What Is Precalculus?

High school students often have difficulty with precalculus and calculus.
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Calculus is a complex branch of mathematics that focuses on continuous change. The history of pre calculus dates back to 17th century Europe, when Sir Isaac Newton and Gottfried Liebniz independently worked out many fundamental calculus concepts. Calculus has many practical applications and is included in degree programs for mathematicians, engineers, computer scientists, economists, statisticians, healthcare providers and many other fields.

Although some high school students study calculus in high school in preparation for college, others come to the subject with no prior knowledge. Success can depend on their understanding of algebra and trigonometry. To prepare for the rigors of calculus, many students take a pre calc course.

Pre Calculus Definition

Pre calculus is the study of the mathematical prerequisites for calculus, including algebra, trigonometry and analytical geometry. The unusual thing about pre calculus topics is that they don’t directly involve calculus. Instead, they give students a strong foundation that will be used throughout their calculus studies.

One way to get a better understanding of the concepts covered by precalculus is to check a sample course syllabus. For example, the self-paced Khan Academy precalculus course includes trigonometry, conic sections, vectors, matrices, complex numbers, probability and series. Additional important topics in any pre calc course are functions, graphing, rational expressions and complex numbers.

Pre Calculus and Trigonometry

Trigonometry is the study of the relationships between the dimensions and angles of triangles. It is a full course by itself in most high school and college math departments, so the coverage in precalculus mostly serves as a refresher. Taking a trigonometry course is often required before enrolling in precalculus. During precalculus, you can expect to solve and graph problems using standard trig functions like sine and cosine. Additional trig topics covered in precalculus include vector operations, sequences and series.

Pre Calculus and Algebra

Many educators say that strong algebra skills are part of the key to success in calculus. In addition to reviewing the trigonometric functions, precalculus courses cover commonly used algebraic functions such as quadratic, exponential, polynomial and logarithmic. The graphing of functions is an important part of precalculus since graphs are used throughout calculus. The domain and range of functions are covered, along with finding the intervals over which a function increases or decreases and performing transformations on a function.

How Do Know If I Need Precalculus?

Many students are on their own when it comes to deciding if they would benefit from a precalculus course. Their first resource should be their college or university math department. Some schools offer a diagnostic test that help students determine how ready they are for either precalculus or calculus. For example, UC San Diego’s Mathematics Diagnostic Testing Project offered a web-based test for precalculus readiness that returns a score as soon as it’s completed. This type of test is not used for official class placement but as measurement tool to help students gauge their own readiness.

It may be helpful for students to commit to a college major before taking precalculus. Some schools offer different flavors of calculus for non-math majors, such as Calculus for Economics or Calculus for Engineers, which typically would put a greater emphasis on trigonometry. Knowing the type of calculus you’ll be doing in the future might help you decide if you need precalculus.

Many students are able to skip a formal precalculus course and prepare on their own for their first college-level calculus course. There are plenty of online resources to support this approach, from Kahn Academy to universities and colleges that share videos of actual lectures. Students who have lower scores in college math placement tests should consider taking intermediate algebra or trigonometry before enrolling in precalculus. The emphasis in precalculus is on refreshing a student’s knowledge rather than teaching the basics from scratch.