# Mathematics Curriculum

## Algebra 1 (Foerster)

### Honors Designation available

### Course Texts:

**Algebra 1 Course Plan & Tests****Honors Algebra 1 Course Plan & Tests**, Textbook**Algebra 1 Expressions, Equations, and Applications**, Solutions Manual**Algebra 1 Expressions, Equations, and Applications**, Tutorial/Solutions Flash Drive, Optional**Algebra 1 Home Study Companion**

### Course Description:

Paul Foerster’s Algebra 1 provides a strong course for the Algebra 1 student. The course moves at a very quick pace as much of the material in the first two chapters is review of Pre-Algebra. A review of decimals, fractions, and percentages is not included so parents should be sure the student is comfortable with those topics before beginning the course. This course provides the backbone of Algebra 1 concepts to prepare the student for taking Algebra 2, and adequately prepare a student to take the Algebra 1 Math sections of the PSAT, SAT, and ACT standardized tests. Additional graphing supplements are provided in the course plan as an introduction to graphing.

Students can succeed in this course after completing any pre-Algebra course, including the Saxon Math 8/7 (with pre-Algebra) text. Students who struggled with Saxon Math 8/7 are advised to use Saxon Algebra 1/2 or another pre-Algebra course prior to beginning this course. Note that about the first five chapters will include much review of pre-Algebra concepts.

This course is typically done in the 8th or 9th grade. Topics include:

- Expressions & equations
- Operations with negative numbers
- Distributing, axioms, & other properties
- Harder equations
- Some operations with polynomials & radicals
- Quadratic equations
- Expressions & equations containing two variables
- Linear functions, scattered data, & probability
- Properties of exponents
- More operations with polynomials
- Rational algebraic expressions
- Radical algebraic expressions
- Inequalities
- Functions & advanced topics

## Geometry: A Guided Inquiry

### Honors Designation available

### Course Texts:

**Geometry Course Plan & Exams**, Textbook**Geometry: A Guided Inquiry**

**Geometry: A Guided Inquiry****Digital License****Geometry: A Guided Inquiry****Home Study Companion**, Tutorial/Solutions Flash Drive, Optional**Geometry Supplemental Chapter Tests**, Optional**Geometry Supplemental Honors Chapter Tests**, Optional**Geometry Supplemental Workbook**, Optional**Geometry Supplemental Honors Workbook**, Optional

**Course Materials:**

- Hand-held Scientific Calculator
- Compass
- Protractor

### Course Description:

This Geometry course can follow any Algebra 1 program, whether the student has used Saxon Algebra 1, Foerster Algebra 1, or another First year Algebra course. If questions should arise about the preparedness of a student for this course, please contact the Academic Advisor department at Kolbe Academy. This course presents all the geometrical concepts in a traditional fashion to the high school student. This course will sufficiently prepare the student for questions on the math section of the PSAT, ACT, or SAT standardized tests.

Students completing this course as well as a previous Algebra 1 program will be ready to take the traditional second year of Algebra 2. Student’s who wish to continue on in the Saxon mathematics series upon completion of Geometry will find much repetition in the Saxon Algebra 2 course because the majority of the material covered is Geometry. Students choosing to continue with Saxon after this course should be prepared to take through Advanced Mathematics 1 in order to complete all the Algebra 2 concepts necessary to succeed on the ACT and SAT standardized tests. It is more desirable for students to pursue a traditional Algebra 2 course following this Geometry course. The Kolbe Academy recommended course of study includes continuing with Foerster’s Algebra and Trigonometry upon completion of the Geometry text.

The *Geometry: A Guided Inquiry* text includes engaging language that will help to keep the interest of the student throughout the duration of the course. The lessons are set up to challenge students, yet offer sound explanations to give students the tools to complete problems efficiently. The text is set up with a Central Problem that allows for learning through discovery, Review Exercises that check for understanding, and Projects that expand and enhance the material covered. Finally, Algebra reviews are located at the end of several chapters in the student textbook.

