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PRE ALGEBRA DEFINITIONS OPEN ALGEBRAIC EXPRESSION
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Mathematics

(301) 649-2870

Department Chair: Shelley Sherman
shermanr@mbhs.edu

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The Staff:

The Courses:

All students must take 4 credits of mathematics, including 1 credit in algebra and 1 credit in geometry. Students who complete a calculus course may be exempted from the 4-credit requirement in mathematics. Students must consult with school counselors in advance to obtain full information about this credit waiver and its advisability.

Calculators

Many of the courses require the use of a TI-83+ Graphing Calculator. These may be rented from the Mathematics Department at a cost of $25 per semester, or purchased for $90 (previous rental costs may be applied toward the purchase of a calculator).

9th Grade

9th graders start their mathematics sequence at Blair at a level corresponding to the level of the classes they have successfully completed in middle school. Students generally start with one of these classes:

Algebra 1 (9th-11th grade; 1 credit) — This course studies the basic structure of real numbers, algebraic expressions, and functions. The topics studied are statistical organization and analysis, linear equations, inequalities, functions and systems, quadratic equations and functions, polynomial and radical expressions, and the elementary properties of functions. Mathematical modeling of real-life problems, problem solving, and the construction of appropriate linear models to fit data sets are the major themes of the course. The course requires a TI-83+ Graphing Calculator (see above for details).

Algebra 1A and B (9th grade; 1/2 credit) — This course has the same curriculum as Algebra I, but is taught in a single semester. It is for students who were in MAPS I or II first semester that successfully passed the Maryland Functional Math Test (MFMT), and were recommended for this accelerated course. The course requires a TI-83+ Graphing Calculator (see above for details).

Algebra 1 with Related Math (9th-10th grade; 1 credit) — This is a double-period course which adds the curriculum of Related Math to the Algebra 1 curriculum. Related math adds essential mathematical concepts and skills necessary to function in authentic problem-solving situations. Essential skill and concept development of algebraic formulas, percent, and ratio and proportion in algebraic problem-solving situations is emphasized. Support of the attainment of algebraic objectives is provided. Use of technology in the problem-solving process is an integral component of the course. The course requires a TI-83+ Graphing Calculator (see above for details).

Geometry (9th-12th grade; 1 credit; may also be taken at the honors level) — Geometry is studied through the deductive development of relationships in the plane and space developed intuitively in previous years. Indicators include the geometry in art and nature, geometry as a mathematical system, congruent segments and angles, circle chords, secants and tangent segments, parallel and perpendicular lines, angle measure in triangles, direct and indirect triangle congruence proofs, solids in revolution, logic, similar triangles, the Pythagorean Theorem, geometric constructions, and surface area and volume of solids. The course requires purchase of a compass and a protractor (available from the Mathematics Department at a cost of $3.50). Students are encouraged to get a TI-83+ Graphing Calculator for the second semester (see above for details).

(Students who have taken geometry or higher in middle school will start the class that follows in their mathematical sequence listed under the 10th-12th grade required courses, below).

10th-12th grades

Following 9th grade, students follow a sequence that loosely runs MAPS->Algebra 1->Geometry->Algebra 2->Precalculus->Calculus, though there are several methods in following this sequence. Here are some of the most common:

course descriptions are listed above.

Algebra 2 (10th-12th grade; 1 credit; Prerequisite: Algebra I) — Algebra 2 is the study of the complex number system, symbolic manipulation, and functions. Advanced algebraic and data analysis techniques incorporating the use of technology enable students to discuss, represent, and solve increasingly sophisticated real-world problems. Topics studied include 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. A principal goal is to apply advanced data analysis techniques to find the best fit model from all the important function models, justify the model,and us it to make predictions. Communication of the problem solving skills used and the conclusion reached is another major emphasis. The course requires a TI-83+ Graphing Calculator (see above for details).

Algebra 2 with Analysis (9th-10th grade; 1 credit; Prerequisite: Geometry) — This is an intensive, accelerated course intended for the student with the motivation to prepare 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. Topics include the properties, applications, algebra, and parametric representation of functions, matrix algorithms, linear, quadratic, radical, exponential, logarithmic, polynomial, and rational functions. Data analysis techniques include the use of re-expression and residuals to find and verify best-fit rules. The final unit includes applications as well as the properties relevant to advanced mathematics. The course requires a TI-83+ Graphing Calculator (see above for details).

A.P. Calculus (12th grade; 1 credit; Prerequisite: Precalculus with Analysis) — The topics studied in A.P. Calculus are those traditional offered in the first year of calculus in college, and design specifically for students who wish to obtain advanced placement in mathematics in college. Concepts are communicated graphically, numerically, analytically and verbally. The basic topics studied include limits and continuity of functions, derivatives and integrals of algebraic and transcendental functions and their applications in problems. The advanced topics developed are applied include integration techniques, convergence tests for series, Taylor or Maclaurin series, elementary deferential equations, and hyperbolic functions. The course requires a TI-83+ Graphing Calculator (see above for details).

