**NC Math 2 Curriculum Overview (NCFE) **

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 Math 3 Curriculum Overview (END OF COURSE EXAM) **

Students graph and analyze piecewise functions. They identify key features and interpret them in context. Students recognize absolute value functions as a type of piecewise function. They solve absolute value equations and inequalities algebraically and use them to solve problems.

Students extend their understanding of exponential functions by building rules and rewriting the rates of change for contextual situations. They define logarithms and use them to solve exponential equations. Students identify inverse functions, describe their characteristics and write them for linear, exponential, and quadratic functions.

Students extend their understanding of polynomial functions to include those with a degree of 3 or higher. They identify and interpret key features. They connect the zeros of the function to the graph. Students use multiple representations of polynomial functions to model and solve problems.

Students use geometry and algebra concepts to model and solve problems. Geometry concepts include perimeter, area, volume. Contextual situations include density, design and optimization.

Students are introduced to rational functions. They graph and identify key features. They operate with rational expressions building upon their understanding of operations with rational numbers. Students build and solve rational equations using tables, graphs, and algebraic reasoning.

Students prove properties of parallelograms. They analyze and apply relationships between angles, arcs, and line segments of a circle. Students use the relationships to solve problems. They understand the proportional relationships within circles to calculate arc length, area of a sector and radians.

Students extend their understanding of the trigonometric ratios to build functions that model periodic change. They understand the relationships between the ratios and points on the circle. Students graph and interpret key features within context.

Students use statistical reasoning to draw conclusions. They distinguish between the different types of statistical studies. They understand the role of random sampling. Students use data from surveys or simulations to make inferences and draw conclusions.

Students extend their understanding of the different types of functions. Students solve non-linear systems of equations using graphs and tables. They also apply transformations to build new functions.