This is our catalog of courses. We will occasionally adjust the course listing to reflect the addition of new courses and the retirement of others.
Are you entering science, technology, engineering, mathematics, or business in college? Then this Pre-Calculus will prepare you with algebraic and trigonometric concepts — including linear and nonlinear functions, complex numbers, polar coordinates, and more. For Pre-College Students.
We will explore all the algebraic and trigonometric concepts; this includes both linear and nonlinear plus functions, complex numbers, and concepts involving trigonometry & polar coordinates. This course will fulfill requirements for Pre-calculus and ready students for High School and college advanced topics in math including Calculus.
Week One – Lessons 1-5:
Geometry review of terms; area of figures, volume of prisms and cones; Pythagorean Theorem, triangle inequalities, similar polygons; constructions; Exponents and radicals, complex numbers, areas of similar figures
Week Two – Lessons 6-10
Topics to include: fractional equations, radical equations, systems of three linear equations; inductive and deductive reasoning, logic, contrapositive, converse and inverse; statements of similarity, proportional segments, angle bisectors and side ratios; congruent figures, proof outlines; equation of a line, rational denominators, completing the square
Week Three: Lessons 11-14
Topics to include: circles, properties of circles, quadratic formula; angles and diagonals in polygons, proof of the chord-tangent theorem; intersecting secants, intersecting secants and tangents, products of chord segments, products of secant and tangent segments; sine, cosine, and tangent, angles of elevation and depression, rectangular and polar coordinates, coordinate conversion; assumptions, proofs
Week Four – Lessons 15-18
Topics to include: complex fractions, abstract equations, division of polynomials; proofs of the pythagorean theorem, proofs of similarity; advanced word problems; nonlinear systems, factoring exponentials, sum and difference of two cubes
Week Five – Lessons 19-22
Topics to include: evaluating functions, domain and range, types of functions, tests for functions; absolute value, reciprocal functions; the exponential function, sketching functions; sums of trigonometric functions, combining functions
Week Six – Lessons 23-26
Topics to include: age problems, rate problems; logarithmic form of the exponential, logarithmic equations; related angles, signs of trigonometric functions; factorial notation, abstract rate problems
Week Seven – Lesson 27-30
Topics to include: the unit circle; addition of vectors; symmetry; inverse functions
Week Eight – Lessons 31-34
Topics to Include: Symmetry, Reflections, Translations; Inverse Functions; Quadrilaterals; Summation Notation
Week Nine – Lessons 35-38
Topics to Include: Line as a locus; fundamental counting principle and permutations; radian measure of angles; argument in mathematics
Week Ten – Lessons 39-42
Topics to include: reciprocal trig functions; conic sections; periodic functions; abstract rate problems
Week Eleven – Lessons 43-46
Topics to include: conditional permutations; complex roots; vertical sinusoid translations; powers of trig functions
Week Twelve – Lessons 47-50
Topics to include: the logarithmic function; trigonometric equations; common logs and natural logs; the inviolable argument
Week Thirteen – Lessons 51-54
Topics to include: Unit Multipliers; Parabolas; Circular Permutations; Triangular Areas
Week Fourteen – Review and Semester Exam
Course Materials: Saxon Advanced Mathematics and Incremental Development, Edition 2, with the test and homeschool pack (www.setonbooks.com/saxon.php), a scientific calculator (TI 30X or the like), graph paper, ruler, protractor, compass, and pencil. Graphing calculators are useful, but not necessary. Instructor will provide a free weekly lecture in addition to the live, interactive classes.
Homework: 4-5 assignments per week with 15-20 problems to work per lesson. Expect to spend approx. 60 minutes a day on homework (may vary depending on the student’s understanding of new concepts).