# Math Department Curriculum

The Presentation Math Department offers students a wide range of course offerings from Algebra I to AP Calculus.

Classes are presented at regular, honors and AP levels, while electives offer variety and the potential to “double up” for students who want to build a strong math resume.

Students may be exempted from taking Algebra I and Geometry by passing challenge tests, which are given in May.

## Math Courses

- Algebra I
- Geometry
- Honors Geometry
- Algebra II
- Honors Algebra II
- Statistics I
- Statistics II
- AP Statistics
- Precalculus
- Honors Precalculus
- Calculus I
- AP Calculus AB
- AP Calculus BC
- Honors Multi-Variable Calculus
- AP Computer Science A

## Algebra I

**Grade: 9Credits: 10**

This is a standard course in algebra designed to develop an understanding of a mathematical system, the algebra of real numbers. It focuses on the properties of real numbers, solving linear and quadratic functions in the coordinate plane, solving linear systems of equations, factoring, applications of algebra in problem solving, functions and relations, polynomials, factoring, simplifying rational expressions, solving rational equations, solving systems of equations, radical expressions, applications with rational numbers, graphing and solving quadratics.

## Geometry

**Grade: 9, 10, 11**

**Credits: 10**

**Prerequisite: ****aD- or better in each semester of Algebra I **

This course includes all of the basic concepts and constructions of plane and solid geometry. Emphasis is placed on the development of logic, beginning with a set of axioms and postulates which are then used in the proofs of theorems and in solving problems. The course emphasizes exploration and testing of mathematical ideas by using manipulatives and open-ended questioning to lead to concepts. This course also includes an introduction to the trigonometry of right triangles, and provides a continuing review of the skills developed in Algebra I.

## Honors Geometry

**Grade: 9, 10
Credits: 10
Prerequisite: **
B+ or better in each semester of Algebra I. Students currently enrolled in the daily Algebra course may not enroll in Honors Geometry.

Honors Geometry covers the topics in the Geometry curriculum at a faster pace and with an emphasis on developing abstract reasoning skills. It is designed to provide a challenge for students who are strong in math and to move them toward a more theoretical approach to the subject matter. Enrichment includes additional trigonometry topics of the Law of Sines and the Law of Cosines, as well as degree and radian measure. Some non-Euclidean topics are also explored.

## Algebra II

**Grade: 10, 11, 12**

**Credits: 10**

**Prerequisite: ****D- or better in each semester of Geometry or Honors Geometry; summer Geometry student with B or better.**

This course continues the development of algebraic structures begun in Algebra I in areas such as linear systems, quadratic functions, polynomial functions, and graphing in the coordinate plane. New topics include quadratic systems, complex numbers, conic sections, exponential functions and logarithms, and series and sequences. This course, together with Algebra I and Geometry, satisfies the requirement of many colleges for three years of college preparatory mathematics.

## Honors Algebra II

**Grade: 9, 10, 11**

**Credits: 10**

**Prerequisite: **
B+ or better unweighted math GPA AND B+ or better in each semester of Geometry or B- or better in each semester of Honors Geometry; summer Geometry student with A-.

This course continues the development of algebraic structures begun in Algebra I with the study of functions, irrational and complex numbers, quadratic functions, systems of equations, conic sections and exponential and logarithmic functions. These topics are the same as regular Algebra II, but will be covered in greater depth. Additionally, it will include the topics of series and sequences, probability, combinatorics, binomial expansion/Binomial Theorem, logic and proof techniques. This course, together with Algebra I and Geometry (or Honors Geometry), satisfies the requirement for three years of college preparatory mathematics. Due to the fast pace and depth of topics, it is recommended for STRONG math students only.

## Statistics I

**Grade: 11-12
Credits: 5
Prerequisites: D- or better in Algebra II**

This course introduces the fundamental ideas of probability and statistics. It is a graphing-calculator based course. There is a heavy emphasis on sampling, simulations, and graphing. The course is designed for students with a wide variety of vocational interests, and applications are taken from many fields. Curriculum includes but is not limited to Observational/Experimental Design; Graphing; Centers and Variation; Linear Regression; Probability; Discrete Distributions.

## Statistics II

**Grade: 11-12 Credits: 5 Prerequisite: D- or better in Statistics I**

This course introduces the fundamental ideas of statistical inference including Confidence Intervals and Hypothesis Testing. It is a graphing-calculator based course. There is a heavy emphasis on sampling, simulations, and graphing. The course is designed for students with a wide variety of vocational interests, and applications are taken from many fields. The curriculum includes but is not limited to Normal Distribution; Sampling Distributions; One Sample CI and Testing for Means and Proportions; Two Sample CI and Testing for Means and Proportions; Chi Squared Testing.

## AP Statistics

**Grades: 10, 11, 12
Credits: 10
Prerequisite: **

**Prerequisite: **
C+ or better in each semester of Honors Algebra II or B+ or better in each semester of Algebra II

The purpose of the AP Statistics course is to introduce major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four broad conceptual themes:

- Exploring Data: Describing patterns and departures from patterns
- Sampling and Experimentation: Planning and conducting a study
- Anticipating Patterns: Exploring random phenomena using probability and simulation
- Statistical Inference: Estimating population parameters and testing hypotheses

Students who successfully complete the course and exam may receive credit, advanced placement, or both for a one-semester introductory college statistics course.

