Calculus I courses provide students with an in-depth introduction to the core concepts of limits, derivatives, and integrals, building on the preliminary understanding of these concepts that students gained in Pre-Calculus courses while preparing them for the more advanced material of Calculus II, Calculus II, and Differential Equations. Calculus courses are often necessary for students to be able to tackle not only these higher-level mathematics courses, but advanced material in the sciences. If you are considering majoring in math, science, or any other quantitative field, taking Calculus before reaching college can be a real boon, as high school Calculus courses often take the material at a somewhat slower pace than collegiate courses, making sure that students fully understand each concept before moving on. Whether you need top Calculus tutors in New York, Calculus tutors in Chicago, or top Calculus tutors in Los Angeles, working with a pro may take your studies to the next level.

The material taught in Calculus I courses can be broken down into three main categories: limits, derivatives, and integrals; however, most Calculus I courses begin with a review of the basic features of functions graphed on the coordinate plane, including continuity, asymptotes, and absolute and local extrema. Students may be asked to find the slope of a line or slope at a point when reviewing these concepts.

When delving into the concept of function limits, Calculus courses typically begin with the process of calculating and estimating simple limits and proceed to introduce concepts of asymptotes and continuity, calculating limits to infinity, and other complexities.

Discussing derivatives is a major part of every Calculus I course. Students are introduced to derivatives through discussions of the definition of a derivative, the limit definition of a derivative, and differential equations in order to bolster students’ conceptual understandings of derivatives. It is crucial that students fully understand what derivatives represent as they progress in Calculus I, as they are soon asked to apply this knowledge by calculating derivatives at a point and of a function, as well as second derivatives. They are also taught the Chain Rule. Students are also asked to graph derivatives and second derivatives, along with linear approximations of derivatives. As student knowledge of derivatives increases, Calculus I introduces the concepts of increasing and decreasing intervals, concavity and convexity, points of inflection, and slope fields. Students are also asked to make use of the Mean Value Theorem. Specific derivatives, such as the derivatives of logarithms, exponents, sums, quotients, products, and trigonometric functions, are taught, as well as implicit differentiation.

The last major topic of every Calculus I course is integrals. Integrals are introduced by talking about the definition of an integral, integral notation, definite integrals, and Riemann sums. After the concept of an integral is introduced in detail, students are taught the Fundamental Theorem of Calculus, how to take the integral of a function, and how to graph integrals. Increasingly difficult problems are likely to appear, as students are asked to take the integral of more complex functions such as sums, quotients, and products, logarithms, exponents, and trigonometric functions. Varsity Tutors offers resources like free Calculus 1 Diagnostic Tests to help with your self-paced study, or you may want to consider an Calculus 1 tutor.

Of all the math courses that students have the opportunity to take during high school, Calculus I has gained the reputation of being notoriously difficult. If you are currently enrolled in a Calculus I course and need to review or study for an exam, or are taking a more advanced math course and need to review the fundamental concepts taught in Calculus I, use Varsity Tutors’ free Calculus I Practice Tests to brush up on your Calculus I knowledge. Each free Calculus I Practice Test contains a dozen Calculus I problems and multiple-choice answers. You receive detailed results after completing each one, as well as access to step-by-step explanations of how to arrive at the correct answer for each problem. If you find yourself needing to focus on problems that address one specific topic, such as the Fundamental Theorem of Calculus, you can do that, as problems are organized into Practice Tests by concept. In addition to the Calculus 1 Practice Tests and Calculus 1 tutoring, you may also want to consider taking some of our Calculus 1 Flashcards.

You might also want to try one of the free Full-Length Calculus I Practice Tests, which ask you questions spanning the full range of topics you’ll encounter within the course. The complete practice tests are a perfect way to get some practice as you check your skills. When you complete the test, you’ll be shown your score accompanied by detailed explanations of each question’s correct answer and links to additional review exercises. These free online practice tests can help you build a custom Calculus study guide, too. By showing you which concepts you should focus on, you can streamline your review. After using some of the other Learning Tools to review, you can track your growth by taking another of the Full-Length Calculus I Practice Tests.

By making use of the variety of free Calculus resources that Varsity Tutors’ Learning Tools website offers, you can vanquish your fear of Calculus and channel your nervousness into studying to master the subject completely.