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Honors Geometry with Integrated PreCalculus

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Online for the 2025-2026 School Year

Teacher: Caleb Alons

Email: calebscottalonsmathematics@gmail.com

COURSE OVERVIEW:

The syllabus for this course is provided below (a fuller version of the syllabus with a week-by-week calendar schedule is available; email calebscottalonsmathematics@gmail.com to request a copy of the 2025-2026 Honors Geometry with Integrated Precalculus syllabus).

TUITION:

Early Bird Special: $700

After June 30: $750

WHY THIS COURSE?

Homeschoolers have an overwhelming number of options for high school math courses online, so why choose this course? I believe that every student (a) learns math at a different pace and (b) requires varying amounts of exposure and time to feel comfortable with certain topics. Given the structure and asynchronous nature of this course, I can offer unparalleled personalized aid, instruction, supplementary tutoring, and resources to each student enrolled. The tuition price encompasses same-day answers to questions posted to the website, unlimited office hours, and additional live tutoring over Zoom on a case-by-case basis. Of course, it is up to the student to take initiative to access this support, and any student who seeks help will receive it. Having taught primarily engineering, computer science, and other STEM students in university courses, I continually fine-tune my understanding of how useful certain concepts are and the extent to which mastery of them affects future studies in STEM.

Syllabus for

Honors Geometry with Integrated Precalculus

2025–2026 Academic Year

I. COURSE DESCRIPTION

Honors Geometry with Integrated Precalculus is an intensive course designed for advanced students seeking mastery over the fundamental concepts of Euclidean geometry and gaining accelerated preparation for standardized testing (ACT/PSAT/SAT). Honors Geometry with Integrated Precalculus is designed to help students construct a sturdy launchpad for future college-level courses. This course builds upon itself, covering points, lines, planes, angles, deduction and writing proofs, parallel lines, planes, congruent triangles, quadrilaterals, geometric inequalities, similar polygons, right triangles, fundamental trigonometric ratios, circles, constructions, loci, areas of plane figures, areas and volumes of solids, coordinate geometry, and transformations. Students will acquire technical and mechanical fluency that translates well into future math courses and solving ACT/PSAT/SAT math problems. Most students should anticipate dedicating 6+ hours each week to keep up with the pace of the course and to perform well.

Prerequisite(s): Students should enter the course with a strong foundation in Prealgebra and Algebra 1. Although not mandatory, familiarity with Algebra 2 will prove helpful in various portions of this course. Any student who takes this course should be fully fluent with elementary mathematical concepts and not depend on calculators or digital aids to perform arithmetic. Students without these prerequisites may struggle to keep up with the pace of the course and should probably take an Honors Algebra 1 course prior to taking this one.

II. STUDENT LEARNING OUTCOMES FOR THIS COURSES

A. COURSE OUTCOMES

After completing this course successfully, students will be able to:

