Course Description: Precalculus is a thoughtful introduction to advanced studies leading to calculus. This course includes a thorough study of differentiation and integration with many applications. You will learn to approximate them graphically and solve for them exactly using algebraGet a conceptual and graphical understanding of what is meant by asymptotes and end behavior and will lay the groundwork for future conceptsLearn the formal definition of continuity, the three types of discontinuities and more about piecewise functionsLearn a new type of transformation called compositionLearn about inverse functions and what they look like graphically and numerically and how to find and verify inverse functions algebraicallyReview factoring techniques from Algebra 1 and 2 in preparation for more advanced factoring techniquesLearn a variety of factoring techniques for special situations and see alternatives to trial and error for factoringExplore patterns with binomial and polynomial expansion and find out how to get coefficients using Pascal’s TriangleAdd, subtract, multiply and divide rational expressions in order to help you solve and graph rational expressions in the future2.5 Polynomial Long Division and Synthetic DivisionLearn how to perform long division with polynomials and see how synthetic division abbreviates this processUnderstand how the remainder root theorem and the rational root theorem operateExtend knowledge of linear and quadratic equations to rational equations in general and gain insight as to what extraneous solutions are and how to identify themstart factoring rational expressions that have holes known as removable discontinuitiesRevisit how to find zeroes of functions by focusing on rational expressions and what to do in special cases where the zeroes and holes seem to overlapLearn to recognize when vertical asymptotes occur and what makes them different from removable discontinuitiesLearn to identify when horizontal asymptotes exist, specify their height and write their equationExtend knowledge of horizontal and vertical asymptotes and learn to identify oblique (slanted) asymptotesLearn to predict the nature of a rational function near the asymptotesExtend knowledge of zeroes, intercepts, holes and asymptotes to sketch rational functions by handExplore exponential functions as a way to model a special kind of growth or decay and learn more about the number Learn how exponents interact in a variety of algebraic situations including addition, subtraction, multiplication and exponentiationReview how to write very large and very small numbers in scientific notation and how to use scientific notation in arithmetic operationsLearn about logarithmic expressions and how they can be combined using properties of arithmeticHere you will extend knowledge of log properties to a simple way to change the base of a logarithmApply the new algebraic techniques associated with logs to solve equationsExplore the graph and equation of the logistic functionLearn how to translate between different ways of measuring anglesReview converting between linear and angular speeds using radians and circumferenceReview properties of 30-60-90 and 45-45-90 right trianglesLearn the six right triangle ratios and how to use them to completely solve for the missing sides and angles of any right triangleExplore solving non-right triangles in cases where a corresponding side and angle are given using the Law of SinesUse the sine ratio to find the area of non-right triangles in which two sides and the included angle measure are knownApply knowledge of trigonometry and problem solving in contextUse knowledge of basic triangle trigonometry to identify key points and angles around a circle of radius one centered at the originUnderstand how the graphs of sine and cosine come from the unit circleUnderstand how changing the radius of a circle affects the graph of the sine function through a vertical stretchExplore the how a vertical shift of a sinusoidal function is represented in an equation and in a graphApply your knowledge of horizontal stretching transformations to sine and cosine functionsApply all the different transformations, including horizontal shifting, to sinusoidal functionsExtend knowledge about rational functions and sine and cosine functions to produce graphs of the four other trigonometric functions: tangent, secant, cosecant, and cotangentGraph the final form of trigonometric functions, the inverse trigonometric functionsSimplify trigonometric expressions using the reciprocal, quotient, odd-even and cofunction identitiesProve and use the Pythagorean identities for the six trigonometric functions to simplify expressions and write proofsExtend knowledge on the sum and difference identities for sine, cosine and tangentProve and use the double, half, and power reducing identitiesSolve equations that contain trigonometric functionsUnderstand what a vector is algebraically and graphicallyAdd and subtract vectors with vectors and vectors with pointsFind unit vectors and you will convert vectors into linear combinations of standard unit vectors and component vectorsCompute the dot product between two vectors and interpret its meaningProject one vector onto another and apply this technique as it relates to forceReview how to solve a system of two equations and two unknowns using the elimination methodExtend knolwedge of systems of equations to three equations and three unknownsLearn what a matrix is and how to use one to represent dataManipulate matrices using row operations into row echelon form and reduced row echelon formSolve systems of equations using augmented matricesLearn how to find the inverse of a matrix and how to solve a system of equations using an inverse matrixApply what you know about systems and matrices to decompose rational expressions into the sum of several partial fractionsUnderstand how each conic section is the intersection of a plane and a cone, review completing the square and start working with the general equation of a conicDefine a parabola in terms of its directrix and focus, graph parabolas vertically and horizontally, and use a new graphing form of the parabola equationFormalize the definition of a circle, translate a conic from standard form into graphing form, and graph circlesTranslate ellipse equations from standard conic form to graphing form, graph ellipses and identify the different axes and identify eccentricity and solve word problems involving ellipsesTranslate conic equations into graphing form and graph hyperbolas and learn how to measure the eccentricity of a hyperbola and solve word problemsDiscover what happens when a conic equation can’t be put into graphing formLearn how to use basic right triangle trigonometry to translate back and forth between the two representations of the same pointFind equations and graphs for various conics, including those whose major axis is at a slantRepresent equations and graphs in a new way with parametric equationsUse your knowledge of both inverses and parametric equations to solve problemsUse parametric equations to represent the vertical and horizontal motion of objects over timeMake the connection between zeroes of a polynomial and the Fundamental Theorem of Algebra and start to use complex numbersUse basic right triangle trigonometry to represent complex points in the polar plane and use the trigonometric form of complex numbers to multiply and divide complex numbersLearn about De Moivre’s Theorem, which will helps to raise complex