# Mathematics Curriculum

## Algebra I (Jacobs)

### Course Texts:

*Elementary Algebra*, Harold Jacobs, © 1979 (T4100)*A Teacher's Guide to Elementary Algebra*, Harold R. Jacobs (T4100A), Optional- Algebra DVD Lectures (T4100D), Optional

### Course Description:

Harold Jacob's Elementary Algebra provides a strong course for the Algebra I student. His text is set up in a traditional style so that students have the opportunity to practice many types of problems taught within each lesson. This course provides the backbone of Algebra I concepts to prepare the student for taking Algebra II, and adequately prepare a student to take the Algebra I 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: fundamental operations, functions and graphs, domain and range of functions, integers, rational numbers, equations in one variable, equations in two variables, simultaneous equations, exponents, polynomials, factoring, fractions, square roots, quadratic equations, graphing quadratic equations, real numbers, fractional equations, inequalities, graphing inequalities in two variables, and arithmetic and geometric sequences.

## Geometry (Jacobs)

### Honors Designation available

### Course Texts:

*Geometry: Seeing, Doing, Understanding*, Harold Jacobs, 3rd edition, © 2003 (T4101)- Teacher's Manual (T4101A), Optional
- Geometry DVD Lectures (T4101D), Optional

### Course Description:

This Geometry course can follow any Algebra I program, whether the student has used Saxon Algebra I, Jacob's Elementary Algebra, 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 I program will be ready to take the traditional second year of Algebra II. Student's who wish to continue on in the Saxon mathematics series upon completion Jacob's Geometry will find much repetition in the Saxon Algebra II 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 I in order to complete all the Algebra II concepts necessary to succeed on the ACT and SAT standardized tests. It is more desirable for students to pursue a traditional Algebra II course following this Geometry course. The Kolbe Academy recommended course of study includes continuing with Foerster's Algebra and Trigonometry upon completion of the Jacob's Geometry text.

The Harold Jacob's Geometry 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 author has set his text up to include three sets of problems with each lesson so as to present the basic concepts in Set I exercises, applications in Set II exercises, and extension of concepts in Set III exercises. Finally, there are Algebra reviews located at the end of most chapters in the student textbook.

This course is typically done in 9th or 10th grade. Topics include: conditional statements, direct and indirect proofs, Pythagorean theorem, lines and angles, congruence, inequalities, parallel lines, quadrilaterals, transformations, area, similarity, the right triangle, circles, the concurrence theorems, regular polygons and the circle, Geometric solids, and non-Euclidean geometry.

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

### Honors Designation available

### Course Texts:

*Algebra and Trigonometry: Functions and Applications,*Paul A. Foerster, © 2006 (T4102)*Solutions Manual (T4102A), Optional Algebra and Trigonometry Graphing Calculator Lab Manual*(T4102B)- Kolbe Academy Solution Manual to the Graphing Calculator Lab Manual (T4102C), Optional
- Foerster DVD Lecture Set (T4102D), Optional

### Course Description:

Topics in the **Algebra II **course include: linear functions, systems of linear equations and inequalities, quadratic functions and complex numbers, exponential and Logarithmic functions, rational Algebraic Functions, irrational Algebraic Functions, quadratic Relations and Systems (circles, ellipses, hyperbolas, and parabolas); those taking** Alg II/Trigonometry **will also cover: trigonometric and circular functions; properties of trigonometric and circular functions; trigonometric Identities; triangle Problems; and vectors.

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 II 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.

The **Algebra II/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 I or Geometry and received at least a B+ in both Algebra I and Geometry. Students who do well in the Honors Algebra II/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.

The **Algebra II **(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 II concepts but also spending a little more time on reviewing Algebra I than the honors course. This course of study can be completed by most average students. Upon completion of Algebra II (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 advisor, but the following modifications could be made – omitting Chapters 9 & 10.

## PreCalculus (Foerster)

Honors Designation Available

### Course Texts:

*Precalculus: Concepts and Applications*, Paul A. Foerster, © 2012 (T4093)- Solutions Manual, Optional, (T4093A)

### 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 II courses, or who have successfully completed the honors Algebra II/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. 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 II/Trig (H) or an "A" in Algebra II (K). 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 any student who has successfully completed Algebra II (K) or Algebra II/Trig (H). 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.

