Welcome to Xian Yun Academy’s Math Department!

**Course Descriptions**

Algebra 1

**Grades Offered:** 9, 10 **Prerequisites:** 8th Grade Math or equivalent **UC Approved:** Yes

In Algebra 1, students will write algebraic expressions, solve linear equations and simple linear systems, and graph relationships. They will solve quadratic equations by factoring, completing the square, and graphically. They will understand rate of change, inequalities, monomial and polynomial expressions, exponents, and functions. They will understand the practical applications and real-world uses of algebra.

*Students may take this course in 7th or 8th grade for high school credit.

**Grades Offered:** 9, 10 **Prerequisites:** Algebra 1 or equivalent **UC Approved:** Yes

In this course, students will:

- Inquire and describe geometric patterns and plane shapes using angles and proportions of side lengths.
- Fold paper shapes to understand congruence by means of the rigid motions translations, rotations, and reflections.
- Understand and write proofs for geometric theorems.
- Make geometric constructions, using compasses and straightedge, to copy, reduce, and enlarge plane shapes, thus understanding similarity.
- Use geometric modeling, and solve problems involving right triangles and their side ratios, as well as angles with circles.
- Express geometric properties of curves such as circles and parabolas, using equations, thus connecting geometry with algebraic methods.
- Use addition and multiplication rules to determine probabilities of chance events, such as with rolling dice.
- Understand and apply the different formulas used with surface area and volume of solids.

Grades Offered: 9, 10 Prerequisites: Algebra 1 or equivalent UC Approved: Yes

In this course, students will:

- Write expressions for various situations, leading to absolute-value and quadratic functions, polynomial and radical functions, as well as exponential and logarithmic, and rational functions.
- Expand the understanding of numbers to imaginary and complex numbers.
- Create, recognize, and solve different types of equations and inequalities, related to the above mentioned functions.
- Get a deeper understanding of trigonometric ratios, using the unit circle and graphs, and proving basic trigonometric identities.
- Understand conics as geometric expressions of equations of second order with emphasis on circles and parabolas, thus connecting algebra with geometry.
- Expand the understanding of data analysis and statistics, using normal distribution.
- Describe sequences and calculate series.

Grades Offered: 10, 11, 12 Prerequisites: Algebra 2 or equivalent UC Approved: Yes

In this course, students will:

- Review functions from Algebra II, representing them with words, tables, graphs, and equations, and use the complex number plane, writing complex numbers in rectangular and polar form.
- Simplify Polynomial, Rational, and Exponential Expressions, and graph various functions showing key features.
- Use trigonometric functions to model phenomena, such as sound.
- Systematically solve systems of linear equations and inequalities.
- Understand and use vectors, for example to describe forces and other physical quantities.
- Understand and use matrices, for example to describe transformations.
- Describe inverse functions graphically and algebraically.
- Expand the understanding of how to describe lines, parabolas, ellipses, and hyperbolas using equations.
- Define functions using parameters and polar coordinates.

Grades Offered: 11, 12 Prerequisites: Algebra 2 and Pre-Calculus or equivalent UC Approved: Yes

In this course, students will:

- Get an idea about the two basic problems of calculus and their meaning from the viewpoints of geometry and physics.
- Learn the rules to calculate derivatives of functions, and use them in various applications such as curve sketching and optimization problems.
- Learn how to calculate integrals, and use them to calculate areas and volumes.
- Expand their understanding of differentiation and integration to exponential and logarithmic functions.
- Understand and solve differential equations, using different methods.
- Prepare for the AP test.
- Know some more applications but also the limits of calculus.

Grades Offered: 11,12 Prerequisites: Geometry and Algebra 2 or equivalent Recommended: Pre-Calculus UC Approved: Yes

Discrete mathematics is the field that underlies much in computer science. This kind of math mostly deals with the use of integers. Our course will also require students to write mathematical proofs. Although we will introduce several computer science type projects during the year, this is __not__ a computer science course. Students must expect to be primarily solving mathematical problems; writing proofs and/or using mathematical induction; studying integers and their divisibility properties; analyzing, searching, and sorting algorithms; and working with graphs and sets. The main topics of the course revolve around basic logic, lists and sets, relations and partitions, advanced proof techniques, recurrence relations, functions and their properties, permutations and symmetry, discrete probability theory, number theory, and graph theory.

This is a full-year course primarily intended for high school seniors. All students must have already taken and passed a high school level geometry course and an algebra II course as a prerequisite. It is recommended that students have also taken and passed a pre-calculus course.

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