For many of us who have Calculus phobia, the whole concept of Pre-Calculus is like a pre-phobia. However, Precalculus leading all the way to calculus, has man real-life applications! I say that in particular because many students would say "Oh well, now why study this in maths! When and where are you going to use it?" Sure. I understand the question and the reason behind it. So, if we start by citing the real life application of the topic, the reception is better and you garner student's active participation.

Typically, most students feel that they are pummeled with a heavy dose of precalculus, and before the damage can heal, it follows another heavy duty dosage of calculus. Why did I use the word damage? Well, first of all, anything that does not get imparted in a practical way and is not accepted by the student with an exciting expression is indeed a damage, besides being a waste of time. Personally, I do not want my students to learn anything in math unless they realize its real value, application and purpose. Once we talk about the real usage, it stirs curiosity and interest - and that lays the foundation for easy assimilation of the concepts. At that point, it does not matter how hard the subject is. The interest drives the appreciation of the subject. "Nothing great was ever achieved without enthusiasm." -- Ralph Waldo Emerson

Here is a brief outline of topics once can cover (master) in Precalculus (sometimes called advanced algebra-2/algebra-3).

Real numbers

Complex numbers

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Concept of co-ordinates and quadrants

Concept of slope

Linear equations (slope, points, perpendicular, parallel)

Distance formula, Mid Point formula

Equation of Circle and its variations with radius, center, tangent etc

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Concept of log and base algorithm

Concept of e

Sets,Functions, Properties of functions

Difference quotients

One-to-One Functions, discontinuous functions,Composite functions, Polynomial functions

Quadratic functions, Inverse Functions,Rational functions, Irrational functions, Exponential functions, Logarithmic functions

Finding the Zeros / roots / critical points, Graphing

Asymptotes, Translation and Reflection,Domain, Range using algebra and using graph, Limits

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Solving inequalities and equations involving all kinds of functions

Intersection of curves and curves and lines

Understanding discriminant concept for quadratic functions

Parametric equations

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Radian and Degree concepts

The unit circle

Trigonometry

Trigonometric functions and their inverses

Trigonometric identities

Graph of trigonometric functions

Polar coordinates, Vectors

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Conic sections - Parabola, ellipse, hyperbola

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Matrices and determinants

Mathematical induction

Factorial. Permutations. Combinations.

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Sigma notation,Sequences and series

Binomial theorem

Exponential growth and decay

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In my next blog I'll talk about some real life usage of calculus and precalculus.

Happy learning!