Book 2: Bridge to Calculus

A guided path from algebra and functions into trigonometry, rates of change, introductory differentiation, and introductory integration.

Move from foundation math into calculus thinking.

Book 2 is the bridge between college math foundations and calculus readiness. Students review algebra, learn function thinking, use trigonometry as a practical tool, understand rates of change, and begin recognizing differentiation and integration.

This path is especially useful for adult learners, STEM-bound students, engineering technology students, robotics students, and anyone who wants calculus to feel less intimidating before taking a formal course.

Recommended Book 2 Learning Path

  1. Make algebra equation-handling automatic.
  2. Understand input, output, and function behavior.
  3. Use trigonometry for motion, geometry, and components.
  4. Understand average and instantaneous rates of change.
  5. Preview differentiation and integration before formal calculus.

Where this fits in DNAPOT

Book 1 builds college math foundations. Book 2 prepares students for calculus thinking. Book 3 continues into Calculus I, Calculus II, and Calculus III.

Book 2 Chapters

Each chapter will become an interactive practice module with mini lessons, worked examples, instant feedback, and mastery checks.

Chapter 1

Algebra Foundations for College Math

Make equation-handling automatic before moving into functions and calculus.

  • Solving linear equations
  • Rearranging formulas
  • Ratios and proportions
  • Squares and square roots
  • Units inside equations
Start Chapter 1
Chapter 2

Functions: Input, Output, and Change

Prepare for function thinking, graphs, and change-based reasoning.

  • What a function means
  • Function notation
  • Linear functions and slope
  • Quadratic functions
  • Reading functions from tables and graphs
Start Chapter 2
Chapter 3

Trigonometry for Motion and Geometry

Use trigonometry as a practical tool, not a memory test.

  • Right triangles
  • Sine, cosine, and tangent
  • Resolving components
  • Direction and sign
  • Degrees and radians
Start Chapter 3
Chapter 4

Rates of Change

Introduce calculus ideas through motion, graphs, tables, and change.

  • Average rate of change
  • Rate from a table
  • Rate from a graph
  • Instantaneous rate concept
  • Acceleration as rate of velocity change
Start Chapter 4
Chapter 5

Introductory Differentiation & Integration

Preview calculus by connecting rates, derivatives, accumulation, and integrals.

  • Differentiation as rate at a moment
  • Derivative notation
  • Simple derivatives
  • Integration as accumulation
  • How differentiation and integration connect
Start Chapter 5
Mastery

Book 2 Mastery Check

Mixed review of all Book 2 topics before moving into Calculus I–III.

  • Algebra readiness
  • Function thinking
  • Trigonometry tools
  • Rates of change
  • Intro calculus ideas
Take Mastery Check