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Precalculus and Calculus

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!

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