• Home
  • TI-84 Tutorials
  • How to Convert HW to a PDF File
  • Graph Paper
  • M105 at IUK
    • TI-84 Tutorials
    • Semester Schedule & M105 At A Glance
    • Course Syllabus & Lecture Content List
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 4
    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • AP Calculus AB at THS
    • Calculus Class Pictures
    • Calculus Student Inventory
    • TI-84 Tutorials
    • Zoom Meeting Recordings
    • Monthly Calendars
    • Web Assignments
    • AP College Board YouTube
    • AP Calculus AB Exam
    • ACP Calculus - IU
    • Memorization Sheets
    • Calculus Memorization Quizzes
    • Test/Quiz Correction Analysis
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Last Chapter/Review
    • Final Exam Review WS
    • The Calculus Life Saver
    • Final Calculus Video Project
    • Past AP Calculus AB Scores
  • Pre-Calculus (H) at THS
    • TI-84 Tutorials
    • Monthly Calendars
    • Pre-Calculus Student Inventory
    • Trig Memorization Quizzes
    • Web Logs >
      • Web Log #1
      • Web Log #2
      • Web Log #3
      • Web Log #4
      • Web Log #5
      • Web Log #6
      • Web Log #7
      • Web Log #8
      • Web Log #9
      • Web Log #10
      • Web Log #11
      • Web Logs #12 - 17
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 8
    • Chapter 7
    • Final Exam Study Guides
    • Regression Project
    • Are You Ready for Calculus? >
      • Independent Calculus Preparation
      • ETSU Calculus I Readiness Assessment
      • University of California Calculus Readiness Test
      • Sample Mathematics Placement Exam
      • Paper & Pencil Practice Exams
  • Pre-Calculus (R) at THS
    • TI-84 Tutorials
    • Pre-Calculus Student Inventory
    • Monthly Calendars
    • Zoom Meeting Recordings
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 10
    • Projects >
      • Math Goes To The Movies
      • Curve Project Screencast
      • Topic Screencast
      • Let The Artist in You Shine! Project
      • Mathematician Presentation Using Google Slides
      • Which Mathematician Was Born on Your Birthday? Project
      • Parabola Project Using Desmos
      • Regression Project
      • Programming the TI-84 Project
      • Law of Sines & Law of Cosines Diorama Project
      • Trigonometry Goes To The Movies A Poster Project
  • Exit Ticket
  • Calculator Recommendation
  • Cole's World of Mathematics Disclaimer
    • Cole's World of Mathematics Privacy Policy
COLE'S WORLD OF MATHEMATICS
  • Home
  • TI-84 Tutorials
  • How to Convert HW to a PDF File
  • Graph Paper
  • M105 at IUK
    • TI-84 Tutorials
    • Semester Schedule & M105 At A Glance
    • Course Syllabus & Lecture Content List
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 4
    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • AP Calculus AB at THS
    • Calculus Class Pictures
    • Calculus Student Inventory
    • TI-84 Tutorials
    • Zoom Meeting Recordings
    • Monthly Calendars
    • Web Assignments
    • AP College Board YouTube
    • AP Calculus AB Exam
    • ACP Calculus - IU
    • Memorization Sheets
    • Calculus Memorization Quizzes
    • Test/Quiz Correction Analysis
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Last Chapter/Review
    • Final Exam Review WS
    • The Calculus Life Saver
    • Final Calculus Video Project
    • Past AP Calculus AB Scores
  • Pre-Calculus (H) at THS
    • TI-84 Tutorials
    • Monthly Calendars
    • Pre-Calculus Student Inventory
    • Trig Memorization Quizzes
    • Web Logs >
      • Web Log #1
      • Web Log #2
      • Web Log #3
      • Web Log #4
      • Web Log #5
      • Web Log #6
      • Web Log #7
      • Web Log #8
      • Web Log #9
      • Web Log #10
      • Web Log #11
      • Web Logs #12 - 17
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 8
    • Chapter 7
    • Final Exam Study Guides
    • Regression Project
    • Are You Ready for Calculus? >
      • Independent Calculus Preparation
      • ETSU Calculus I Readiness Assessment
      • University of California Calculus Readiness Test
      • Sample Mathematics Placement Exam
      • Paper & Pencil Practice Exams
  • Pre-Calculus (R) at THS
    • TI-84 Tutorials
    • Pre-Calculus Student Inventory
    • Monthly Calendars
    • Zoom Meeting Recordings
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 10
    • Projects >
      • Math Goes To The Movies
      • Curve Project Screencast
      • Topic Screencast
      • Let The Artist in You Shine! Project
      • Mathematician Presentation Using Google Slides
      • Which Mathematician Was Born on Your Birthday? Project
      • Parabola Project Using Desmos
      • Regression Project
      • Programming the TI-84 Project
      • Law of Sines & Law of Cosines Diorama Project
      • Trigonometry Goes To The Movies A Poster Project
  • Exit Ticket
  • Calculator Recommendation
  • Cole's World of Mathematics Disclaimer
    • Cole's World of Mathematics Privacy Policy
COLE'S WORLD OF MATHEMATICS
Are You Ready for Calculus?
Picture
Calculus is not as difficult as you may have heard, but if you want to succeed in your study of the subject, then you have to have the proper foundations.