1. Identify, define, and create points, lines, and planes

2. Identify, define, and create segments, rays, and distances

3. Identify and compute angles

4. Memorize and apply postulates and theorems relating points, lines, and planes

5. Identify and create statements in logical argumentation

6. Identify and create if-then statements and their converses

7. Prove theorems with fundamental logic

8. Plan deductive proofs

9. Apply the properties of parallel lines

10. Prove that lines are parallel

11. Memorize and apply the angles of triangles and polygons

12. Prove statements inductively

13. Identify congruent figures

14. Prove triangles are congruent

15. Identify and apply medians, altitudes, and perpendicular bisectors

16. Memorize and apply the properties of parallelograms

17. Prove that quadrilaterals are parallelograms

18. Categorize special parallelograms and trapezoids

19. Identify and apply geometric inequalities

20. Use the inverses and contrapositives in indirect proofs

21. Solve problems with similar polygons

22. Memorize the Pythagorean theorem and its converse

23. Memorize the properties of special right triangles

24. Memorize and apply fundamental trigonometric ratios

25. Identify circle concepts

26. Solve circle problems involving tangents, arcs, and inscribed angles

27. Perform geometric constructions

28. Compute areas of rectangles, parallelograms, triangles, rhombuses, trapezoids, and regular polygons

29. Compute circumferences and areas of circles

30. Compute arc lengths and areas of sectors

31. Compute areas and volumes of prisms, pyramids, cylinders, cones, and spheres

32. Perform elementary Euclidean coordinate geometry

33. Perform geometric reflections, translations, rotations, and dilations

34. Identify and compute mappings, functions, composite mappings, inverses, and identity

B. GENERAL OUTCOMES

Students will develop the following skills that do not necessarily have restricted application to this course specifically:

1. Advanced creative problem solving

2. Study discipline and mental toughness

3. Seeking help and offering help to peers

4. Collaborative learning

5. Increased proficiency in standardized math testing

III. TEXTBOOKS AND OTHER LEARNING RESOURCES

A. REQUIRED MATERIALS

1. Textbooks:

a. Jurgensen, Ray C., Richard G. Brown, and John W. Jurgensen. Geometry. Evanston, IL: McDougal Littell, 2000. ISBN-13: 978-0-395-97727-9.

b. Jurgensen, Ray C., Richard G. Brown, and John W. Jurgensen. Geometry Solution Key. Evanston, IL: McDougal Littell, 2000. ISBN-13: 978-0-395-67766-7.

It is possible to find both books being sold as used copies individually, but just make sure BOTH books are purchased, as weekly homework assignments require ownership of the Geometry Solution Key in addition to the text itself.

2. Other:

a. Access to the Internet to log onto the course website

IV. POLICIES AND PROCEDURES

A. COURSE POLICIES AND PROCEDURES

1. Attendance: Honors Geometry with Integrated Precalculus does not have a live component. Instead, students will engage on the class website throughout the week with the instructor and their fellow peers as they progress through the course material. Students desiring additional help from the instructor need only reach out to the instructor via email for one-on-one tutoring and office hours.

2. Evaluation Procedures:

a. Weekly Homework Assignments:

Sections from the textbook are assigned each week. For each section, the student must do the following:

Read the textbook section and take notes: 3 points

Watch the assigned video(s): 2 points

Complete the exercises at the end of the section: 3 points

Self-grade work with solutions key: 2 points

___________________________________________

Expected Section Total: 10 points

Each item listed above is based on completion. Students will report their own completion scores per section by the Sunday of each week before 11:59 PM (EST). If a section does not contain a video or exercises, students should simply reward themselves with the points of the missing items automatically to their section score.

Since there are 92 total sections overall, the expected weekly homework total is 920 points for the entire course.

b. Student Engagement:

Student engagement and peer collaboration is STRONGLY encouraged in this course. Students may earn bonus points each week for their engagement on the course website.

Students who post genuine and insightful questions to the course website will receive up to 0.5 bonus points per question, and students who post substantially helpful and insightful answers on the course website will receive up to 1 bonus point per response. Additionally, students who simply engage with the material and post productive and thoughtful messages to the course website will receive up to 2 bonus points per week.

Positive, collaborative, and productive engagement on the course website strongly and positively influences a student's overall course grade.

c. Quarterly Tests:

Students will take four quarterly tests throughout the course. Each quarterly test is worth 500 points (so 2,000 points of the final course grade come from quarterly tests).

Each quarterly test must be proctored by a parent/guardian and taken in one uninterrupted sitting; aside from this, students may take as much time as needed to finish. The use of class notes, formula sheets, calculators, digital aids, the Internet, etc. are strictly prohibited.

d. Final Examination:

Students will take a final examination at the end of the course.

The final examination is worth 680 points. The final examination is comprehensive for all content covered in the entire course.

