Unit 12 — Introduction to Calculus

Unit 12 · Introduction to Calculus

Introduction to Calculus

Bridge precalculus and calculus — limits, continuity, and the derivative — building the conceptual and algebraic foundation for AP Calculus and college-level mathematics.

Estimated Time

2–3 weeks

Difficulty

Advanced

4 Lessons
5 Learning Goals
12 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 12 — Introduction to Calculus is your bridge to the next level of mathematics. You will estimate and evaluate limits numerically, graphically, and analytically, classify discontinuities, and define the derivative as the limit of the difference quotient. Every concept here is a direct prerequisite for AP Calculus AB, AP Calculus BC, or college calculus.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Estimate limits numerically and graphically; evaluate limits analytically using limit laws.
Goal 2Apply limit properties to evaluate limits of sums, products, quotients, and compositions.
Goal 3Define continuity at a point and on an interval; identify and classify discontinuities.
Goal 4Define the derivative as the limit of the difference quotient and interpret it as instantaneous rate of change.
Goal 5Find derivatives of polynomial and simple functions using the limit definition.

Skills You Will Master

Limits numerically & graphically
Limit laws & analytic evaluation
Continuity & discontinuities
The derivative & tangent lines

Real-World Connection

Calculus is the mathematics of change and accumulation — and Unit 12 is your gateway to it. Limits describe what happens at the edge of what we can directly compute. Continuity tells us when a model is reliable. The derivative measures instantaneous speed, the rate a drug leaves the bloodstream, the marginal cost of producing one more unit, or the slope of a hillside at a single point. Every field that studies how quantities change — physics, economics, biology, engineering — uses calculus as its primary language. Completing Unit 12 means you are ready for AP Calculus AB, AP Calculus BC, or any college-level calculus course.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter