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The A+LS Mathematics curriculum is a comprehensive, completely integrated curriculum for grade levels 1-12. A sequence of 18 titles provides an extensive, integrated solution that is fully correlated to major mastery standards and leading, adopted textbooks.
In addition to a complete mathematical curriculum that is appropriate at each grade level, each title contains exercises that require the student to choose operations and develop strategies to solve problems. Students learn to use common sense, mental math, estimation, and other methods to solve problems and check answers for reasonableness.
The Mathematics titles develop knowledge of mathematics skills and their use in practical situations by utilizing a four-step approach: Study, Practice, Test, and Essay modules are used to define the instructional environment. The Study module provides a text- and graphics-based delivery of material that is reinforced by pictures and diagrams supported by a wealth of content. All graphics magnify to full screen size to concisely present and reinforce these concepts. The Practice module provides the students, in a non-scored and non-graded environment, to practice skills acquired through studying. Engaging, interactive feedback prompts the student to right answers when wrong answers to questions are entered. The student has instant access to the study material for reference. In the Test module, the student takes a scored examination, the results of which are recorded in the A+LS Management System. Upon completion of the Test, the student electronically "turns in" the test and may instantly see test results and correct answers to questions missed. The Essay module allows the student to compose individual, free-form answers to a wide variety of questions and problems.
| LESSON # | LESSON TITLE | LESSON CONTENT |
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Limits | Calculating x-values and corresponding values, approaching function values, limits, and notation. |
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Continuous Functions | Definition of continuous function, continuous graphs of polynomial functions, sine, and cosine, evaluating the limits of continuous function. |
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Discontinuous Functions 1 | Examining various types of discontinuities: holes, asymptotes, and jumps and their graphs |
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Discontinuous Functions 2 | Approaching negative and positive infinities |
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Discontinuous Functions 3 | One-sided limits |
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Special Trig Functions | Trigonometric limits of sine and cosine functions, graphing tangents, cotangents, secants, cosecants |
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Limits at Infinity | Polynomials as they approach infinity, negative infinity, and infinity squared, definition of infinity squared, examples of how changing the argument of the function changes the limit. |
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Limit Unit Review | Review of limit lessons. |
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Derivatives | Derivatives and determining the slope of a tangent at a given point, using the derivative as a velocity, the derivative as a function; Liebniz notation |
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Derivative Shortcuts 1 | Using the mathematical definition of a derivative to find general pattern, constant functions and derivatives; the Power Rule and coefficients of sums and differences |
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Derivative Shortcuts 2 | Negative exponents, derivatives of sine and cosine, derivatives at specific points |
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Some Derivative Rules | Functions that are products, the Product Rule, rational functions and the Quotient Rule, the derivative as a reciprocal of sine. |
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The Chain Rule | Derivatives of composite functions, definition of the chain rule, extending the chain rule. |
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Higher Derivatives | Acceleration as a derivative of velocity, notation and use of higher derivatives. |
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Implicit Differentiation | Examples of finding the derivative implicitly without solving for y. |
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Derivative Unit Review | Review of derivatives. |
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Maximum / Minimum Values 1 | Determining maximum and minimum values of given functions on closed intervals |
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Maximum / Minimum Values 2 | Using zero-slope to determine maximum and minimum values, critical points and relative extrema. |
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Maximum / Minimum Tests 1 | The first derivative tests, increasing and decreasing slopes, finding relative extrema |
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Maximum / Minimum Tests 2 | Second derivative tests, finding relative extrema |
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The Second Derivative | Concavity and inflection points of graphs, definition and determination of inflection points, sign graphs |
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Application Review 1 | Review of maximum and minimum values and tests |
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Applications of Extrema | Determining need to find maximum and minimum values in real life situations |
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Related Rates 1 | Problems with derivatives that are related; problems involving related rates and spheres |
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Related Rates 2 | Using related rates to determine the volume of cones; using the Pythagorean relationship in related rate problems |
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Graphing Using Extremes 1 | Understanding the nature of graphing, determining graphing data |
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Graphing Using Extremes 2 | Asymptotes as related to graphs |
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Application Review 2 | Review of related rates and graphing |
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Antiderivatives | Determining the original function from the derivative, definition of antiderivatives, proving antiderivatives, antiderivatives with negative exponents. |
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Comprehensive Exam | Review of all material presented in Calculus I |
