What is Calculus?
The word strikes fear in people. It sounds ominous. That course for the “smart kids.”
However, your student has been preparing for Calculus since Middle School Mathematics:
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- The slope of a line?
- Rate of change, the foundation of Differential Calculus.
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- Rate x Time = Distance?
- The area under a curve, the foundation of Integral Calculus.
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- Distance between two points on a line?
- Length of an arc, a commonly tested equation in Integral Calculus
It troubles me when teachers try to strike fear in the hearts of the newly minted Calculus students. This only scares them and turns them off to this fascinating and integral (no pun intended) branch of higher mathematics.
However, I often find that the main reason students have trouble with Calculus is that their skills in high school mathematics need to be fortified. All those things they learned back in Algebra II and Trigonometry will return with a vengeance!
So, if your student wants to be an ace Calculus student, here are the ten most important skills she/he needs to master:
- Radian measurement of angles: Kiss degrees goodbye. You will not see them in this course.
- The Unit Circle: Know the values of the vital trig functions.
- Trigonometric Identities: Review the Pythagorean and Quotient relationships.
- Factoring: Identify the Greatest Common Factor in any expression or equation.
- Quadratic Inequalities: Solve any quadratic equation.
- Complex Fractions: Use your algebra skills to simplify any complex fraction.
- Logarithms: Manipulate a logarithmic function and solve a logarithmic equation.
- Exponential Equations: Solve a simple exponential equation; use logs as needed.
- Interpret End Unit Behavior of Functions: Understand what happens to a function value as x approaches positive or negative infinity.
- Identify Intercepts and Asymptotes: Be able to solve this algebraically or interpret graphically.
Calculus is an intense mathematical exercise. It requires outstanding skills, as well as knowing the rules of Calculus. Believe it or not, the rules are the easy thing. The skills take practice and patience.
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