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).