Who This Page Is For
Students prepping for AP Calc / college calc
You want the calc transition to feel smooth, not chaotic. We focus pre-calc work on the exact skills calc will use.
Students struggling mid-course
Trig identities or log rules became a wall. We rebuild from the gap and get you caught up.
Students who need to retake or self-study
Pre-calc is a big course. We can do a full review at your pace.
What We Cover
Functions
- Domain, range, function notation
- Transformations (shifts, stretches, reflections)
- Composition and inverses
- Piecewise functions
- Even / odd, symmetry
Polynomial & Rational
- End behavior, multiplicity
- Synthetic and long division
- Rational root theorem
- Asymptotes, holes
- Graph sketching
Exponential & Logarithmic
- Exponential growth/decay
- Log properties, change of base
- Solving exponential equations
- Compound interest
Trigonometry
- Unit circle mastery
- Graphing sin, cos, tan
- Trig identities and proofs
- Solving trig equations
- Inverse trig functions
- Law of sines / cosines
Vectors & Polar
- Vector arithmetic, dot product
- Polar coordinates and graphs
- Parametric equations
- Complex numbers in polar form
Sequences & Limits
- Arithmetic and geometric series
- Sigma notation
- Intro to limits
- Conic sections
The Unit Circle Trick That Saves Every Trig Identity Problem
- Recognize the Pythagorean identity. sin²θ + cos²θ = 1. Rearranged: 1 − cos²θ = sin²θ. That's the one substitution that unlocks the whole problem.
- Substitute. The left side becomes sin²θ / sin θ.
- Simplify. sin²θ / sin θ = sin θ. Done.
- The meta-skill. Trig identity proofs almost always reduce to recognizing one of three identities: Pythagorean, double angle, or sum/difference. We build a flowchart so you stop staring.
Common Sticking Points
"The unit circle is just memorization"
Until you see why — sin and cos are coordinates. We rebuild the unit circle from geometry so it stops being a chart to memorize.
"Log rules feel arbitrary"
Log rules are exponent rules in disguise. We derive them once, and they stick.
"Trig identities seem random"
There are about 10 you need. We learn the 3 most important ones cold, then derive the rest as needed.
"Polar / parametric is a different language"
It is — until you connect it back to x and y. We translate both ways until the modes feel like the same idea.
FAQ
What pre-calculus topics do you tutor?
Functions and their transformations, polynomial and rational functions, exponentials and logarithms, trigonometric functions and identities, vectors, polar coordinates, parametric equations, conic sections, sequences and series, and an intro to limits.
How is pre-calculus different from algebra 2?
Algebra 2 builds the toolset (functions, exponents, logs). Pre-calc adds trigonometry depth, polar/parametric, and intro to limits so you're ready for calculus. Many topics overlap — we focus on the bridge to calc.
Can pre-calc help me prep for AP Calc?
Yes — a strong pre-calc foundation is the single biggest predictor of success in AP Calc. We focus on the topics that actually show up: trig identities, function behavior, limits, and algebra fluency.