One of the foundations that you will need is a familiarity with certain basic concepts.

The most important precalculus concept is the notion of a functional relationship between two variable quantities. This relationship may take many forms: linear functions, power functions, exponential functions, logarithmic functions, trig functions, polynomial functions, rational functions, etc. Functions from these basic families may be combined, transformed, and inverted to produce still more functional forms. Functions also appear in various representations: formulas, graphs, data sets. You will have to be familiar with the basic families of functions, and all of their representations, in order to succeed in your study of calculus. The concept of a function underlies everything that calculus considers.

You will also need to be able to carry out certain computational tasks with efficiency and accuracy if you are going to succeed in calculus. These include manipulations of functional symbolism, solving algebraic equations involving the functions mentioned above, interpreting numerical values given by formulas, graphs, and tables, using and manipulating data, and knowing how, and when, to use your computer.


Finally, it is helpful to be acquainted with the main ideas of calculus, even before you get there. These are the ideas of rate of change and accumulation. If you have an intuitive understanding of how these ideas appear in discussions of functions, and you have some familiarity with the sorts of applications that lead to these ideas, then you are in good shape. You will define these ideas carefully in calculus, and then practice them repeatedly.

But there is more to being prepared for calculus than memorizing definitions, acquainting yourself with basic concepts, and mastering computational skills. Being prepared for calculus means more than making it through the prerequisite courses, having "seen" functions, or knowing how to solve certain equations. Calculus requires a new kind of mathematical maturity from you.

The strategies that may have worked for you in previous math courses may not have worked as well for you in this course. Precalculus and calculus are more conceptual than any of the mathematics you have studied before. To succeed in calculus you must know more than "how" to do things, you must also understand "why". You must also see how the different things that you do fit into a bigger picture: understanding functions and how they behave. If you have worked through the materials in this course, you should have a good foundation in both the "how" and the "why" of solving precalculus and calculus problems.

Don't hurry to study calculus. Calculus is the lingua franca of mathematics, engineering, and all of the sciences. You want to speak it well, with genuine understanding. You want to carry out calculations involving realistic problems with confidence. You want to savor calculus, and appreciate all of the truly beautiful things that it reveals about the world around you. Prepare yourself to enjoy it.


​Don't be afraid to take the next step, however. Calculus is not brand new, it only involves a deeper understanding, and a more efficient use, of the concepts in this course. Want to learn more? Then it's time to move on...
Picture
Copyright © 2013-21
​Cole's World of Mathematics.
ALL RIGHTS RESERVED.
Picture
Picture