HS
MA100 INTEGRATED MATH 1 Credit: 1.0
Gr.: Ability Level
Prerequisite: None
Content: Algebra, Geometry, Statistics, Discrete Mathematics, and Probability
This course is designed for students to develop the following: ability to make sense out of real-world data using graphical displays and summary statistics, ability to recognize important patterns of change among variables and to represent those patterns using tables of numerical data, coordinate graphs, verbal descriptions and symbolic rules, confidence and skill in using linear equations to model and solve problems in situations which exhibit constant (or near constant) rate of change or slope, visualization skills and the understanding of properties of space and shapes including symmetry area and volume, ability to use vertex-edge graphs to represent and analyze real-world situations involving relationships among a finite number of elements, including managing conflicts, and finding efficient routes; confidence and skill in using simulation methods, particularly those involving the use of random numbers, to make sense out of real-world situations involving change; and ability to use exponential functions to model and solve problems in situations that exhibit exponential growth and decay.
Unit 1 - Patterns of Change
Unit 2 - Patterns in Data
Unit 3 - Linear Functions
Unit 4 - Vertex Edge Graphs
Unit 5 - Exponential Functions
Unit 6 - Patterns in Shape
Unit 7 - Quadratic Equations
Unit 8 - Patterns in Chance
HSMA200 INTEGRATED MATH 2
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Integrated Math 1 is strongly recommended
Content: Algebraic Functions, Algebra 2, Geometry, Discrete Mathematics, Trigonometry, and Statistics
In this course the students would develop and extend the following: ability to recognize, describe, and use functional relationships among quantitative variables, with special emphasis on relationships that involve two or more independent variables; understanding of matrices and ability to use matrices to represent and solve problems in a variety of real-world and mathematical settings; understanding of coordinate methods for representing and analyzing properties of geometric shapes, for describing geometric change and for producing animations; understanding of the characteristics of interpretation of the least squares regression equation and of the use of correlation to measure the strength of the linear association between two variables; ability to construct and reason with functions that model parabolic shapes and other quadratic relationships in science and economics, with special emphasis on formal symbolic reasoning methods, and introduces common logarithms and algebraic methods for solving exponential equations; understanding of trigonometric functions and the ability to use methods to solve triangulation and indirect measurement problems.
Unit 1-Functions, Equations and Systems
Unit 2-Matrix Methods
Unit 3- Coordinate Methods
Unit 4-Regression and Correlation
Unit 5-Non-Linear Functions and Equations
Unit 6-Trigonometric Methods
HSMA300 INTEGRATED MATH 3, HSMA310 INT MATH 3A, HSMA320 INT MATH 3B
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Integrated Math 2 is strongly recommended
Content: Algebraic Functions, Algebra 2, Geometry, Discrete Mathematics, Trigonometry, and Statistics
In this course the students would develop and extend the following: understanding of formal reasoning in geometric, algebraic and statistical contexts and of basic principles that underlie those reasoning strategies; ability to reason both algebraically and graphically to solve inequalities in one and two variables, introduces systems of inequalities in two variables, and develops a strategy for optimizing a linear function in two variables within a system of linear constraints on those variables; understanding of similarity and congruence and their ability to use those relations to solve problems and to prove geometric assertions with and without the use of coordinates; understanding of the measurement of variability, develops student ability to use the normal distribution as a model of variation, introduces students to the binomial distribution and its use in decision making, and introduces students to the probability and statistical inference involved in control charts used in industry for statistical process control; ability to represent and draw inferences about polynomial and rational functions using symbolic expressions and manipulations; understanding of relationships among special lines, segments, and angles in circles and the ability to use properties of circles to solve problems; understanding of circular functions and the ability to use these functions to model periodic change ability to reason deductively in geomantic settings; ability to represent analyze, and solve problems in situations involving sequential and recursive change; understanding of inverses of functions with a focus on logarithmic functions and their use in modeling and analyzing problem situations and data patterns.
HSMA210 GEOMETRY
Credit: 1.0
Gr.: Ability Level
Prerequisite: B or better in Integrated Math 1 equivalent class recommended
Coordinates are studied beginning in the first chapter. Measurement ideas, including the ideas of area and volume so important both for consumer applications and for later mathematics are studied. Ideas of congruence and similarity are developed through transformations. Two-dimensional work is studied throughout. A goal is that all students be successful at proofs and other mathematical arguments. In the first half of the course, emphasis is placed on writing sequences of statements and on simple proofs. Algebraic manipulation of triangles, circles, prisms and pyramids occur in the second half of the course.