## Calculus (Foerster)

Honors Designation Available

### Course Texts:

*Calculus: Concepts and Applications*, Paul A. Foerster, © 2012 (T4094)- Solutions Manual, Optional, (T4094A)

### Course Materials:

- Programmable Graphing Calculator, preferably TI-83 or TI-84 model (required)
- Calculator Programs – download at www.keymath.com, scroll down, and click on Calculus
- Not available from Kolbe- An AP Calculus prep book for students interested in taking either AP exam.

### Course Description:

This course plan includes a one year course (10 credits) in high school Calculus. The Kolbe Honors Calculus I and II (H) course prepares the student for the AP Calculus BC exam, which typically gives Calculus I and II 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 I 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: a "A" or better in Algebra II/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 II/Trig (H), or successful completion of PreCalculus (K or H).

## Algebra I (Saxon)

### Course Texts:

*Saxon Algebra 1, 3rd*edition (T4091)Solution Manual for*Saxon Algebra 1*(T4091A), Optional

### 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 I course. Upon completion of Saxon's Algebra I, 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 I, Algebra II, 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.

This course covers the following topics: division by zero, reciprocal and multiplicative inverse, exponents, algebraic phrases, word problems, canceling, ratio, conjunctions, dividing fractions, domain, elimination, closure, probability, algebraic proofs, rational equations functions.

## Algebra II 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 II."*

### Course Texts:

*Saxon Algebra 2, 3rd*edition (T4092)- Solution Manual for
*Saxon Algebra 2*(T4092A), Optional

### Course Description:

The following course covers the basics of Algebra II and good deal of Geometry. The only students that should be using this Algebra II course are those who have completed Saxon's course in Algebra I. Please be advised that Saxon does not have a separate Geometry course. The author instead integrates all Geometry concepts throughout the Algebra I, Algebra II, 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, and 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:

*Saxon Advanced Mathematics*, 2nd edition. (T4098)- Solution Manual for
*Saxon Advanced Math*(T4098A), Optional

### 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 I and II two-year (20 credits) track.

This course provides, among other topics, in-depth coverage of the following: trigonometry, logarithms, geometry, analytic geometry.

## Advanced Math I: Algebra III 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:

*Saxon Advanced Mathematics*, 2nd edition. (T4098)- Solution Manual for
*Saxon Advanced Math*(T4098A), Optional

### 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 I and II two-year (20 credits) track, beginning with this course, Algebra III with Geometry.

This course provides, among other topics, in-depth coverage of the following: trigonometry, logarithms, geometry, analytic geometry.

## Advanced Math II: Precalculus (Saxon)

### Course Texts:

*Saxon Advanced Mathematics*, 2nd edition. (T4098)- Solution Manual for
*Saxon Advanced Math*(T4098A), Optional

### Course Description:

The only students that should be using this PreCalculus course are those who have completed Advanced Math I: Algebra III 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 III 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 I (Saxon)

### Course Texts:

*Saxon Calculus*, 2nd Edition, © 2007 (T4099)- Solutions Manual for
*Saxon Calculus*(T4099A), Optional

### 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 I course will have a firm foundation in Calculus I concepts and a brief introduction to Calculus II concepts. Students may wish to proceed for an additional full year of Calculus II 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 II/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 I and II course described below.

Topics include: PreCalculus review, limits and their properties, introduction to differentiation, techniques of differentiation, applications of differentiation, and an introduction to integration.

## Calculus II (Saxon)

### Course Texts:

*Saxon Calculus*, 2nd Edition, © 2007 (T4099)- Solutions Manual for
*Saxon Calculus*(T4099A), Optional

### 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 II course will have a firm foundation in Calculus II concepts. After completing Calculus I 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 and sequences.

## Calculus I and II (Saxon)

### Honors Designation Available

### Course Texts:

*Saxon Calculus*, 2nd Edition, © 2007 (T4099)- Solutions Manual for
*Saxon Calculus*(T4099A), Optional

### 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 I and II track will have a firm foundation in Calculus I and II 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 II/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 and their properties, introduction to differentiation, techniques of differentiation, applications of differentiation, introduction to integration, applications of integration, techniques of integration, analytical geometry, series and sequences.