FLEX 課程 - 初級微積分

Esta clase también puede darse en español. Si prefiere el español, por favor contacte a la maestra antes del inicio de la clase.

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In this class, learners will receive short video explanations, created by the instructor, of important pre-calculus and trigonometry concepts as well as written posts explaining different skills and problem-solving methods. No outside video content will be used in this class. Each week, 2-3 short videos will be posted, along with 2-3 additional written explanations of concepts, tips, tricks, and so on, that will be posted into the classroom discussion. All content will be shared by 12pm ET (9am PT) on Monday of each week.

Students will also receive optional PDF assignments to practice each week’s concepts if they choose to do so. These assignments will be posted by 12pm ET (9am PT) on Monday of each week. They will receive feedback about their assignments after they turn them in to the instructor. Assignments should be turned in by midnight on Thursday of each week in order to receive timely feedback.

Students will also be able to message the instructor directly to receive individualized help with math assignments. All messages will receive responses within 24 hours of receiving them, though usually I will respond much more quickly.

Week 1: review imaginary/complex numbers and simplifying radicals, discriminant and number of real/imaginary roots. I will present imaginary/complex numbers and their relationship with radicals and roots of quadratics. I will review how to simplify radicals, including negatives. I will also review quadratic equation and explain what the discriminant is and how to use it to determine the number of real/imaginary roots a quadratic expression has and how to find them.

Week 2: completing the square, finding the equation given a graph. I will explain the steps for completing the square and using that to find the roots and vertex of a graph. I will review transformations of graphs and how to write an equation for a given graph in vertex form, standard form, and factored form. I will briefly touch on how to sketch a graph using transformations when given an equation.

Week 3: division of polynomials and synthetic division. I will present division of a polynomial by a binomial and also explain how to set up the same type of problem using synthetic division. I will also briefly discuss the factor theorem and how to use division to determine if a given number is a root for an expression or not.

Week 4: exponential functions and logarithms. I will explain how to solve exponential and logarithmic equations and graph exponential/logarithmic functions. I will present properties of logarithms and change of base and how to use this to simplify expressions and solve equations.

Week 5: composite functions and operations on functions. I will present composite functions and explain how to do the four basic operations (add, subtract, multiply, divide) on two or more functions. I will also explain how to find domain/range of the new function given the domain/range of the original functions, and how to sketch a graph of the composite function.

Week 5: trig functions and basic identities. I will review right triangles and how to find missing sides. I will also go over the six trig functions, how to find them and how to use basic trig identities to switch between functions, such as going from tangent to sine/cosine, or from secant to cosine. I will review important trig identities and use them to find the value of other trig functions (for example, given tangent, find sine and cosine)

Week 6: graphing trig functions. I will explain how to graph basic trig functions and review maximums, minimums, and asymptotes. I will also explain important features of trig functions, such as amplitude, period, vertical and horizontal shift, and the relationship between functions such as sine and cosine.

Week 7: law of sines/cosines. I will explain how to use inverse of trig functions (arcsin, arccos, arctan) to find the measure of an unknown angle in a triangle. I will then show students how to use law of sines and law of cosines to find unknown angles or sides of a triangle, and how to apply this to real-world situations.

Week 8: review week. I will show examples of word problems involving all of the previously-covered material and how to pull important information out of the word problem and set up an equation to find the solution. I will review trig functions and composite functions as well as completing the square and complex roots.