numbers to powers and find roots of complex numbersDefine patterns recursively and use recursion to solve problemsIdentify different types of sequences and use sequences to make predictionsLearn how to represent the sum of sequences of numbers using sigma notation Learn to compute finite arithmetic series more efficiently than just adding the terms together one at a timeSum infinite and finite geometric series and categorize geometric series as convergent or divergentReview counting using decision charts, permutations and combinationsCalculate the probability of simple and compound events.Apply the Binomial Theorem to expand binomials that are raised to a powerLearn how to prove statements about numbers using induction.Calculate the effect of time on the balance of a savings account growing by simple interestExplore how to compute an investment’s growth given time and a compound interest rateCompute future values with interest that accumulates semi-annually, monthly, daily, etc.Use the force of interest to compute future values when interest is being compounded continuouslyCompare rates for loans and savings accounts to find more favorable dealsWrite and read limit notation and use limit notation to describe the behavior of a function at a point and at infinityUse graphs to help you evaluate limits and refine your understanding of what a limit representsDetermine one sided limits graphically, numerically and algebraically and use the concept of a one sided limit to define continuityUse continuity to explore the intermediate and extreme value theoremsLearn about instantaneous rate of change and the concept of a derivativeEstimate the area under a curve and interpret its meaning in context.Calculate three measures of the center of univariate data and decide which measure is best based on contextApply knowledge about mean and averages to weighted averages and expected valueCalculate quartiles and produce five number summaries for data setsDisplay data using bar charts, histograms, pie charts and boxplotsCalculate population variance, sample variance and standard deviation from univariate dataDefine the standard normal distribution and learn how standard deviation and the area under the curve are connectedWork with bivariate data as you learn about linear correlation, correlation coefficients, and regressionUse regression on a variety of different types of data to make reasonable predictionsUse the words “and” and “or” as logical connectives in complex statements and use set theory and logical notation to diagram logical statementsIdentify different parts of if-then statements and determine when an if-then statement is true or false and use traditional set theory graphical representationsNegate statements and use graphical representations and set theory to explore the implications of negative statements and learn about De Morgan’s LawExamine the implications of the inverse, converse and contrapositive statements as they relate to a conditional statementSmartFox integrates SIS, LMS, and online courseware, all on a mobile-friendly, open-source platform. Limits and continuity are investigated in-depth. Limits and continuity are investigated in-depth. 1.0 Credit.
What calculus course should I take?. The course will emphasize the importance of mathematics studied to date. I graduated from forest trail academy in 2009. Students are advised to retain course outlines for future use in support of applications for employment or transfer of credits. An AP Calculus AB course is typically equivalent to one semester of college calculus. Here is a set of notes used by Paul Dawkins to teach his Calculus I course at Lamar University. Prerequisite: Algebra 2 . I don’t have the pressures of exams and trying to keep up with the rest of the class. AP Calculus AB and BC Course and Exam Description This is the core document for the course. For old course outlines from previous years, explore our Undergraduate Course Outline Archive. Credits: 5 credits per semester course/10 credits total. Math 400 Special Problems for Advanced Undergraduates (pdf) Math 440 Topology I (pdf) High School Calculus Math Course Outline. I transferred out during my junior year after having a rough time in public high school…”“Forest Trail Academy has been a blessing to me. Course Description: This course in calculus is intended to develop practical skills in differential and integral calculus. COURSE DESCRIPTION Pre-Calculus weaves together previous study of algebra, geometry, and mathematical functions into a preparatory course for calculus. A syllabus or course outline, detailing how course requirements are met, is submitted by the AP teacher for review by college faculty. The course briefly reviews linear equations, inequalities, and systems and moves purposefully into the study of functions. The course concludes with a short study of probability and statistics.This course includes a broad series of lessons and activities that offer a variety of modalities for ultimate student engagement and content retention. Please visit After completion of this course, the student may wish to take the Advanced Placement Test.Copyright © 2007-2020 – Forest Trail Academy – All Rights Reserved.“Forest Trail Academy is the BEST school ever, the staff is amazing!! PDF; 5.2 MB; See Where AP Can Take You. The course focuses on mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Throughout the course, Common Core Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series.This subject constitutes a major part of contemporary mathematics education.Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient. I recently graduated from Forest Trail Academy after going there for 2 years. I didn’t fit in at my old school, i had trouble learning in such a disruptive classroom which meant my grades falling, coming…”“Thank you Forest Trail Academy for helping my student excel! Scaffolding rigorous content with clear instruction, the course leads students through an advanced study of trigonometric functions, matrices, and vectors. This course includes a thorough study of differentiation and integration with many applications.
Guidelines for choosing Math/Stats elective courses. The course briefly reviews linear equations, inequalities, and … For the most up-to-date and accurate course description information, please visit the 2020 / 2021 Undergraduate Calendar. Included are detailed discussions of Limits (Properties, Computing, One-sided, Limits at Infinity, Continuity), Derivatives (Basic Formulas, Product/Quotient/Chain Rules L'Hospitals Rule, Increasing/Decreasing/Concave Up/Concave Down, Related Rates, Optimization) and basic Integrals … Precalculus is a thoughtful introduction to advanced studies leading to calculus. Subject Area: Math. I compete in the sport of rodeo across many states, and it takes time and dedication to train and condition both …”“FTA gave me HOPE. The AP Course Audit form is submitted by the AP teacher and the school principal (or designated administrator) to confirm awareness and understanding of the curricular and resource requirements. A collaboration built by people who understand what charters, districts, and, most importantly, students and families need.© Copyright 2018 Method Schools, a California Public Benefit Corp. | All Rights Reserved The material includes limits, differentiation, integration, applications of the previous, and other topics covered in standard college calculus courses.
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