If you’re a grade 11 or 12 high school student, there’s a good chance you have university on your mind – along with the courses that might be in your future based on your chosen program of study.

Thinking ahead is always a good idea when it comes to your post-secondary studies because it gives you time to make sure you take the right prerequisite courses at the best time.

Whether you love math or loathe it, it’s worth keeping in mind that many university bachelor’s programs will require at least a few math courses, and quite possibly calculus. This branch of mathematics deals with continuous change (in contrast to algebra, which deals with the generalizations of arithmetic operations, and geometry with the study of shapes).

If you’re just discovering calculus for the first time, you’ll probably come across the terms “Pre-Calculus” and “Advanced Functions.” Wondering if Advanced Functions is the same thing as Pre-Calculus?” This article aims to clear things up.

Why study calculus?

Calculus is widely used by mathematicians, computer scientists, engineers, statisticians, economists and healthcare providers and others. If you’re considering a future career in a field that involves working with numbers or models, there’s a good chance you’ll need to know calculus!

Most university calculus courses have pre-calculus as a prerequisite. But even if they don’t, taking a pre-calculus course at the high school level can give you a big leg up.

Blyth Academy follows the Ontario curriculum, which offers the Calculus and Vectors university preparation course in grade 12.

The prerequisite for this course is the grade 12 Advanced Functions, another university preparation course. You can take this course at the same time as Calculus and Vectors, but most students find it more helpful to take the Advanced Functions course first.

What is precalculus?

As its name suggests, pre-calculus prepares students for learning calculus.

In a calculus class, you’ll be asked to find the derivatives and antiderivatives of functions, among other operations. In order to solve these types of questions, you’ll need to have a solid understanding of algebraic and trigonometric expressions, particularly their modification and transformation.

This is the type of thing you’ll learn in a pre-calculus class, otherwise known as Advanced Functions.

Did you know?

The history of precalculus dates back to 17th century Europe, when famous mathematicians Sir Isaac Newton and Gottfried Liebniz worked out many fundamental calculus concepts – completely independently of one another!

Advanced functions is just that: it takes your knowledge of functions and rates of change further. For example, in the grade 12 Advanced Functions course you’ll look at the following:

• Exponential and logarithmic functions
• Trigonometric functions
• Polynomial and rational functions
• Characteristics of functions

Tips & tricks for learning precalculus

Many students find precalculus more confusing and frustrating than other subjects, but it really doesn’t have to be. With the right preparation and attitude, you’ll be breezing through your homework and acing your exams.

Follow these tips to start and end your “precal” class on the right note:

1. Get a graphing calculator
• Having the right tools for the task is essential. You’ll need:
• Pencils
• Ruler
• Notebook paper
• Graph paper
• And, most importantly: a graphing calculator!
• You’ll need to regularly use your graphic calculator to plot graphs, solve equations and perform a variety of other tasks involving functions. You’ll probably end up using this calculator every day, so take the time to learn how to use it.
• You can read the owner’s manual, ask your teacher or watch some YouTube videos on the subject. Khan Academy has a number of good videos on how to use a graphing calculator.
2. Learn the language
• Precalculus has its own language with specific terms that may be new to you, such as:
1. Variables
2. Exponents
3. Functions
4. Polynomials
5. Etc.
• It can be helpful to make a list of any new terms along with their definition so that you can refer to it when needed. If you don’t understand a particular term, ask your teacher right away. Never wait until the night before your exam.
• Do the assigned reading and try to complete a few questions before class. This will allow you to see what you understand and what areas you’re having trouble with so that you can ask the teacher for help.
4. Make the most of class time
• Always attend your classes and ask the teacher right away if you don’t understand something.
• If you’re having trouble understanding a particular concept, ask your teacher for help right away so that you don’t fall behind in your coursework.
6. Don’t cram
• Some high school subjects involve a fair amount of memorization. Calculus is not one of them. Instead, you need to understand the concepts and be able to apply them in a variety of situations. Getting to this point takes time, so don’t wait until the night before the exam to start preparing. Instead, make it a habit to regularly…
7. Practice, practice, practice
• Do as many problems as you can, even if your teacher only assigns a few for homework. You can find additional problems in your textbook and on the Internet. Do a search for “precalculus practice” and you’ll get a long list of websites offering free homework sets with answers. We’ve included a few below.

Resources for learning

There are a number of online pre-calculus (or advanced functions) exercises or courses that you can do to help you better prepare:

Blyth Academy’s grade 12 Advanced Functions and Calculus and Vectors university preparation course prepares you to successfully complete university-level calculus courses.