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# High School Math

## Objectives/ Alabama State Standards

Our math program is designed to provide students with learning experiences which will provide them with college and career readiness. A strong focus is put on students learning to apply math skills to real world situations and developing a deep understanding of higher level math concepts. Math courses are based on STEM principles and integrate technology into learning. Courses offered include Algebra 1, Algebra 2, Geometry and Precalculus all of which are aligned to the Common Core State Standards.

### Algebra 1

#### Course Description

Algebra 1 introduces students to variables, algebraic expressions, equations, inequalities, functions, and all their multiple representations. In this class, students will develop the ability to explore and solve real-world application problems, demonstrate the appropriate use of graphing calculators, and communicate mathematical ideas clearly. This course lays the foundation for mathematical literacy that will help students be successful in every subsequent course in mathematics.This course is aligned to the Common Core State Standards for Algebra 1.

#### By the end of this course, students will be able to:

• Understand and represent properties through quantities, patterns, and relationships
• Understand equivalencies, solve equations, and understand proportions
• Represent relationships between quantities that are not equal
• Solve and understand inequalities
• Represent and describe functions and use them in real world situations
• Interpret equations of lines, make predictions based on scatter plots, and interest lines on a graph
• Solve a system of equations or inequalities and use them in real world settings
• Know the characteristics of exponential functions and simply expressions involving exponents
• Understand differences between algebraic expressions and relate properties of real numbers to polynomials
• Understand, interpret, and solve the quadratic equation
• Use functions in real world situations
• Understand, represent, and solve radical expressions and equations
• Understand, represent, and solve rational expressions and equations
• Collect and analyze data and interpret different representations of data
• Use probability in real world settings

### Algebra II

#### Course Description

In this course students will learn about a variety of advanced topics in algebra. Students will expand their understanding about functions by learning about polynomial, logarithmic, and trigonometric functions. These new functions along with linear, quadratic, and exponential, will be used to model a variety of problems, including compound interest, complex numbers, growth and decay, projectile motion, and periodic phenomena. Polynomial and rational algebra is extensively covered including advanced factoring and polynomial long division. Advanced work in probability is included that focuses on the use of conditional probability. Extensive statistics work is done to help students understand how population parameters can help to infer properties about populations. This course is aligned to the Common Core State Standards for Algebra II.

#### By the end of this course, students will be able to:

• Perform arithmetic operations with complex numbers
• Use complex numbers in polynomial identities and equations
• Interpret the structure of expressions
• Write expressions in equivalent forms to solve problems
• Perform arithmetic operations on polynomials
• Understand the relationship between zeros and factors of polynomials
• Use polynomial identities to solve problems
• Rewrite rational expressions
• Create equations that describe numbers or relationships
• Understand solving equations as a process of reasoning and explain the reasoning
• Represent and solve equations and inequalities graphically
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations
• Build a function that models a relationship between two quantities
• Build new functions from existing functions
• Construct and compare linear and exponential models and solve problems
• Extend the domain of trigonometric functions using the unit circle
• Model periodic phenomena with trigonometric functions
• Prove and apply trigonometric identities
• Summarize, represent, and interpret data on a single count or measurement variable
• Understand and evaluate random processes underlying statistical experiments
• Make inferences and justify conclusions from sample surveys, experiments, and observational studies
• Use Probabilities to make fair decisions

### Geometry

#### Course Description

In this course students will acquire tools to help them explore two-dimensional and three-dimensional space. These tools include Euclidean geometry, rigid motion transformations, dilations and similarity, and coordinate geometry. Students will learn how to prove various geometric facts about triangles, quadrilaterals, and circles by using axiomatic proof and coordinate geometry proof. Finally, students will model real world objects using geometric formulas for perimeter, area, and volume. Three dimensional objects such as prisms, pyramids, cones, cylinders, and spheres will be used in a variety of models. This course is aligned to the Common Core State Standards for Geometry.

#### By the end of this course, students will be able to:

• Experiment with transformations in the plane
• Understand congruence in terms of rigid motions
• Prove geometric theorems
• Make geometric constructions
• Understand similarity in terms of similarity transformations
• Prove theorems involving similarity
• Define trigonometric ratios and solve problems involving right triangles
• Apply trigonometry to general triangles
• Understand and apply theorems about circles
• Find arc lengths and areas of sectors of circles
• Translate between the geometric description and the equation for a conic section
• Use coordinates to prove simple geometric theorems algebraically
• Explain volume formulas and use them to solve problems
• Visualize relationships between two-dimensional and three-dimensional objects
• Apply geometric concepts in modeling situations
• Understand independence and conditional probability and use them to interpret data
• Use the rules of probability to compute probabilities of compound events in a uniform probability model
• Use Probability to evaluate outcomes of decisions

### Precalculus

#### Course Description

Precalculus builds on the study of algebra and functions in Algebra II with Statistics, adding rational functions, all trigonometric functions, and general piecewise-defined functions to the families of functions considered. In addition to focusing on the families of functions, Precalculus takes a deeper look at functions as a system, including composition of functions and inverses. Precalculus also expands on the study of trigonometry in previous courses and considers vectors and their operations.