This course is typically done in 9th or 10th grade. Topics include:

- Conditional statements
- Direct & indirect proofs
- Pythagorean theorem
- Lines & angles
- Congruence
- Inequalities
- Parallel lines
- Quadrilaterals
- Transformations
- Area
- Similarity
- Right triangle
- Circles
- Concurrence theorems
- Regular polygons & the circle
- Geometric solids
- Non-euclidean geometry

## Algebra 2 & Algebra 2/Trigonometry (Foerster)

### Honors Designation available

### Course Texts:

**Algebra 2 Course Plan & Tests****Honors Algebra 2/Trigonometry Course Plan & Tests**, Textbook**Algebra & Trigonometry: Functions & Applications**Solutions Manual**Algebra & Trigonometry**,, Tutorial/Solutions Flash Drive, Optional**Algebra 2/Trig Home Study Companion**, Student Book**Graphing Calculator Lab Manual**, Teacher Edition*Graphing Calculator Solution Manual*

### Course Description:

The **Algebra 2 **(K) course moves at a very reasonable pace for most high school students. It is meant to be a college preparatory course in nature, taking the student through a great number of Algebra 2 concepts but also spending a little more time on reviewing Algebra 1 than the honors course. This course of study can be completed by most average students. Upon completion of Algebra 2 (K), students will be ready to tackle any Precalculus course the following year. If a student is struggling with this course, parents may want to call and speak with an adviser, but the following modifications could be made – omitting Chapters 9 & 10.

The **Algebra 2/Trigonometry** (H) course moves at a very quick pace and emphasizes the more difficult concepts and mathematical applications in the text. This course of study, although up to the parent’s discretion, is recommended for students who received an A in either Algebra 1 or Geometry and received at least a B+ in both Algebra 1 and Geometry. Students who do well in the Honors Algebra 2/Trig course will find themselves ready for the study of Calculus during the following year. All students pursuing honors should expect to find the content and pace of the coursework challenging and should be sure to allot extra time for their studies. Those wishing to pursue the Honors designation in this course will have a heavier emphasis on the mathematical applications of concepts learned in the course.

Additionally, a Graphing Calculator Supplement is assigned in the course plan as they correspond with the appropriate sections. While it isn’t absolutely essential for students to learn how to use a graphing calculator, it is preferable, especially in courses of Algebra 2 and beyond. Students need to know how to graph things on paper, but it is very useful to know how to appropriately use a graphing calculator for the more complex problems where graphing (or other calculations) would bog the student down with unnecessary busy work. Furthermore, the ACT and SAT both allow the use of a graphing calculator, so it can greatly benefit students to know some short cuts to aid them on the math portions of these exams.

Topics in the **Algebra 2 **course include:

- Linear functions
- Systems of linear equations & inequalities
- Quadratic functions & complex numbers
- Exponential & logarithmic functions
- Rational algebraic functions
- Irrational algebraic functions
- Quadratic relations & systems (circles, ellipses, hyperbolas, & parabolas)

Those taking** Algebra 2/Trigonometry **will also cover:

- Trigonometric & circular functions
- Properties of trigonometric & circular functions
- Trigonometric identities
- Triangle problems
- Vectors

## PreCalculus (Foerster)

### Honors Designation Available

### Course Texts:

**Precalculus Course Plan & Tests****Honors Precalculus Course Plan & Tests**, Textbook*Precalculus: Concepts and Applications**Precalculus*Tutorial/Solutions Flash Drive, Optional**Home Study Companion**,, Digital, Teacher edition not available for individual sale, but is provided gratis to enrolled families. (Single Course enrollment is available.)*Precalculus Solutions Manual*

### Course Materials:

- Programmable Graphing Calculator, preferably TI-83 or TI-84 model (required)

### Course Description:

This course is a one year course (10 credits) in high school Precalculus. The honors track, although up to the parent’s discretion, is aimed for students who have shown aptitude toward mathematics in their Geometry and Algebra 2 courses, or who have successfully completed the honors Algebra 2/Trig course. All students pursuing honors should expect to find the content and pace of the coursework challenging and should be sure to allot extra time for their studies. If a student finds the work load unbearable, please contact the advisor department so that suggestions can be made for the student to succeed in this course.

The Kolbe Core (K) track is recommended for any student who has successfully completed Algebra 2 (K) or Algebra 2/Trig (H). The Kolbe Honors (H) track, although up to the parent’s discretion, is recommended for students who have achieved one of the following: a “B” or better in Algebra 2/Trig (H) or an “A” in Algebra 2 (K).

## Calculus (Foerster)

### Honors Designation Available

### Course Texts:

**Calculus Course Plan & Tests**, Textbook*Calculus: Concepts and Applications*, Tutorial/Solutions Flash Drive, Optional**Calculus Home Study Companion**, Digital, Gratis for currently enrolled Kolbe families**Calculus Solutions Manual**

### Course Materials:

- Programmable Graphing Calculator, preferably TI-83 or TI-84 model (required)
- Calculator Programs available with purchase of textbook
- AP Prep book recommended

### Course Description:

This course plan includes a one year course (10 credits) in high school Calculus. The Kolbe Honors Calculus 1 and 2 (H) course prepares the student for the AP Calculus BC exam, which typically gives Calculus 1 and 2 credit at many colleges and universities. The Kolbe Core Calculus (K) course prepares the student for the AP Calculus AB exam, which typically gives Calculus 1 credit at most colleges and universities. (See each university’s AP policy for credits.)

