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This course is the equivalent of an introductory college-level calculus course. Calculus helps scientists, engineers, and financial analysts understand the
complex relationships behind real-world phenomena. Students learn to evaluate the soundness of proposed solutions and apply mathematical reasoning to
real-world models. This is the second semester of MTH500.
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This course is the equivalent of an introductory college-level calculus course. Calculus helps scientists, engineers, and financial analysts understand the complex relationships behind real-world phenomena. Students learn to evaluate the soundness of proposed solutions and apply mathematical reasoning to real-world models. Students also learn to understand change geometrically and visually (by studying graphs of curves), analytically (by studying and working with mathematical formulas), numerically (by seeing patterns in sets of numbers), and verbally. Students prepare for the AP Exam and further studies in science, engineering, and mathematics. This is the second semester of MTH500.
Students prepare to study calculus by reviewing some basic precalculus concepts from algebra and trigonometry. They learn what calculus is, why it was invented, and what it's used for.
The topics referred to below are those listed in the College Board's Calculus AB topic outline. This unit addresses Topic I: Functions, Graphs, and Limits. Students learn two important concepts that underlie all of calculus: limits and continuity. Limits help students understand differentiation (the slope of a curve) and integration (the area inside a curved shape). Continuity is an important property of functions.
This unit addresses Topic II: Derivatives. Students learn how to calculate a derivative, the slope of a curve at a specific point. They learn techniques for finding derivatives of algebraic functions (such as y = x2) and trigonometric functions (such as y = sin x).
This unit focuses on Second Derivatives and Applications of Derivatives within Topic II: Derivatives. Students learn how to use calculus to model and analyze changing aspects of our world.
Students review what they have learned so far and take the semester exam.
This unit focuses on Topic III: Integrals. Students learn numerical approximations to definite integrals, interpretations and properties of definite integrals, the Fundamental Theorem of Calculus, and techniques of antidifferentiation. They learn how to find areas of curved shapes.
This unit focuses on Topic III: Integrals. Students learn to use integrals and antiderivatives to solve problems.
This unit focuses on Topic II: Derivatives and Topic III: Integrals. Students learn to calculate and use derivatives, antiderivatives, and integrals of exponential functions (such as y = 3x where the input variable is an exponent), logarithmic functions (the inverses of exponential functions), and inverse trigonometric functions (such as y = secant(x)).
This unit focuses on Topic II: Derivatives; specifically, on Equations Involving Derivatives. Students investigate differential equations, and solve the equations using a technique called "separating the variables."
Students review what they have learned and prepare for the AP Exam with practice tests that simulate the AP test experience.
Teachers may choose to assign a final project.
Courses with a teacher have designated start dates throughout Fall, Spring, and Summer. Full-year courses last 10 months and semester courses last 4 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.
To use this course, you'll need a computer with an Internet connection. Some courses require additional free software programs, which you can download from the Internet.
CPU: 1.8 GHz or faster processor (or equivalent)
RAM: 1GB of RAM
Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher
CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor
Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)
It is highly recommended that a broadband connection be used instead of dial up.
(excludes shipping, other exclusions apply)
Calculus, Part 2 (MTH433B)
AP® Calculus AB, Part 1 (MTH500A)