Calculus with Applications (12th grade; 1 credit; Prerequisite: Precalculus) — The introductory topics of this course include limits and continuity of functions, derivatives of functions, and their applications to problems. Students find derivatives numerically, represent derivatives graphically, and interpret the meaning of a derivative in real-world applications. Models of previously studied functions will be analyzed using calculus concepts. The topics developed include the relationship between the derivative and the definite integral. The understanding, properties, and applications of the definite integral are included as students learn to explain solutions to problems. Students will model real-world situations involving rates of change using difference or differential equations. The course requires a TI-83+ Graphing Calculator (see above for details).

Consumer Math (12th grade; 1 credit) — Designed for 12th graders who need a math credit and are not going to take Algebra 2, Precalculus, or Statistics. Consumer education is combined with the mathematics necessary for making wise consumer decisions. Topics include income, budgeting, purchasing, banking, credit, and investments. Spreadsheets are studied and used in consumer and business applications. Emphasis is placed on the mathematics involved in various careers. The mathematical aspects of taxation, transportation and travel, housing, insurance, and the operation of a small business are studied to illustrate business applications. Much of the material is presented in the context of problem solving situations, and the use of technology is integrated. Materials from daily newspapers, consumer magazines, web sites, and federal supplement standard text materials publications keep the content relevant and current.

ESOL Related Mathematics (10th grade; 1 credit) — Designed for ESOL Level 1 and 2 students who have not passed the MFMT. This course reinforces essential pre-algebra concepts necessary for the MFMT. Topics of study include skill and concept development of algebraic formulas, percent, and ratio and proportion in algebraic problem-solving situations.

Precalculus (11th-12th grade; 1 credit; Prerequisite: Algebra 2) — This course completes the formal study of the elementary functions begun in Algebra 1 and 2. Students use the mathematical and modeling skills previously developed to study and apply the trigonometric functions. The use of technology and problem solving are emphasized in units covering data analysis, circular functions, and trigonometric inverses and identities. Students will conduct research and write extensively as they prepare for higher levels of mathematics. The concepts of trigonometry are extended to the study of polar coordinates and complex numbers. conics and quadratic relations are introduced through a locus definition using polar representations. Discrete topics include the principals of mathematical induction, the Binomial Theorem, and sequences and series, where sequences are represented both explicitly and recursively. An oral and written modeling presentation by students provides culminating synthesis to the concept of function. The course requires a TI-83+ Graphing Calculator (see above for details).

Precalculus with Analysis (10th-11th grade; 1 credit; Prerequisite: Algebra 2 with Analysis) — The formal study of elementary functions is extended with the introduction of the trigonometric functions. Students apply technology, modeling, and problem solving skills to the study of these functions in units on circular functions, trigonometric identities and inverses, and applications of trigonometric functions. Vectors in two and three applications of trigonometric functions. Vectors in two and three dimensions are studied and applied. Problem simulations are explored in multiple representations: algebraic, graphical, and numeric. The trigonometric functions are applied to the study of polar coordinates and complex numbers. Conic sections and quadratic relations are introduced in polar representations. The concept of limit is applied to rational functions and to discrete functions such as indefinite sequences and series. The formal definition of limit is applied to proofs of the continuity of functions and provides a bridge to calculus. A culminating project provides synthesis of the concepts studied. The course requires a TI-83+ Graphing Calculator (see above for details).

Principles of Geometry and Algebra (10th-11th grade; 1 credit; not open to students who have successfully completed their first semester of Algebra 2) — The course is designed for 10th-12th grade students who have not mastered basic algebra skills. This course integrates the basic concepts of algebra and geometry in the solution of real life problems. Topics of study include perimeter, first-degree sentences, angle relationships, linear functions, construction and triangles, area and polynomials, quadratics and special quadrilaterals, radicals and right triangles, data analysis and probability, volume and number concepts, and right triangle applications. The course requires purchase of a compass and a protractor (available from the Mathematics Department at a cost of $3.50). Students are encouraged to get a TI-83+ Graphing Calculator for the second semester (see above for details).

SAT Prep () —

Statistics and Mathematical Modeling (11th-12th grade; 1 credit; Prerequisite: Algebra 2) — The course requires a TI-83+ Graphing Calculator (see above for details).

There are also several mathematics courses offered by the Magnet Program that are available to any Blair students who have completed the appropriate prerequisites. Students completing A.P. Calculus may take Multivariable Calculus and Differential Equations (also known as Magnet Analysis 2) or Linear Algebra. Those completing Precalculus or higher may take Applied Statistics. Discrete Mathematics is offered for those who have completed Precalculus with Analysis and A.P. Computer Science (See the Business/Computer Science Department page for more information on A.P. Computer Science). Finally, if a student manages to finish Multivariable Calculus and Differential Equations before graduation, he/she may move onto Complex Analysis. Some of these courses may have additional prerequisites or other requirements; please see the Magnet Program's webpages and/or your guidance counselor for more information.

Summer Courses:

There are several summer courses Blair students who need an extra leg up can take:

Algebra Boost — This is a four-week program for students who have passed Algebra 1A and B during the second semester of school. This program is for Blair students only. There is no cost for this program.

MFMT —This course is for students who have not passed the MFMT.