bythreedu · Math Tracks · Curriculum v1.0 · 2026

Functions,
trig, and the
language of limits.

A ground-up precalculus education — starting with how functions actually behave, moving through every major function family, and building toward a confident entry into Calculus I.

Total Lessons29at your pace
Units9progressive phases
Assignments9+problem sets
DestinationCalculus I
Ready
00Approach
Course Philosophy

Functions First, Formulas Second

Most students hit precalc and try to memorize formulas. That works until it doesn't — usually around trig identities or limits. This course builds understanding instead. Every formula is derived or explained before it's used.

Built for Calculus, Not Just the Test

The goal isn't to pass precalc. The goal is to walk into Calculus I with no gaps. That means taking limits seriously, not treating trig as a memorization exercise, and understanding function behavior at a level most precalc courses don't require.

01Curriculum
Learning Path
01
Unit 1 · Weeks 1–3
Functions: The Core Idea
3 lessons · Domain and range · Function behavior · Transformations
domain & rangefunction notationtransformations
+
02
Unit 2 · Weeks 4–6
Polynomial and Rational Functions
3 lessons · Polynomial graphs · Asymptotes · Sign charts
multiplicityasymptote behaviorsign chart
+
03
Unit 3 · Weeks 7–9
Exponential and Logarithmic Functions
3 lessons · Base e · Log rules · Solving equations
base elog rulesexponential equations
+
04
Unit 4 · Weeks 10–12
Trigonometry: The Unit Circle
3 lessons · Radian measure · Unit circle · Six trig functions
radian measureunit circle derivationsix trig functions
+
05
Unit 5 · Weeks 13–15
Trig Graphs and Identities
3 lessons · Amplitude and period · Trig graphs · Fundamental identities
amplitudeperiod & phase shiftPythagorean identities
+
06
Unit 6 · Weeks 16–18
Triangle Trig and Applications
3 lessons · Right triangle trig · Law of Sines · Law of Cosines
SOH-CAH-TOAambiguous caselaw selection
+
07
Unit 7 · Weeks 19–21
Analytic Geometry and Systems
3 lessons · Conic sections · Nonlinear systems · Sequences and series
conic standard formsnonlinear systemssigma notation
+
08
Unit 8
Discrete Mathematics and Foundations of Calculus
3 lessons · Logic and sets · Combinatorics · Rates of change
logic & proofcombinatoricsaverage rate of changedifference quotient
+
09
Unit 9
Introduction to Limits and Capstone
4 lessons · Limit intuition · Limit laws · Continuity · Capstone exam
limit notationone-sided limitscontinuity types
+
02Capstone
Mock Exam and Final Review

The capstone is a full-length timed mock exam built from every unit in the course. Every missed problem becomes a lesson: we go through the reasoning together and you write out the corrected approach in your own words.

○
Gap Identification Session
Before the exam, you select the three units you're least confident in. We do a targeted review of each before the clock starts.
○
90-Minute Timed Exam
Full coverage across all 9 units. Timed and taken independently — same conditions as a real exam.
○
Written Corrections
Every missed problem gets a written correction with reasoning — not just the right answer, but the decision that should have been made at each step.
○
Calculus I Readiness Review
A final session mapping your precalc skills to what Calc I will demand — so you know exactly where you stand on day one.
03Investment
Pricing Options
Location
per Session
$125
1.5 hrs · online only
Session length
  • —Flexible scheduling
  • —1-on-1 focused attention
  • —No long-term commitment

Best for trying the curriculum before committing to a plan.

Popular
per Month
$500
4 sessions · 1.5 hrs/session
Frequency
Session length
  • —Session notes after every lesson
  • —Async DM support between sessions
  • —Priority scheduling

Adjust frequency and session length above — price updates automatically.

Per Semester
$2,000
16 sessions · 1.5 hrs/session
Term length
Frequency
Session length
  • —All 9 units — full course arc
  • —Session notes after every lesson
  • —Capstone mock exam + written corrections
  • —Calculus I readiness review at completion

The full Precalculus arc — from functions to limits — in one commitment.

📍
In-person available · NYC onlyMonthly and semester plans can be done in-person. Select "In-person · NYC" above to see adjusted pricing.
04Contact
Let's Talk

Not sure which plan is right for you? Start with one session and see how it feels.

Do I need to be currently enrolled in a precalculus course?+
What do I need to know coming in?+
Are lessons online or in-person?+
Can I switch plans later?+
What if I need to reschedule?+