## Introduction to Precalculus

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• Introduction to Precalculus

Precalculus is a high school and college-level course that prepares pupils for Calculus.

Now that calculus is the study of how things change over time, the purpose of precalculus is to prepare students to deal with complex and dynamic concepts by assisting them in connecting their prior knowledge from Algebra and Geometry.

## Precalculus categories

Precalculus is broken into two essential categories: Trigonometry and Math Analysis.

### Course on Trigonometry

Trigonometry, or the study of triangles, usually starts with a fundamental understanding of functions and then moves on to how triangles and their angles can be drawn and represented in rotations, degrees, and radians.

Next, students are exposed to the Unit Circle, which allows them to learn about trigonometric graphs, trig identities, trig equations, and how to solve right and oblique triangles.

Finally, students will investigate the Polar and Complex Coordinate Systems, which are new graphing planes.

### Course in Math Analysis

Math Analysis, sometimes known as Algebra 3, delves deeper into algebra fundamentals. Functions, domain, range, and end behavior, in particular.

Math analysis aims to demonstrate to students how to represent more complicated equations in multiple representations rather than just review or solve them (i.e., graphically, numerically, and verbally).

Students will learn how to express their findings using various modalities while studying polynomial functions, rational functions, exponential and logarithmic processes, and limits.

## Precalculus Prerequisites

Before you start Calculus, there are a few things you should know.

In some ways, having a general understanding of algebra, geometry, and trigonometry can help to understate Calculus. After all, each new topic in arithmetic builds on the preceding ones, which is why proficiency at each level is critical.

This page is meant to highlight a few of the more key abilities you should have going into the course for those who have completed courses in these topics but are looking to brush up on the principles before commencing calculus quickly.

### Algebra

Manipulating expressions

1. Understand how to work with polynomial expressions.

• Adding: (x2+2x+3) + (3x2−3x) = 4x2−x+3
• Factoring and Multiplying: (x+2) (3x−5) ⇔ 3x2+ x – 10

2. Understand how to solve basic linear equations, 4x + 3 = 7x – 9 is an example.

3. You should know how to solve quadratic equations like 3x2 + 5x – 7=0.

• Finishing the square
• The formula for quadratic equation

4. Exponent qualities should be understood.

• x2 + y2 = (xy)2
• (2x) (2y) = 2x+y

5. Understand how some expressions are exponentials in disguise.

• Reciprocals:
• Roots: √x = x1\2

6. Understand what logarithms are and how they work.

• y=2x is the same as log2(y) = x
• log(x) + log(y) = log(xy)
• log(ax) = xlog(a)

### Functions

Calculus is all about functions; therefore, it helps to be very fluent in thinking about functions, graphing functions, and using the correct vocabulary when discussing them.

1. Understand what a function is.

2. Understand how to use a graph to express a function.

3. Understand the graphs of several basic functions.

• Linear functions
• Have a rudimentary notion of what an nth degree polynomial’s graph would look like.
• Exponentials
• Logarithms

4. Understand how to use functions.

• Functions that multiply

5. It’s also beneficial to have a basic understanding of function nomenclature.

• Domain
• Range
• Functions that are odd and even
• Periodic
• Zeros
• Intercepts

### Geometry

1. Understand how to find the area of simple forms.

• Rectangles
• Triangles
• Trapezoids
• Circles

2. Understand how to calculate the volume of simple three-dimensional shapes.

• Cube
• Prism
• Sphere

3. Understand how to consider a 3D shape’s cross-section.

4. Geometry in analytic form

• In the coordinate plane, reasoning about points, lines, and forms.
• Equations for perpendicular and parallel lines.
• A circle’s equation

### Trigonometry

Know how to use the basic trigonometric functions sin(x), cos(x), and tan (x)

• Understand what each one stands for.
• Understand how each of these functions’ graphs looks.