The Kolbe Honors (H) track, although up to the parent’s discretion, is recommended for students who have achieved one of the following: an “A” or better in Algebra 2/Trig (H), an A in PreCalculus (K), or a “B+” in PreCalculus (H). All students pursuing honors should expect to find the content and pace of the coursework challenging and should be sure to allot extra time for their studies.

The Kolbe Core (K) track is recommended for students who have achieved one of the following: a “B” or better in Algebra 2/Trig (H), or successful completion of PreCalculus (K or H).

## Algebra 1 (Saxon)

### Course Texts:

Home Study Kit, Text & Workbook**Saxon Algebra 1**,, Solutions Manual, Optional*Saxon Algebra 1*

### Course Description:

Students may begin this course after completing any pre-Algebra course, including the Saxon Math 8/7 (with pre-Algebra) course. Students who struggled with Saxon 8/7 are advised to use Saxon Algebra 1/2 prior to beginning an Algebra 1 course. Upon completion of Saxon’s Algebra 1, students may either continue with the Saxon program by using Saxon’s Algebra 2 book, or may switch into a standard Geometry course using Jacob’s Geometry. Please be advised that Saxon does not have a separate Geometry course. The author instead integrates all Geometry concepts throughout the Algebra 1, Algebra 2, and Advanced Math programs. It is advisable that all college bound students exclusively using the Saxon program complete through Advanced Math in order to cover all the Geometry and Trigonometry concepts that might appear on the PSAT, ACT, and SAT standardized tests.

Topics include:

- Division by zero
- Reciprocal & multiplicative inverse
- Exponents
- Algebraic phrases
- Word problems
- Canceling
- Ratio
- Conjunctions
- Dividing fractions
- Domain
- Elimination
- Closure
- Probability
- Algebraic proofs
- Rational equations functions

## Algebra 2 with Geometry* (Saxon)

**Students who opt to do a separate Geometry course in addition to this course will have a course title of simply “Algebra 2.”*

### Course Texts:

Home Study Kit, Text & Workbook**Saxon Algebra 2**,Solutions Manual, Optional**Saxon Algebra 2**,

### Course Description:

The following course covers the basics of Algebra 2 and good deal of Geometry. The only students that should be using this Algebra 2 course are those who have completed Saxon’s course in Algebra 1. Please be advised that Saxon does not have a separate Geometry course. The author instead integrates all Geometry concepts throughout the Algebra 1, Algebra 2, and Advanced Math programs. It is advisable that all college bound students exclusively using the Saxon program complete through Advanced Math in order to cover all the Geometry and Trigonometry concepts that might appear on the PSAT, ACT, and SAT standardized tests.

Topics include:

- Absolute value
- Percent
- Pythagorean theorem
- Substitution
- Scientific notation
- Area
- Trinomial factoring
- Chemical compounds
- Abstract fractional equations
- Radical equations
- Ideal gas laws
- Quadratic formula
- Force
- Vectors
- Slope formula
- Discriminant number
- Word problems

## Precalculus with Geometry* (Saxon)

### Honors Designation available

**Students who opt to do a separate Geometry course in addition to this course will have a course title of simply “Precalculus.”*

### Course Texts:

, Home Study Kit, Text & Workbook*Saxon Advanced Mathematics*, Solutions Manual, Optional**Saxon Advanced Mathematics**

### Course Description:

The only students that should be using this Precalculus with Geometry course are those who have completed Saxon’s course in Algebra 2. The Advanced Mathematics book by Saxon can be used in 2, 3, or 4 semesters. Kolbe Academy offers a course in two (10 credits) and four (20 credits) semesters. Those students who are more proficient in math, may want to use this one year honors Advanced Math course (10 credits), calling the course “Precalculus with Geometry.” Students will be prepared for Calculus after this one year study of Advanced Mathematics. Students wishing to pursue a less rigorous approach to the advanced mathematics course should follow the Advanced Math 1 and 2 two-year (20 credits) track.

