Assessment: Pre-Test, Lesson Practice, Unit Exams, Mid-Term Exam, Final Exam
Language: English
Course Overview
Pre-Calculus, a full year course, is recommended for high school students seeking a high school diploma having a strong aptitude for math. It covers the foundational skills needed for success in Calculus. Recommended for students planning to pursue a college career path, especially for those planning a career in STEM fields of study. Students should successfully complete Algebra II and Trigonometry before taking this course. Students will review various functions – equations and graphs – and transformations thereof. They know that functions can be used to model real-world situations. They will be familiar with linear, quadratic, power, polynomial, rational, exponential, logistic, and logarithmic functions. Students attain a deeper understanding of complex numbers and what they mean. Trig skills have been reinforced as students use the trig functions to find unknown sides and angles of right triangles. Students have gained confidence working with graphs of trig functions and translating them. They are familiar with harmonic motion and know how to use it to solve real-world problems. Their proficiency using the basic trig identities is improved as they continue to solve problems using them. Students learn about vectors and dot products. They learn about polar coordinates and how to express complex numbers in this form. Students are familiar with several uses of matrices in solving real-world problems. Student skills using conic sections are reinforced. Students also have a basic fundamental understanding of the concept of the limit, tangent lines, and finding the area underneath a curve – all in preparation for continued studies in Calculus. Acellus Pre-Calculus is taught by award-winning Acellus Master Teacher, Patrick Mara. Acellus Pre-Calculus is A-G Approved through the University of California.
Scope and Sequence
Unit 1 – FunctionsThis unit covers definition, domain, range, continuity, increasing, decreasing, symmetry, asymptotes, end behavior, and extrema. Also presented are a function tool kit, piecewise defined functions, combining functions, composition, implicitly and parametrically defined, inverse functions, translations, dilations, modeling, and sequences.Unit 2 – Polynomial, Power, and RationalThis unit discusses linear, quadratics, power, polynomial, long division, synthetic division, remainder and factor theorems, rational zeros, complex numbers and zeros, the fundamental theorem of algebra, rational functions and equations, inequalities, and interval notation.Unit 3 – Exponential, Logistic, and Logarithmic FunctionsThis unit covers exponential, logistic, modelling with sequences, logarithmic, properties of log functions, equation solving, compound interest, sum of a geometric sequence, continuous compounding, and exponential modeling. Following this unit students are presented with the Mid-Term Review and Exam.Unit 4 – Trigonometric FunctionsThis unit discusses angles, arc length, trig functions of acute angles, special angles, circular functions, graphs of sine and cosine, translations of trig functions, tangent, cotangent, secant, cosecant, harmonic motion, and inverse trig functions.Unit 5 – Analytic TrigonometryThis unit covers basic identities, sums and differences, multiple angles, solving right triangles, the laws of sines and cosines, and area.Unit 6 – Vectors, Parametric, and PolarThis unit discusses vectors, dot products, parametric equations, polar coordinates and their graphs, complex numbers in polar form, DeMoivre’s Theorem, and complex roots.Unit 7 – Systems and MatricesThis unit discusses solving systems of two equations, matrices, inverse matrices, amd other uses of matrices. Also covered are multivariate systems and systems of inequalities.Unit 8 – ConicsThis unit includes parabolas, completing the square, distance, midpoint, circles, ellipses, and hyperbolas.Unit 9 – CalculusThis unit covers binomial theorem and regression, finding limits, tangent lines, and area under a curve. Following this unit students are presented with the Final Review and Exam.