### Course Overview

NC Math 2 Curriculum Overview

Students explore two new functions: inverse variation and square root. They use the functions to model contextual situations, interpret their key features, and solve problems. Students identify the effect of transformations on the graphs & tables of functions. Lastly, they extend their understanding of expressions as they work with radical expressions and rational exponents.

Students extend their understanding of quadratic functions from Math 1. They rewrite quadratic expressions into vertex form by completing the square. They solve quadratic equations with real and complex solutions using quadratic formula. Students build quadratic functions using a variety of different strategies.

Students analyze and compare functions. They solve one variable inequalities using different methods. Students create and solve systems of equations that include any combination of equation types: linear, quadratic, inverse variation, and square root.

Students develop an understanding of proof while examining the properties of angles and parallel lines. They extend their understanding of transformations from middle grades to develop more formal definitions. Students use transformations as a foundation for establishing congruency and properties of geometric figures.

Students recognize dilations produce similar figures and learn to identify and use the scale factor and center of dilation to solve problems. They establish the AA criteria for similar triangles. Students reason with similar right triangles to define the trigonometric ratios and use them to solve problems.

Students use sample spaces to calculate probabilities. They develop an understanding of conditional probability and independence. Students generalize their repeated reasoning to develop probability rules and strategically use the rules to solve problems. Students compare results from simulations to theoretical probability.

NC PreCalculus Curriculum Overview

The purpose of Precalculus is to build upon the study of algebra, functions, and trigonometry experienced in previous high school mathematics courses. This course will build on students’ algebraic skills and understanding of functions to delve into real world phenomena and to deepen understanding of the functions in the course. This course is designed for students pursuing careers in STEM-related fields. Students will be prepared for Calculus, AP Calculus and any entry-level college course.

Goal 1: Number and Operations - The learner will describe geometric figures in the coordinate plane algebraically. Transform relations in two dimensions; describe the results algebraically and geometrically.
- Objective 1.01 Transform relations in two dimensions; describe the results algebraically and geometrically.
- Objective 1.02 Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results. • Solve using tables, graphs, and algebraic properties. • Interpret the constants and coefficients in the context of the problem.
- Objective 1.03 Operate with vectors in two dimensions to model and solve problems.

Goal 2: Algebra - The learner will use relations and functions to solve problems.
- Objective 2.01 Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results. • Solve using graphs and algebraic properties • Interpret the constants, coefficients, and bases in the context of the problem.
- Objective 2.02 Use trigonometric and inverse trigonometric functions to model and solve problems; justify results. • Solve using graphs and algebraic properties. • Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts. • Develop and use the law of sines and the law of cosines.
- Objective 2.03 For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions. • Interpret the constants, coefficients, and bases in the context of the data. • Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions.
- Objective 2.04 Use the composition and inverse of functions to model and solve problems.
- Objective 2.05 Use polar equations to model and solve problems. • Solve using graphs and algebraic properties. • Interpret the constants and coefficients in the context of the problem
- Objective 2.06 Use parametric equations to model and solve problems.
- Objective 2.07 Use recursively-defined functions to model and solve problems. • Find the sum of a finite sequence. • Find the sum of an infinite sequence. • Determine whether a given series converges or diverges. • Translate between recursive and explicit representations.
- Objective 2.08 Explore the limit of a function graphically, numerically, and algebraically.