#### By the end of this course, students will be able to:

• Identify functions and determine their domains, ranges, y-intercepts, and zeros
• Evaluate continuity, end behavior, limits, and extrema of a function
• Calculate rates of change of nonlinear functions
• Identify parent functions and transformations
• Perform operations with functions, identify composite functions, and calculate inverse functions
• Graph and analyze power, radical, polynomial, and rational functions
• Divide polynomials using long division and synthetic division
• Use the Remainder and Factor Theorems
• Find all zeros of polynomial functions
• Solve radical and rational equations
• Solve polynomial and rational inequalities
• Identify the mathematical domains, ranges, and end behaviors of exponential and logarithmic functions
• Use the properties of exponents and logarithms to solve exponential and logarithmic equations
• Collect and organize data, make and interpret scatter plots, fit the graph of a function to the data, and interpret the results
• Use the function models to predict and make decisions and critical judgements
• Use nonlinear regression
• Solve right triangles using trigonometric and inverse trigonometric functions
• Convert between degrees and radians
• Solve real-world problems using trigonometric functions
• Graph trigonometric functions and their inverses
• Solve oblique triangles and find their area using various laws and formulas
• Identify and use trigonometric identities to find trigonometric values
• Use trigonometric identities to simplify and rewrite trigonometric expressions
• Verify trigonometric identities
• Solve trigonometric equations
• Use sum and difference identities to evaluate trigonometric functions
• Use double-angle, power-reducing, half-angle, and product-to-sum identities to evaluate trigonometric expressions and solve trigonometric equations
• Solve systems of linear equations using matrices and Gaussian or Gauss-Jordan elimination
• Multiply matrices
• Find determinants and inverses of 2 X 2 and 3 X 3 matrices
• Solve systems of linear equations using inverse matrices and Cramer’s Rule
• Write partial fraction decompositions of rational expressions with linear and irreducible quadratic factors
• Use linear programming to solve applications
• Recognize situations in which there are no solutions or more than one solution of a linear programming application
• Analyze, write, and graph equations of parabolas, ellipses, circles, and hyperbolas
• Use equations to identify types of conic sections
• Use rotation of axes to write equations of rotated conic sections
• Graph rotated conic sections
• Graph parametric equations
• Solve problems related to the motion of projectiles
• Represent and operate with vectors both geometrically and algebraically
• Resolve vectors into their rectangular components
• Write a vector as the linear combination of unit vectors
• Find the dot product of two vectors and use the dot product to find the angle between them
• Find the projection of one vector onto another
• Graph and operate vectors in space
• Find the dot and cross products of and angles between vectors in space
• Find areas of parallelograms and volumes of parallelepipeds in space
• Graph points with polar coordinates
• Graph polar equations
• Identify and graph classic polar curves
• Convert between polar and rectangular coordinates
• Convert between polar and rectangular equations
• Identify polar equations of conics
• Write and graph the polar equation of a conic given its eccentricity and the equations of its directrix
• Convert complex numbers from rectangular to polar form and vice versa
• Find products, quotients, powers, and roots of complex numbers in polar form
• Use sigma notation to represent and calculate sums of series
• Find nth terms of arithmetic sequences and arithmetic series
• Find nth terms of geometric sequences and geometric series. Find the sums of infinite geometric series
• Use mathematical induction to prove summation formulas and properties of divisibility involving positive integer n
• Use Pascal’s triangle or the Binomial Theorem to write binomial expansions
• Use Binomial Theorem to find the coefficients of specified terms in binomial expansions
• Use a power series to represent a rational function
• Use power series representations to approximate values of transcendental functions
• Identify shapes of distributions
• Construct probability distributions, including binomial distributions
• Find probabilities for normal distributions and data values given probabilities
• Understand and apply Central Limit Theorem
• Find confidence intervals using both t and z statistics
• Formulate and test hypotheses using test statistics and p-values
• Find and interpret linear correlation coefficients
• Find linear regression lines
• Determine the appropriateness of using a linear model
• Estimate limits of functions at fixed values and at infinity
• Evaluate limits of polynomial and rational functions at selected points and at infinity
• Find instantaneous rates of change by calculating slopes of tangent lines
• Find instantaneous rates of change by calculating derivatives
• Use the Product and Quotient Rules to calculate derivatives
• Approximate the area under a curve using rectangles
• Approximate the area under a curve using definite integrals and integration
• Find antiderivatives
• Use the Fundamental Theorem of Calculus