability and odds of various events utilizing permutations and combinations
- Convert algebraic, tabular, and graphic representations of functions

**Algebra 2**

This course is designed to provide a foundation of Algebraic concepts, techniques, and applications to help the students increase their reasoning and problem-solving skills.

**Course Objectives**

- The student will see how math is used and is evident throughout God's creation.
- The student will understand the language and symbols of Algebra.
- The student will improve his/her skills in predicting, reasoning, inferring, communicating, and problem solving in the mathematical realm.
- The student will improve his/her skill in the fundamental operations of mathematics, which are essential in everyday life.
- The student will learn skills that will help him/her for further mathematical and scientific investigations in Geometry, Chemistry, Physics, and Algebra 2.
- The student will learn how technology can be used as a tool for learning and doing mathematics.
- The student will gain a deeper appreciation for math.

**Algebra 2 & Pre-Trigonometry**

Algebra 2 & Pre-Trigonometry is the advanced study of algebraic theory and functions laying the foundation for future advanced math exploration. The math in Algebra 2 includes: equations, inequalities, functions, matrices, quadratics, complex numbers, polynomial functions, properties of logarithms, rational functions, conics, sequences and series. In the Pre-Trigonometry portion, all the trig ratios, their inverses, radians, and graphing of trig functions are covered.

**Course Objectives**

- To see structure through the interpretation and writing of mathematical expressions.
- To perform arithmetic operations to solve problems.
- To be able to create equations that describe numbers or relationships from data presented.
- To understand solving equations and systems of equations as a process of reasoning and represent equations and inequalities graphically.
- To make sense of problems and persevere in solving them by attending to precision and by reasoning abstractly and quantitatively.
- To model with mathematics through structure and repeated reasoning
- To be able to use multiple technology tools appropriately and strategically to solve problems

**Geometry**

This is a course examining two and three dimensional geometric figures and their properties, geometric constructions, making conjectures, drawing conclusions, and the development of formal logical proofs. Properties and relationships of geometric objects include the study of: (1) points, lines, angles and planes; (2) polygons, especially focusing on quadrilaterals, triangles, and right triangles; (3) circles; and (4) polyhedra and other solids.

**Course Objectives**

- The student will learn that in mathematics the order of God’s creation is very evident.
- The student will understand the structure of geometry and its place in the total structure of mathematics.
- The student will improve his or her skills in predicting, analyzing, inferring, communicating, and problem solving in the mathematical realm.
- The student will learn to apply the geometric properties learned in the solution of mathematical problems.
- The student will gain understanding of the deductive method of reasoning.
- The student will continue to grow in understanding algebraic concepts especially as they are related to work in geometry.
- The student will learn to recognize and appreciate the connection between geometric concepts and the world around him or her

**PreCalculus**

This is an upper level elective course which challenges students to better prepare them for Calculus and the robust rigor of a college level mathematics course. In the first semester, students study the graphs and properties of linear, polynomial, rational, power, root, inverse, exponential, and logarithmic functions. The goal is for students to link multiple representations in their minds (equation, table, and graph) as they work toward solving for the solution(s) of any type of function.

**Course Objectives**

The student will:

- Demonstrate the ordered and mathematical nature of God’s creation
- Link multiple representations (algebraic, tabular, and graphic) in problem-solving settings
- Discuss the definition of a function, the basic properties of a function and its graph, and function operations and transformations
- Recognize conic sections by their equations and can discuss their geometric properties

**Trigonometry**

The course features an in-depth analysis of trigonometry. Graphs of the trigonometric functions, verifying trigonometric identities, solving trigonometric equations, sketching and applying vectors, and other applications of trigonometric functions are studied. Finite and infinite arithmetic and geometric sequences and series are covered. Time permitting, an introduction to Calculus concepts such as limits, differentiation, and the definite integral will be investigated.

**Course Objectives**

The student will:

- Recite the six trigonometric functions and how they are useful in right triangle trigonometry settings
- Identify the properties of the unit circle and explain how to use it for any central angle measure
- Graph the periodic functions and evaluate trigonometric functions for any angle measure
- Verify that given identities are true and use these identities to solve equations
- Solve for the three sides and three angles in any triangle, using the Law of Sines and Law of Cosines, or other formulas as needed
- Represent a series using summation notation
- Use technology as a tool to facilitate learning and explore mathematical concepts

**AP® Statistics**

Statistics surround us in numerous facets of life: education, the marketing strategies employed in business and personal finance, the drafting of government policies, pharmaceutical testing of new drugs, and they even contribute to coaching and front office decision making in sports. There is a growing demand for statisticians and there is a great need for statistical literacy in our country. Students will dive much deeper than the basic statistics with which they have already been acquainted. Major topics include displaying and summarizing categorical and quantitative data, correlation, linear regression and re-expression, surveys, observational studies and experiments, randomness, probability, confidence intervals, and hypothesis testing used in making inferences about a population. The expectation for this course is that every student will take the AP® Exam at the conclusion of the school year. The goal is that every student can pass that exam and receive college credit for Statistics.

