Math

Algebra 1 – 0391T

Grades: 9, 10, 11, 12 Length: 2 Semesters Credits: 1

Description: Students extend their understanding of functions to explore specific function families, including linear, exponential, quadratic, linear absolute value, and linear piecewise functions. Students analyze and search for patterns in sequences of numbers to recognize that all sequences are functions. Finally, students analyze patterns in data to formalize their understanding of lines of best fit. Students investigate linear functions as the most basic polynomial function and prove that linear functions grow by equal differences over equal intervals. They are introduced to function transformation and investigate dilations and vertical translations of linear functions. They extend their knowledge of solving one-variable equations to solve more complex equations and inequalities; and they learn more sophisticated strategies to solve linear systems of equations. Finally, students connect what they know about the absolute value of a number and the line y = x to build the basic absolute value function. They transform and learn strategies to solve absolute value functions. Students learn that certain geometric sequences can be defined as exponential functions. Through the investigation of exponential functions, they develop an understanding of rational exponents. Students transform exponential functions and distinguish between growth and decay scenarios. Students summarize, represent, and interpret data on a single count and on two categorical variables. They analyze the shape of data distributions and identify possible outliers and their impact on measures of center and spread. They learn to calculate and interpret standard deviations of symmetrical data sets. Students explore quadratic functions in real-world situations using graphing technology. They rewrite quadratic functions in different equivalent forms to reveal certain properties and apply what they know about function transformation. Students solve quadratic equations and complete the square to derive the Quadratic Formula. Students apply what they know about inequalities, systems, and regressions to solve real-world problems. Students will need a TI-84 Graphing Calculator.

Geometry - 03870

Grades: 10, 11, 12 Length: 2 Semesters Credits: 1

Prerequisite: Successful completion of Algebra 1.

Description: Students are introduced to the goal of the course at the beginning: to move from informal to formal geometric thinking. They construct a coordinate plane from squares, explore parallel and perpendicular lines and their equations, and then reason about distances on the coordinate plane to classify polygons. Students compose and decompose shapes to develop conjectures about the properties of shapes. They then formally define rigid motions in terms of parallel lines, distances across perpendicular lines, and distances around concentric circles. Students move from analysis to abstraction, where they define properties and congruence relationships precisely and construct informal arguments as to whether these properties and relationships are true in all cases. Once students understand the formal definitions of geometric functions, they can use them to determine whether two figures are congruent by specifying a sequence of rigid motion transformations that maps one figure onto the other. As students work through the module, they learn to construct formal proofs. In Module 3, students extend the proportional reasoning they developed in middle school. This involves learning the properties of similar figures, dilating figures, and recognizing when figures are similar or distorted. From similarity, students discover the sine, cosine, and tangent ratios along with the related cosecant, secant, and cotangent ratios. They use these ratios to solve problems for unknown side lengths and angles. In Module 4, proportionality is further explored and students define radian measure as a constant of proportionality. They calculate arc length and determine the area of a sector. Students develop the volume formulas. They then connect the algebraic and geometric representations of two conic sections on the coordinate plane. In Module 5, students discover the Counting Principle. They then calculate the probabilities of the intersection of events and the union of events, establishing the Rule of Compound Probability involving and the Addition Rule for Probability. Students learn how to use permutations and combinations to count the number of elements in a sample space and extend the pattern to connect Pascal’s Triangle to the probability of multiple trials of independent events. Students will need a TI-84 Graphing Calculator, a compass, and a protractor.

Algebra 2 - 03915

Grades: 10, 11, 12 Length: 2 Semesters Credits: 1

Prerequisite: Successful completion of Algebra 1 and Geometry.

Description: Students explore patterns modeled by functions and review the structure of quadratics. They interpret and build polynomial functions of higher degree using key characteristics and transformations. Students focus on interpreting polynomial functions that arise in applications and analyzing them using different representations. They then synthesize their understanding of rational numbers and polynomial functions to investigate rational functions. Students invert exponential functions to explore key characteristics of logarithmic functions. Students build on their knowledge to solve exponential and logarithmic equations arising from real world situations. Students express trigonometric functions as coordinate pairs on the unit circle. They model real world phenomena with trigonometric functions and solve trigonometric equations. Students explore the characteristics of normal distributions. They consider methods of collecting data and then explore specific techniques to select representative samples. Students will need a TI-84 Graphing Calculator.

Algebra 3 - 03928

Grades: 11, 12 Length: 2 Semesters Credits: 1

Prerequisite: Successful completion of Algebra 1, Geometry, and Algebra 2.

Description: The Algebra 3 course will further develop the Algebra 2 skills for students entering the Pre-Calculus Honors course or a College Algebra course after high school. This course can be thought of as a bridge between Algebra 2 and Pre-Calculus Honors. This course will cover but is not limited to the following: review of linear and quadratic functions; analyzing polynomial, radical, rational, exponential, logarithmic functions; sequences and series; quadratic relations and conic sections; probability and statistics; matrices; periodic functions and trigonometry; trigonometric identities and equations. Students will need a TI-84 Graphing Calculator.

Calculus AB Honors AP – 04050 & 04060

Grades: 12 Length: 2 Semesters Credits: 1

Dual Credit: St. Louis University – MATH 1510 (4 credit hours @ $75/credit hour)

Prerequisite: To reach this level, students must start in Geometry Honors as a freshman, or concurrently take two math

classes in the honors math pathway prior to their senior year.

Description: This course is designed to develop students’ understanding of the concepts of Calculus and provide experience with its methods and applications. The concepts, results, and problems, will be expressed geometrically, numerically, analytically, and verbally. Students should understand the meaning of the derivative in terms of rate of change and local linear approximations; work with functions represented graphically, numerically, analytically or verbally, and should understand the connections among these representations. Students should understand the meaning of the definite integral both as a limit of Riemann sums and as a net accumulation of rate of change, and understand the relationship between the derivative and integral. They should be able to model problem situations with functions, differential equations or integrals, and communicate both orally and in written form, represent differential equations with slope fields, solve separable, differential equations analytically, and solve differential equations using numerical techniques such as Euler’s method. Students are encouraged to take the AP Exam: Calculus AB. Students will need a TI-84 or TI-Nspire graphing calculator.

Statistics Honors- Honors AP - 03880

Grades: 12 Length: 2 Semesters Credits: 1

Dual Credit: LCCC - Math 235- LCCC charges $40 for this course.

Prerequisite: District Prerequisites include: Successful completion of Algebra 1, Geometry, and Algebra 2. To receive dual credit, additional prerequisites may apply.

Description: The Statistics course brings together prior Algebra and Geometry concepts. The course provides students the skills and ideas necessary for a seamless transition into a college entry-level mathematics course. Students in Statistics will cover various topics including: survey design, data display and descriptive values, probability, confidence intervals, hypothesis testing, correlation and regression, ChiSquare test, the F-distribution, and nonparametric tests. Students will need a TI-84 or TI-Nspire graphing calculator.

Trigonometry - 03882

Grades: 12 Length: 1 Semester Credits: 1/2

Prerequisite: Students must have passed both semesters of Algebra 1, Geometry and Algebra 2 with a grade of C or better.

Description: Students are required to have a TI84 graphing calculator. The Trigonometry course brings together prior Algebra and Geometry concepts. The course provides students the skills and ideas necessary for a seamless transition to a college entry-level mathematics course. Students in Trigonometry will cover the topics of: trigonometric functions in acute, right, and obtuse triangles, radian measure and circular functions, graphs of circular functions, trigonometric identities, inverse circular functions and trigonometric equations, and applications of trigonometry. Students will need a TI-84 or TI-Nspire graphing calculator.