### Math in Upper School 3

Upper School students are able to take the appropriately-challenging math class based on their understanding and skills in math. Math placement is based on a number of factors including demonstrated skills and knowledge, prerequisite experience, and past performance on classes and tests. The following math courses may be offered to Upper School 3 students:

### Algebra A

Students begin their exploration of the first half of the Algebra I curriculum with a focus on problem-solving, discussion, and developing confidence in math. Students develop advanced problem-solving skills, perseverance, and creativity through explorations of progressively complex mathematical concepts from the *Pearson* text series.

Students will:

- Evaluate and simplify expressions
- Master divisibility, factors, exponents, radicals and rational numbers.
- Solve equations and inequalities.
- Work with exponents and scientific notation.
- Graph and find equations of lines and systems on the coordinate plane.

### Algebra I

Students delve deeper into foundations of Algebra using Pearson’s* Algebra I *textbook and *The Art of Problem Solving: Introduction to Algebra* as core texts. Students develop advanced problem-solving skills, perseverance, and creativity through explorations of progressively complex mathematical concepts.

Students will:

- Identify arithmetic, geometric, and exponential patterns.
- Graph linear and quadratic equations and inequalities, and absolute value functions.
- Factor polynomials, exponentials, logarithms, and other functions.
- Analyze complex numbers.
- Solve one-variable equations and linear systems with multiple variables.

### Algebra II

Students build on foundations of algebra utilizing *The Art of Problem Solving: Intermediate Algebra* as a core text. In this Algebra course, students delves deeper into the algebraic concepts with progressively greater complexity. While the focus remains on students developing advanced problem-solving skills, perseverance, and creativity skills while learning the mathematical topics, this course allows for students to be challenged with more advanced Algebraic problems as they master each concept.

Students will:

- Manipulate linear and polynomial functions.
- Graph polynomial, exponential, logarithmic, rational functions, and complex numbers and functions on the polar plane.
- Recognize factoring patterns.
- Model using linear and exponential relationships.
- Understand Conic sections.
- Practice Trigonometric functions and identities.

### Geometry

Students focus on geometry, trigonometry, and advanced topics in Algebra. Using *The Art of Problem Solving: Introduction to Geometry* as a core text, students continue to utilize advanced problem-solving skills, perseverance, and creativity through projects and explorations of mathematical topics. This integrated “hands-on” course enables students to explore design-thinking and STEM-based projects and ideas into their learning.

Students will:

- Explore the geometric definitions of and derive equations for the conic sections.
- Explore and use the characteristics and properties of triangles, quadrilaterals and circles to solve problems.
- Find the area of composite shapes.
- Explore different types of formal proof. Use deductive reasoning to construct proofs.
- Build on an understanding of 2-dimensional geometry to expand problem solve to figures in 3 dimensions.
- Explore trigonometry, including right triangle trigonometry and the law of sines and cosines

### Pre-Calculus

This course is primarily concerned with developing the student’s understanding of the concepts of Pre-calculus and providing experience with its methods and applications, with strong emphasis on graphical, numerical, analytical and verbal expressions.

Students will:

- Have the opportunity to work with functions represented both numerically and verbally
- Have the opportunity to apply the knowledge of pre-calculus to real-world examples
- Learn how to explain solutions to problems orally in written expressions
- Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurements
- Develop an appreciation of pre-calculus as a coherent body of knowledge
- Meaning of trigonometric functions and model a written description of a physical situation with various functions
- Communicate mathematics and explain solutions to problems both verbally and in written sentences
- Have the opportunity to explore different coordinate systems and limits

Topics explored in this course include (subject to change):

- Exponential, logarithmic, polynomial and rational functions
- Conic sections
- Partial fractions
- Polar Coordinates
- Vectors
- Trigonometric functions and their properties
- Introduction to Calculus: Differentiation and their applications

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