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Recorded HS
Math
Saxon Advanced Mathematics (Pre-Calculus) Part One

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.

Total classes: 14

Prerequisite: Algebra II and Geometry

Suggested grade level: 11th to 12th

Suggested credit: One full semester Pre-Calculus or Math

##### Description

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.

##### Outline

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

##### Materials and Homework

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).

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