Functions in depth
Composition, inverses, transformations, piecewise functions, and function notation.
Precalculus & trigonometry tutoring
Online Precalculus Tutor: the bridge into calculus.
Precalculus is where gaps from earlier courses tend to surface, and where calculus readiness is really decided. Northstar works on both at once: the current coursework and the foundations underneath it.
$50 / 60 minutes · No long-term commitments · No required prepaid packages · 12-hour cancellation policy
What we cover
What precalculus sessions can cover
The unit circle & trig graphs
Building real intuition for the unit circle instead of memorizing a table.
Trigonometric identities & equations
Pythagorean, sum and difference, and double-angle identities, and solving trig equations.
Exponentials & logarithms
Log rules, solving exponential equations, and modeling growth and decay.
Polynomials & rational functions
End behavior, zeros, asymptotes, and sketching accurate graphs.
Vectors, polar & sequences
Vector operations, polar coordinates, and sequences and series.
Founded by a mathematics specialist
Northstar was founded by Joshua Lizardi, who holds an M.S. in Applied Mathematics, an M.S. in Data Analytics, a B.S. in Mathematics, and a Graduate Certificate in Applied Statistics, with 9+ years of teaching mathematics, including college and graduate-level instruction.
- Live one-to-one sessions through Zoom
- $50 per 60-minute session
- No long-term commitments or required prepaid packages
- 12-hour cancellation policy
- Flexible scheduling
- Payment through Zelle
Family cancellation policy, effective November 1, 2026
Cancel or reschedule with at least 12 hours' notice without charge. With less notice, the full $50 session fee may be charged. Student no-shows are generally charged the full scheduled fee. If Northstar cancels, you are not charged; any payment collected for that session is refunded or credited as appropriate. Rescheduling depends on mutual availability. Previously agreed individual exceptions are honored, and this policy does not apply to earlier sessions.
Private tutoring is $50 per 60-minute session. Invoices are typically issued after 4 tutoring sessions and paid through Zelle. Late-cancellation or no-show fees may appear on an invoice. No required prepaid packages or long-term commitments.
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