This course provides, among other topics, in-depth coverage of the following:

- Trigonometry
- Logarithms
- Geometry
- Analytic geometry

## Advanced Math 1: Algebra 3 with Geometry* (Saxon)

**Students who opt to do a separate Geometry course in addition to this course will have a course title of simply “Algebra III.”*

### Course Texts:

, Home Study Kit, Text & Workbook*Saxon Advanced Mathematics*Solutions Manual, Optional**Saxon Advanced Mathematics**,

### Course Description:

The only students that should be using this Precalculus with Geometry course are those who have completed Saxon’s course in Algebra 2. This course covers the first 60 lessons of the Saxon Advanced Mathematics textbook and is the final step in fulfilling a Geometry requirement. The Advanced Mathematics book by Saxon can be used in 2, 3, or 4 semesters. Those students who are more proficient in math, may want to use the one year honors Precalculus with Geometry course (10 credits) outlined above. Students wishing to pursue a less rigorous approach to the advanced mathematics course should follow the Advanced Math 1 and 2 two-year (20 credits) track, beginning with this course, Algebra 3 with Geometry.

This course provides, among other topics, in-depth coverage of the following:

- Trigonometry
- Logarithms
- Geometry
- Analytic geometry

## Advanced Math 2: Precalculus (Saxon)

### Course Texts:

Home Study Kit, Text & Workbook**Saxon Advanced Mathematics**,Solutions Manual, Optional**Saxon Advanced Mathematics**,

### Course Description:

The only students that should be using this Precalculus course are those who have completed Advanced Math 1: Algebra 3 using the Saxon Advanced Math book. This course covers the last 60 lessons of the Saxon Advanced Mathematics textbook. The Advanced Mathematics book by Saxon can be used in 2, 3, or 4 semesters. This course plan is a continuation of the Algebra 3 with Geometry course. Students completing this course will be prepared to take Calculus next year.

This course provides, among other topics, in-depth coverage of the following:

- Trigonometry
- Logarithms
- Geometry
- Analytic geometry

## Calculus 1 (Saxon)

### Course Texts:

, Home Study Kit, Text & Workbook*Saxon Calculus*, Solutions Manual, Optional**Saxon Calculus**

### Course Description:

This book is designed for prospective mathematics majors as well as for students whose primary interests are in engineering, physics, business, or the life sciences. This course covers the first half of Saxon Calculus. Students taking this Calculus 1 course will have a firm foundation in Calculus 1 concepts and a brief introduction to Calculus 2 concepts. Students may wish to proceed for an additional full year of Calculus 2 and complete the latter half of the textbook.

The book contains a sufficient review of Precalculus concepts. However, students should not attempt this Calculus course without completing one of the following: Algebra 2/Trigonometry, Precalculus, Saxon Advanced Mathematics, or other equivalent Precalculus course. Students who excelled in mathematics throughout high school or who are highly motivated, might consider pursuing the Honors Calculus 1 and 2 course described below.

Topics include:

- Precalculus review
- Limits & their properties
- Introduction to differentiation
- Techniques of differentiation
- Applications of differentiation
- Introduction to integration

## Calculus 2 (Saxon)

### Course Texts:

, Home Study Kit, Text & Workbook**Saxon Calculus**, Solutions Manual, Optional**Saxon Calculus**

### Course Description:

This book is designed for prospective mathematics majors as well as for students whose primary interests are in engineering, physics, business, or the life sciences. This course covers the last half of Saxon Calculus. Students taking this Calculus 2 course will have a firm foundation in Calculus 2 concepts. After completing Calculus 1 and upon completion of this course, students will be prepared well for the AP Calculus AB exam. Students will also be prepared sufficiently well for the AP Calculus BC exam, but a few select topics may need to be supplemented.

Topics include:

- Introduction to integration
- Applications of integration
- Techniques of integration
- Analytical geometry
- Series & sequences

## Calculus 1 & 2 (Saxon)

### Honors Designation Available

### Course Texts:

, Home Study Kit, Text & Workbook*Saxon Calculus*, Solutions Manual, Optional**Saxon Calculus**

### Course Description:

This book is designed for prospective mathematics majors as well as for students whose primary interests are in engineering, physics, business, or the life sciences. Students pursuing this course will be working at a very quick pace and should expect to put in a significant amount of time into their studies as the entire book is covered in one year. Students following the Kolbe Honors Calculus 1 and 2 track will have a firm foundation in Calculus 1 and 2 concepts. The Honors course prepares a student for taking the AP Calculus AB Exam as well as preparing them fairly well for the AP Calculus BC Exam.

The book contains a sufficient review of Precalculus concepts. However, students should not attempt this Calculus course without completing one of the following: Algebra 2/Trigonometry, Precalculus, Saxon Advanced Mathematics, or other equivalent Precalculus course. Students who excelled in mathematics throughout high school or who are highly motivated, should be encouraged to pursue the Honors track.

Topics include:

- Precalculus review
- Limits & their properties
- Introduction to differentiation
- Techniques of differentiation
- Applications of differentiation
- Introduction to integration
- Applications of integration
- Techniques of integration
- Analytical geometry
- Series & sequences