Mathematical Approach to Problem Solving (MAPS)
MAPS is designed for students who need additional instruction prior to taking Algebra 1. It is primarily for students who have had an interrupted education (e.g., coming to MCPS from out of state or country). Calculators and computers are used in problem solving situations and in the development of number, algebra, geometry, measurement, probability and statistics concepts and skills.
This course examines the basic structure of real numbers, algebraic expressions, and functions. The topics studied are linear equations, inequalities, functions and systems, quadratic equations and functions, polynomial expressions, data analysis, probability, and the elementary properties of functions. Mathematical modeling of real-life problems and problem solving are major themes of the course.
This course is taken in conjunction with Algebra 1A and 1B. This course reinforces the essential pre-Algebra and Algebra concepts and skills necessary to function in authentic problem-solving situations. Students focus on skills and applications related to success in Algebra. Students learn how to use technology in the problem-solving process.
Quantitative Literacy is designed to enhance students' abilities in mathematical decision-making and financial literacy. Emphasis is on the mathematical aspects of savings and investments, loans and credit, budgeting, chance, decision-making, and starting a business.
Geometry / Honors Geometry
Students study Geometry as a mathematical system through the deductive development of relationships in the plane and space developed intuitively in previous years. Students study congruent segments and angles, circle chords, secants and tangent segments, parallel and perpendicular lines, angle measure in triangles, direct and indirect triangle congruence and similarity, proofs, solids of revolution, logic, similar triangles, transformations, the Pythagorean Theorem, geometric constructions, coordinate geometry, and surface area and volume of solids.
Algebra 2 is the study of the complex number system, symbolic manipulation, and functions. Students discuss, represent, and solve increasingly sophisticated real-world problems using advanced algebraic and data analysis techniques incorporating technology. They also study the properties of functions, the algebra of functions, matrices, and systems of equations. Linear, quadratic, exponential, logarithmic, polynomial, and rational functions are studied with an emphasis on making connections to other disciplines and as preparation for a multitude of careers. Students apply advanced data analysis techniques to find, justify and use the best-fit model from all function models. Communication of the problem-solving skills used is an important part of this course.
Honors Algebra 2
Algebra 2 with Analysis is an intensive, accelerated course intended to prepare students for advanced mathematics courses. Algebra 2 with Analysis focuses on the use of technology and data analysis to develop students' thinking, problem-solving, and communication skills. Properties, applications, algebra, and parametric representation of functions; matrix algorithms; and linear, quadratic, radical, exponential, logarithmic, polynomial, and rational functions are studied. Data analysis techniques include the use of re-expression and residuals to find and verify best-fit rules. Applications as well as the properties relevant to advanced mathematics also are studied.
Precalculus completes the formal study of the elementary functions begun in Algebra 1 and Algebra 2. Students focus on the use of technology, modeling, and problem solving involving data analysis, trigonometric and circular functions, their inverses, polar coordinates, complex numbers, conics, and quadratic relations. Discrete topics include the Principles of Mathematical Induction, the Binomial Theorem, and sequences and series.
The formal study of elementary functions is extended in this course. Students apply technology, modeling, and problem-solving skills to the study of trigonometric and circular functions, identities and inverses, and their applications, including the study of polar coordinates and complex numbers. Vectors in two and three dimensions are studied and applied. Problem simulations are explored in multiple representations-algebraic, graphic, and numeric. Quadratic relations are represented in polar, rectangular, and parametric forms. The concept of limit is applied to rational functions and to discrete functions such as infinite sequences and series. The formal definition of limit is applied to proofs of the continuity of functions and provides a bridge to calculus.
Calculus with Applications
The introductory topics of this course include limits and continuity of functions, derivatives of functions, the definite integral, and their real-world applications. Students find derivatives numerically, represent derivatives graphically, and interpret the meaning of a derivative in applications. Previously studied functions will be analyzed using calculus concepts. The relationship between the derivative and the definite integral is developed as well. Students will model real-world situations involving rates of change using difference or differential equations.
Statistics and Mathematical Modeling (SAMM)
Semester A: Topics of this course include data analysis, probability, simulations, inferential statistics, normal and binomial distributions, techniques of sampling, confidence intervals and hypotheses testing. Students use exploratory methods to identify patterns and make decisions. Emphasis is placed on applications and the use of statistics to solve real-life problems. Semester B: Topics presented in this course are chosen from discrete mathematics topics including Cryptography and Coding, Game and Graph Theory, Architecture, Trigonometry, Fairness and Apportionment, Careers, Investment and Finance, and College Placement Test Review. Students learn an application-based approach to the study of mathematical modeling.
Students engage in the exploratory analysis of data making use of graphical and numerical techniques. They generate conjectures about relationships among variables. Association is distinguished from causation. Data sets are collected according to a well-developed plan from which inferences will be made. These data sets lay the groundwork for an ongoing, yearlong project. Students are expected to produce appropriate models using probability and simulation, and statistical inference. Models and data interact in statistical work; models are used to draw conclusions from data, while the data may support or discredit the model when analyzed with inferential methods. This course is the equivalent of a non-Calculus-based introductory college statistics course.
Calculus AB: The topics studied in AP Calculus AB are those traditionally offered in the first year of calculus in college, and designed for students who wish to obtain a semester of advanced placement in college. The topics studied include limits, continuity, derivatives, and integrals of algebraic and transcendental functions and their applications, and elementary differential equations.
Calculus BC: The BC course includes all of the topics in the AB course, as well as convergence tests for series, Taylor or Maclaurin series, vector, polar, and parametric functions. Students in BC Calculus generally receive two semesters of advanced placement in mathematics.
This course aims to introduce students to aspects of elementary differential geometry, optization and physics that , while important and relevant to the needs of practicing scientists and engineers, are often omitted in traditional text. The emphasis is on the geometric, symbolic, and interprative thinking beyond rote manipulation of algebra and calculus formulas.Topics covered include: Vectors, Geometry of curves, partial and directional derivatives and multiple integrals.
IB Math Studies
This course builds on the concepts of Algebra 2 and Geometry in preparation for the standard-level IB Mathematical Studies examination. Students examine functions (transformation and applications), linear programming, probability, statistics, trigonometry, sequences and series, and solid geometry.
IB Mathematics HL
This course is for students who have completed the AP Calculus BC. It prepares students for the Higher Level IB Mathematics examination. Topics covered include additional calculus, sets, relations, groups, discrete mathematics, series and differential equations, and statistics and probability theory.