OVERVIEW

Pre-calculus is a high school subject that serves as a preparatory course for students before they delve into college-level calculus. In the context of senior high school (SHS), it typically covers mathematical topics and concepts that are fundamental to understanding calculus. The goal is to equip students with the necessary mathematical background and skills to succeed in a calculus course. The following usually the topics that are tackled in Pre-Calculus

Algebra Review: An in-depth examination of algebraic ideas and skills, such as equations, inequalities, functions, and their properties.
Trigonometry is the study of angles and triangles, as well as the trigonometric functions sine, cosine, and tangent.
Analytic Geometry: The study of geometry by algebraic methods, such as line equations and conic sections.
Investigation of sequences (ordered lists of numbers) and series (sums of sequences), including arithmetic and geometric sequences.

CONIC SECTION

Conic sections are mathematical curves formed when a plane intersects a double-napped cone. Conic sections are classified into four types: circles, ellipses, parabolas, and hyperbolas. Each type has unique properties and equations.

Arithmetic Sequence:

In an arithmetic sequence, each number comes from adding the same number every time. Imagine you start with a number and keep adding the same value to get the next one, and then do it again to get the one after that, and so on.

For example: 2,5,8,11,14,…

Here, you add 3 each time to go from one number to the next. That's the idea behind an arithmetic sequence.

FORMULA: an= a1 + (n - 1) * d
where a1 is the first term, n is the nth term and d is the common difference.

Geometric Sequence:

In a geometric sequence, each term is found by multiplying the previous term by a fixed number (the common ratio). This formula allows you to calculate any term in the geometric sequence without having to list out all the terms individually. If you know the first term, the position of the term you're interested in, and the common ratio, you can use this formula to find the desired term.

FORMULA: a * r ^ (n-1)
where a is the first term, r is the radius, n is the nth term.