The final examination must be proctored by a parent/guardian and taken in one uninterrupted sitting; aside from this, students may take as much time as needed to finish. The use of class notes, formula sheets, calculators, digital aids, the Internet, etc. are strictly prohibited.

e. On a test/examination week, access to the test/examination will be given on the Friday of that week from 12 PM EST–11:59 PM (EST). If a student has special circumstances and needs to take the test/examination at a different time/date, the student should email the instructor directly in advance for accommodation, which will be given for all legitimate situations.

f. Grading Scale:

A: 3,200–3,600 points

B: 2,800–3,199 points

C: 2,500–2,799 points

D: 2,100–2,499 points

F: 0–2,099 points

The numeric grading scale is not completely fixed, as the instructor will consider other holistic factors into the overall final grade. The final grade is designed to reflect the student's holistic growth and progress made throughout the course. Students who score poorly earlier in the course, but who demonstrate an eagerness and initiative to truly learn and overcome challenges, can earn higher grades than their total point sum is at the end of the course. A student's progress over time is also factored into potentially raising a student's final letter grade: steady improvements from poor to excellent scores will be awarded.

Other factors for raising a student's final letter grade include the student's level of engagement, participation, activity on the course website (asking questions, answering questions, cultivating community with peers, creating a welcoming learning environment, etc.), and communication with the instructor throughout the course.

The end goal of this course is for the student to acquire genuine comprehension and mastery of the material, so the final course grade is designed to reflect the student's ability to learn, willingness to struggle, and desire to overcome deficits and setbacks. Since mathematics in the real world is messy and characterized by "being stuck," the grading system for this course hopes to incentivize students to think independently and creatively and to reward students for embracing challenges and learning how to handle struggle.

V. COURSE CALENDAR

Note on Due Dates:

Completion scores for assigned sections will ALWAYS be due by the Sunday of their assigned week at 11:59 PM (EST).

Review section IV.A.2.e of the syllabus above for information concerning due dates for quarterly tests and the final examination.

To see the full week-by-week course calendar, please send an email to  calebscottalonsmathematics@gmail.com so that I can email you a PDF copy of the entire syllabus that includes all calendar information.

IMPORTANT DATES AT A GLANCE:

First Day of Class: Aug 11, 2025

Quarterly Test 1: Sep 26

Thanksgiving Break: Monday, Nov 24 – Sunday, Nov 30

Quarterly Test 2: Dec 5

Winter Break: Monday, Dec 22 – Sunday, Jan 4 (2026)

Quarterly Test 3: Feb 13, 2026

Quarterly Test 4: Apr 24

Final Exam: May 15

VI. INSTRUCTOR QUALIFICATIONS

Caleb Scott Alons will receive his B.S. in Mathematics in May 2025. Caleb is a returning AP Homeschoolers instructor, having previously taught two years of supplementary and preparatory summer courses in both mathematics and science. After developing a love for teaching mathematics, Caleb started professionally tutoring mathematics in 2020 and has been an assistant lecturer at Oral Roberts University for the past four years, teaching several hundred students in Calculus I/II/III, Vector Calculus, Differential Equations, Discrete Mathematics, Linear & Matrix Algebra, Abstract Algebra, Real Analysis, General (Point-Set) Topology, and Algebraic Topology. In his undergrad, Caleb led as president the KME Honors Mathematical Society and Association of Computing Machinery in addition to being an active participant in the Mathematical Association of America, presenting award-winning research in MAA sectionals and the MAKO UG Research Conference. Caleb also scored three consecutive years in the William Lowell Putnam Mathematical Competition, which is esteemed as the hardest UG mathematical exam in the world.

As someone who formerly struggled with mathematics in high school himself, Caleb is deeply invested in seeing every student succeed no matter the circumstances and has personally tutored many students with learning disabilities to help them achieve 5's on AP Calculus AB/BC, score above the 90th percentile on the PSAT/SAT/ACT math tests, and rank in the top 5% of their university math courses. Ultimately, teaching mathematics is a source of great joy for Caleb, and he delights in serving each student under his instruction.

The teacher is the servant of his students. – CSA

 

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