Geometry - Unit 1 - Basics of Geometry [1055]
Geometry - Unit 2 - Reasoning and Proof [1550]
Geometry - Unit 3 - Perpendicular and Parallel Lines [1551]
Geometry - Unit 4 - Congruent Traingles [1703]
Geometry - Unit 5 - Properties of Triangles [1709]
Geometry - Unit 6 - Quadrilaterals [1711]
Geometry - Unit 7 - Transformations [1713]
Geometry - Unit 8 - Similarity [1714]
Geometry - Unit 9 - Right Triangles and Trigonometry [1725]
Geometry - Unit 10 - Circles [1728]
Geometry - Unit 11 - Area of Polygons and Circles [1729]
Geometry - Unit 12 - Surface Area and Volume [1730]
HSMA310 ALGEBRA 2
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Geometry is strongly recommended
This course emphasizes the development of facility with algebraic forms, linear and quadratic expressions, powers and roots, and functions based on these concepts. Logarithmic, trigonometric, polynomial, and other special functions are also studied. The use of these forms and functions to model real world situations is a major theme. Geometric ideas are used throughout the course. Measurement relationships are analyzed from an algebraic viewpoint. Transformations are employed to analyze graphs. In general, graphing is emphasized to take advantage of the geometric intuition that students have. Notions of a mathematical system found in geometry (postulates, theorems, etc.) are utilized. Many connections with calculators are made in this course. Moreover, certain subjects, such as discrete and continuous domains and work with algorithms have been included because of their importance in a computer age.
Unit 1: Equations and Inequalities
Unit 2: Linear Equations and Functions
Unit 3: Systems of linear Equations and Inequalities
Unit 4: Matrices and Determinants
Unit 5: Quadratic Functions
Unit 6: Polynomials and Polynomial Functions
Unit 7: Powers, Roots, and Radicals
Unit 8: Exponential and Logarithmic Functions
Unit 9: Rational Equations and Functions
Unit 10: Sequences and Series
Unit 11: Trigonometric Ratios and Functions
HSMA410 TRIGONOMETRY AND VECTORS
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Algebra 2 is strongly recommended
In this course students will explore in great detail vectors, complex numbers, and circular as well as triangular trigonometric relations and functions. Graphical, numerical, and algebraic analysis of each ear will be emphasized. Students will also make connections between each of these areas of study.
Unit 1: Prerequisites
Unit 2: Fundamentals of Trigonometry
Unit 3: Analytic Trigonometry
Unit 4: Additional Topics in Trigonometry
Unit 5: Complex Numbers
Unit 6: Exponential and Logarithmic Functions
Unit 7: Analytic Geometry
HSMA510 PRE-CALCULUS
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Trig/Vectors is strongly recommended
Pre-Calculus topics emphasize the background theory a student must know to be successful in many calculus courses, including analysis of functions, notions of limit, and analytic geometry. Discrete mathematics topics include formal logic, properties of natural numbers, mathematical induction, sequences, combinatorics, and graph theory. There is also manipulative algebra, handling manipulations that have been de-emphasized in the previous years, and careful development of mathematical reasoning and proof.
Chapter 1 Graphs [1051]
Chapter 2 Functions and Their Graphs [1062]
Chapter 3 Quadratic Functions [1066]
Chapter 5/6/8/9 Trigonometric Functions [1243]
Chapter 7 Right triangle Trigonemtry [1266]
HSMA690 AP STATISTICS
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Trig/Vectors is strongly recommended
This course incorporates four major themes: exploratory analysis, planning a study, probability inference and statistical inference. Graphical and numerical techniques will be used to study patterns and departures from patterns. An examination will be made of relationships among variables and unusual values, as well as characteristics, shape, location, and variability of distributions. Collecting data based on a well-developed plan, identifying important variables and specifying how they are measured, and formulating a mathematical model for which inference can be drawn will be important activities. Probability will be used to anticipate what the distribution of data should look like under a given model. Key concepts of randomness and variation will be discussed in detail.
Unit 1-Organizing Data
Unit 2-Planning a Study
Unit 3-Laws of Probability and Randomness
Unit 4-Binomial, Geometric and Sampling Distributions
Unit 5-Statistical Inference
HSMA790 AP CALCULUS AB
Credit: 1.0
Gr.: Ability Level
Prerequisite: C or better in Pre-Calculus is strongly recommended
This course is a thorough introduction to calculus for students who intend to continue in mathematics, and for those who will use calculus in other fields of study. Topics include: finite and nonexistent limits, continuity, definition of derivatives, statements and applications of theorems about derivatives and applications of derivatives, linear approximation, rates of change, properties of graphs, The Fundamental Theorem of Calculus, and a limited introduction to definite and indefinite integration. Students will investigate applications in related rates, optimization, solid geometry and elementary mechanics.
HSMA890 AP CALCULUS BC
Credit: 1.0
Gr.: Ability Level
Prerequisite: Calculus AB
This course is an extension of the work done in Calculus AB. Additional topics will include: vector functions, parametric equations, polar coordinates and related equations, rigorous definitions of limits, derivatives of vector functions and parametrically defined functions, further explorations of L’Hopital’s Rule, tangent lines to parametrically defined curves, velocity and acceleration vectors for motion on a plane curve, additional techniques for integration, area bounded by polar curves, conic functions, and a study of the convergence of divergence of sequences and series.
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Mathematics Course Sequence