College algebra and precalculus are different courses at different levels. College algebra is another name for elementary algebra: the basic concepts of algebra, built on arithmetic and centred on variables, expressions and equations, taught to secondary school students and at the introductory college level in the United States. Precalculus is a course, or set of courses, that includes algebra and trigonometry at a level designed to prepare students for calculus, and it assumes you already have college-algebra skills.
In short, college algebra teaches you to work with algebraic expressions and equations; precalculus takes those skills further into functions, trigonometry and the ideas that lead into calculus.
College Algebra vs Precalculus at a Glance
| Feature | College algebra | Precalculus |
|---|---|---|
| Also known as | Elementary algebra, high school algebra | Algebra and trigonometry (often taught as two parts) |
| Purpose | Basic concepts of algebra: variables, operations on expressions, solving equations | Preparation for calculus |
| Core content | Numerical variables, algebraic operations, notation, equations | Functions, composition and inverses, polynomials and rational functions, trigonometric functions and identities |
| Extra topics | None beyond algebra | Binomial theorem, polar coordinates, parametric equations, limits of sequences and series |
| Where taught | Secondary school and introductory college level | Late high school or college, after algebra |
| Comes before | Precalculus or other college math | Calculus |
What Is College Algebra?
College algebra is the college-level name for elementary algebra, the branch of mathematics that introduces numerical variables, quantities without fixed values, so that general relationships between quantities can be expressed and a broader range of problems solved. Where arithmetic performs operations only on numbers, algebra performs them on numbers, variables and terms. It is typically taught to secondary school students and at the introductory college level in the United States, and it builds directly on arithmetic. Unlike abstract algebra, it stays with real and complex numbers.
What Is Precalculus?
Precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level designed to prepare students for the study of calculus, which is where the name comes from. A standard course considers functions, function composition and inverse functions, often in connection with sets and real numbers; develops polynomials and rational functions; exercises algebraic skills with trigonometric functions and identities; and commonly covers the binomial theorem, polar coordinates, parametric equations and the limits of sequences and series. Schools often split the material into separate algebra and trigonometry parts. Precalculus courses usually contain little or no actual calculus, but they cover algebraic topics that earlier algebra courses may have skipped, because students need facility with algebraic expressions to find derivatives and antiderivatives later.
Why People Mix Them Up
- Precalculus contains algebra. Its first half is often labelled “algebra”, so it looks like a repeat of college algebra rather than a continuation.
- Course names vary. One school’s “college algebra” may reach into functions that another school places in precalculus, and honors-level precalculus may add conic sections and vectors that a regular class does not.
- Both satisfy a math requirement. Many degree programs accept either course, so students assume they are interchangeable.
Which Course Should You Take?
- Take college algebra if your program needs a general math credit, if you have been away from math for a while, or if your placement test points you there.
- Take precalculus if your major requires calculus, such as engineering, science, medicine or economics, and you already handle algebraic expressions comfortably.
- Take both, in order, if you need calculus but your algebra is weak: college algebra first, then precalculus.
Frequently Asked Questions
- Is college algebra the same as precalculus? No. College algebra is elementary algebra; precalculus is the algebra-and-trigonometry course that prepares you for calculus.
- Is precalculus harder than college algebra? It is more advanced, because it assumes college-algebra skills and adds functions, trigonometry and topics such as polar coordinates and limits.
- Can I skip college algebra and go straight to precalculus? If your placement test or high school record shows strong algebra skills, many schools allow it.
- Does precalculus teach calculus? Only small amounts, if any. It prepares you for calculus rather than teaching it.