**Course Objectives**

The student will:

- Analyze and interpret data that has been represented graphically in forms such as a box and whisker plot, dot plot, stem plot, histogram, two-way table, and cumulative frequency plot.
- Calculate descriptive statistics such as the five-number summary, mean, median, standard deviation, and variance by hand or by use of a graphing calculator.
- Discuss the degree of association between variables and apply transformations to achieve linearity when it is not first observed between variables.
- Discuss the appropriateness of using simple random, stratified random, and systematic sampling in different situations.
- Plan and justify a sampling procedure for given real-life sampling problems, while being able to identify sources of potential bias.
- Model random behavior of a real context using by building a simulation.
- Design and administer a survey, observational study, or experiment by collecting and analyzing data, and drawing conclusions from descriptive and inferential statistics.
- Identify the probability of any event occurring through visual aids such as tree or Venn diagrams.
- Construct confidence intervals and implement hypothesis testing for proportions and means of a population given the sample statistics.
- Write formal assignments, essays, projects, or class presentations that utilize the language and vocabulary of statistics to describe their statistical methods and interpretations.

“AP® and Advanced Placement® are registered trademarks of the College Board. Used with permission.”

**AP® Calculus AB**

This course is designed to set college-bound students up for success in taking the AP® Calculus AB exam at the end of the school year. Students entering Calculus must not have only demonstrated an interest and aptitude for mathematics up through Precalculus, but must have a deep understanding of the language of algebra, geometry, and trigonometry. Most of the course will be devoted to differential and integral calculus. These topics are the focus of the AP® Exam questions. Students will be expected to work with the content in a variety of methods and understand the connection of these different representations: graphical, algebraic, and tabular. Topics of study include limits, the derivative, rules of differentiation, the first and second derivative tests, antiderivatives and indefinite integration, Riemann sums, the two parts of the Fundamental Theorem of Calculus, definite integration and finding area under a curve, differential equations, slope fields, and finding volumes of three-dimensional solids of revolution. Students should recognize Calculus as a remarkable human accomplishment and as a beautiful language of God’s created universe.

**Course Objectives**

The student will be able to:

- Estimate, express, and interpret limits expressed symbolically using the correct notation.
- Deduce and interpret behavior and continuity of functions using limits.
- Identify the derivative of a function as the limit of a difference quotient.
- Estimate and calculate first and higher-order derivatives.
- Use derivatives to analyze properties of a function.
- Link differentiability and continuity.
- Interpret the meaning of the derivative in related rates and optimization problems and solve them using the slope of the tangent line.
- Estimate and verify solutions to differential equations.
- Identify the antiderivatives of basic functions.
- Express the limit of a Riemann sum in integral notation.
- Calculate a definite integral using areas and properties of integrals.
- Apply definite integrals to problems involving area, volume, motion and the average value of the function.
- Interpret, create, and solve differential equations for general and specific solutions from problems in context.

“AP® and Advanced Placement® are registered trademarks of the College Board. Used with permission.”

**Personal Finance**

The course touches on economic topics such as supply, demand, and economic systems. The majority of the class, however, deals with personal finance. The students demonstrate competence in such topics as formulating a budget, managing a check book, completing income tax forms, personal investing, understanding and buying insurance, and using credit wisely. All of these personal finance topics are taught in the light of what God’s Word teaches us about Christian stewardship.

**Course Objectives**

- Students will learn that because resources in this world are limited they cannot have all the goods and services they want and as a result they must choose some things and give up others.
- Students will learn that the choices that they make concerning the resources with which God has blessed them should be based on what our God tells us about being good Christian stewards. (I Corinthians 16:2)
- Students will learn the importance of budgeting understanding that budgeting is a plan for distributing the money God with which God has blessed them.
- The students will study personal finance topics such as saving and investing, using credit, types of insurance, using a checking account, understanding and doing taxes, buying verses renting, and wills.