## Precalculus

**Grades: 11, 12
Credits: 10
Prerequisite: **
B- or better in each semester of Algebra II or C or better in each semester of Honors Algebra II

This course includes the study of trigonometry, analysis of functions with graphing including linear, absolute value, rational, irrational, quadratic and higher powers,log, an introduction to vectors, polar, and parametric functions and graphing. The course concludes with an introduction to calculus covering limits, continuity and basic derivatives.

## Honors Precalculus

**Grade: 11, 12**

**Credits: 10**

**Prerequisite: **
B- or better in each semester of Honors Algebra II or A in both semesters of Algebra II.

In the first semester, this course provides a comprehensive study of trigonometry, including circle trigonometry, triangle trigonometry, trigonometric identities and formulas, graphing trigonometric functions, inverse trigonometric functions, solving trigonometric equations, polar coordinates, and two and three dimensional vectors. It also covers parametric equations, rotation of conic sections, and polar equations in parametric form. In the second semester, concepts covered on the AP Calculus AB test will be introduced: the concept of limits, continuity of functions, differentiation and applications of derivatives, such as maximum and minimum problems as well as distance, velocity, and acceleration will be covered. Because of the difficulty in concepts, and the amount of time needed for study, this course is recommended only for VERY STRONG students in math.

## Calculus I

**Grade: 12**

**Credits: 10**

**Prerequisite: **
C or better in each semester of Honors Precalculus or B- or better in each semester of Precalculus

This year-long course is for students who wish to take a beginning Calculus course, without the rigor of the AP Calculus courses and without the full range of AP Calculus topics. This class will move more slowly and provide more assistance and practice time than the AP Calculus courses. This class will provide a solid foundation for students wishing to take Calculus in college. This course includes a study of functions and graphing, limits, continuity, differential Calculus and its applications, and integral Calculus and its applications.

## AP Calculus AB

**Grade: 10-12 **

**Credits: 10 **

**Prerequisite: B- or better in each semester of Honors Precalculus or A in each semester of Precalculus**

This course will review and build on derivatives and their applications and introduce the concept of integration, its techniques and applications. The course will cover the range of topics on the AP Calculus AB test with some review of the AP Calculus AB test offered. Strong honors math students with a B+ or better in Honors PreCalculus are encouraged to bypass AB and enroll in AP Calculus BC. Passing the College Board AP Calculus AB exam gives the student credit for ONE semester of college calculus, where taking the AP Calculus BC course and passing the AP Calculus BC exam gives the student TWO semesters of college calculus credit.

## AP Calculus BC

**Grade: 10-12**

**Credits: 10**

**Prerequisite: B or better in each semester of Honors Precalculus or B- or better in each semester of AP Calculus AB**

The first semester will introduce the concept of integration and its techniques. It will cover applications of integral calculus, such as solids and surfaces of revolution, and the range of topics on the AP Calculus AB test. The second semester will continue with advanced techniques of integration and applications of integration, such as average value of a function and arc length. It will also cover differential equations, slope fields, sequences and infinite series, parametric equations, polar coordinates, vectors and vector functions, and the range of topics on the AP Calculus BC test with some review of the AP Calculus AB and BC test offered.

Strong honors math students with a B+ or better in Honors PreCalculus are encouraged to bypass AB and enroll in AP Calculus BC. Passing the College Board AP Calculus AB exam gives the student credit for ONE semester of college calculus, where taking the AP Calculus BC course and passing the AP Calculus BC exam gives the student TWO semesters of college calculus credit.

## Honors Multi-Variable Calculus

**Grade: 11-12**

**Credits: 10 **

**Prerequisite: **
B- or better in each semester of AP Calculus BC

This year-long course is designed to provide students who have completed AP Calculus BC with the opportunity to take a third year or fourth year of math and prepare them for further studies of mathematics. It will offer rigorous preparation for college level math and deepened their understanding of what they have learned in previous math classes. Students will study vectors and geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. They will also use maple software to assist them with visualizing objects in 3-Ds, computing problems and checking their answers, doing projects and independent exploration.

## AP Computer Science A

**Grade: 10, 11, 12**

**Credits: 10**

**Prerequisite: **
B or better in each semester of Algebra II or C or better in each semester of Honors Algebra II. (UC approved G (elective) category only)

The AP Computer Science A course is an introductory course in computer science. Because the design and implementation of computer programs to solve problems involve skills that are fundamental to the study of computer science, a large part of the course is built around the development of computer programs that correctly solve a given problem. These programs should be understandable, adaptable, and, when appropriate, reusable. At the same time, the design and implementation of computer programs is used as a context for introducing other important aspects of computer science, including the development and analysis of algorithms, the development and use of fundamental data structures, the study of standard algorithms and typical applications, and the use of logic and formal methods. In addition, the responsible use of these systems is an integral part of the course. The topic outline on pages 8–10 summarizes the content typically taught in the AP Computer Science A course.

## Contact

Shikha Naik

Department Chair

(408) 264-1664, ext. 2936

snaik@presentationhs.org