Advanced Placement · College Board

AP Precalculus.

Premium AP Precalculus preparation with personalized one-on-one instruction by Mr. Sharma.

AP Precalculus prepares students for AP Calculus, college-level mathematics, and the quantitative sections of the SAT and ACT. Strong work here is the cleanest path into Calculus AB or BC.

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Exam Snapshot

AP Precalculus at a glance.

The format, scoring, and tools every family should know before starting preparation.

Exam Length
3 hours
Multiple Choice
40 MCQ · 2 hours
Free Response
4 FRQ · 1 hour
Calculator
Graphing calculator on portions of both sections
Scoring
1–5 scale
Administered
May, College Board AP Exam window

Section 01 · Units

College Board Units

The full AP Precalculus curriculum, unit by unit. Every unit is taught from first principles on the digital whiteboard before any free-response practice begins.

Core

Unit 1 · Polynomial and Rational Functions

Topics

  • End behavior
  • Zeros and multiplicity
  • Rational function asymptotes
  • Polynomial long division
Core

Unit 2 · Exponential and Logarithmic Functions

Topics

  • Exponential growth and decay
  • Logarithm properties
  • Modeling with exponentials
  • Inverse functions
Core

Unit 3 · Trigonometric and Polar Functions

Topics

  • Unit circle
  • Sinusoidal modeling
  • Identities
  • Polar coordinates and graphs
Core

Unit 4 · Functions Involving Parameters, Vectors, and Matrices

Topics

  • Parametric equations
  • Vector operations
  • Matrix transformations
  • Linear systems

Section 02

Skills Tested

What AP Precalculus really measures beyond memorized formulas — and where Mr. Sharma focuses instruction.

Skill

Function Fluency

Reading function behavior across multiple representations — graphs, tables, equations, and verbal descriptions.

Skill

Modeling

Selecting the right function family for a real-world situation and validating predictions.

Skill

Calculator Strategy

Using the graphing calculator efficiently on the calculator-permitted sections without becoming dependent.

Skill

Free-Response Writing

Justifying answers in writing the way College Board readers expect.

Section 03

Common Student Challenges

Patterns Mr. Sharma sees most often on AP Precalculus — and how each is addressed during tutoring.

Section 04

Mr. Sharma's Teaching Process

A six-step path from diagnostic to test day, used with every AP Precalculus student.

  1. Step 01

    Initial Diagnostic Assessment

    A full-length diagnostic establishes the student's true starting point across every tested area.

  2. Step 02

    Identify Strengths & Weaknesses

    Results are mapped to specific subtopics — not just section scores — so the plan targets the right work.

  3. Step 03

    Build Conceptual Foundations

    Underlying content is rebuilt where needed so test strategies have something solid to stand on.

  4. Step 04

    Practice Official-Style Questions

    Curated, exam-aligned problems are worked through together on the digital whiteboard.

  5. Step 05

    Learn Time-Saving Strategies

    Pacing, elimination, and figure-reading techniques tuned to this exam's format.

  6. Step 06

    Build Confidence Through Full-Length Practice Tests

    Regular timed practice tests turn preparation into performance — and reveal exactly what to refine next.

Section 05

Why Parents Choose Mr. Sharma

What families consistently point to when describing preparing for AP Precalculus with Mr. Sharma.

Included

30+ Years Teaching Experience

Decades of one-on-one and classroom instruction across every level of mathematics and science.

Included

Individualized Instruction

Every session is built around the student in front of the camera — never a group class.

Included

Concept-Based Learning

Students learn why the material works, not just which button to press.

Included

Digital Whiteboard Lessons

Live, written, step-by-step instruction that mirrors a real classroom whiteboard.

Included

Customized Homework

Assignments written for the student's plan — never generic worksheets.

Included

Progress Tracking

Clear, ongoing measurement so families see exactly where their student stands.

Included

Flexible Online Scheduling

Sessions fit around school, sports, and family life — anywhere in the country.

Included

Patient Teaching Style

Questions are welcomed, not rushed. Students learn to think out loud.

Included

Exam-Oriented Preparation

Every lesson connects back to how the concept actually appears on the exam.

Section 07

Frequently Asked Questions

The questions parents and students ask most often about this exam and how Mr. Sharma prepares his students.

Advanced STEM Library

Comprehensive Formula Sheet & Free Resources

Downloadable formula sheets, study guides, and reference materials for AP Precalculus Tutoring — curated by Mr. Sharma and continuously expanded as part of the Advanced STEM Library.

Coming Soon

Comprehensive Formula Sheet

Every formula, identity, and relationship a student needs for AP Precalculus Tutoring — organized by topic and printable in one page.

Publishing shortly
Coming Soon

Concept Study Guide

A structured written companion covering the core content areas tested on AP Precalculus Tutoring, section by section.

Publishing shortly
Coming Soon

Topic Review Notes

Concise topic-by-topic reviews with worked examples — designed to be re-read the week before test day.

Publishing shortly
Coming Soon

Practice Plan Templates

Four-, eight-, twelve-, and sixteen-week study calendars aligned to a student's timeline and current level.

Publishing shortly
Coming Soon

Common Mistakes Reference

The specific errors that quietly cost points on this exam — with the fix Mr. Sharma teaches for each.

Publishing shortly
Coming Soon

Score-Building Question Set

A curated set of exam-aligned practice questions targeting the highest-yield subtopics.

Publishing shortly

The Advanced STEM Library

One growing library of formula sheets, study guides, and topic reviews.

Every resource on this page will live in the Advanced STEM Library — a single, expanding home for the formula sheets, study guides, topic reviews, encyclopedia entries, practice plans, and reference materials Mr. Sharma uses with his own students.

Open the Advanced STEM Library

Ready When You Are

Ready to Earn a 5 on AP Precalculus?

Begin with a free strategy session. Mr. Sharma will identify exactly where AP Precalculus understanding is strongest, where it is weak, and what the path to a top score looks like.

Schedule Your Free Consultation

Begin

Start with a focused strategy conversation.

The strategy session is the first step of working together — a focused academic planning and diagnostic conversation used to understand the student before any ongoing academic support begins.

Book a Free Consultation