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Saxon Advanced Mathematics: Pre-Calculus, Part One

With Jean Hoeft, MA

Want to be ready for all of those high-stakes tests in your future? Saxon Advanced Math is just what you need to score well on the SAT and college placement tests. We explore the content of all advanced topics in readiness for calculus

This is a high school-level advanced math – pre-calculus course. Students will complete four to five lessons per week with a test every other week. Students must view the recorded lectures before attending class, and then participate in class by working problems when requested and answering questions when called upon. Extra help is offered on Fridays during office hours, and students are encouraged to bring questions to class.

**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__, a scientific calculator (TI 30X or the like), graph paper, ruler, protractor, compass, and pencil. Graphing calculators are useful, but not necessary. The instructor will provide a free weekly lecture in addition to the live, interactive classes.

**Homework**: Students will be required to complete four to five lessons per week (15 problems per lesson), and a 20 question test every other week. Students may bring questions to class but are asked to attempt all work.

**Class Dates:** Mondays, August 26 to December 9, 2024. (No class Sept. 2 for Labor Day & Oct. 28)

**Starting Time:** 11:30 AM Eastern (10:30 Central; 9:30 Mountain; 8:30 Pacific)

**Duration:** 55 minutes

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