What’s the difference between Precalc and Algebra II?
I took honors level math b (that’s trig/algebra II), and I bought a precalc book today, but I see all the same concepts.
Tags: algebra, between, difference, Precalc, What's
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January 24th, 2011 at 7:38 am
More emphasis on trig functions than algebra II—at least thats what it was for me.
And an intro to analysis.
January 24th, 2011 at 8:32 am
some lessons in pre-calc are the same material you look at in algebra 2/trig. pre-calc is basically more thorough and the material is at a deeper level, but not all the lessons are the same.
January 24th, 2011 at 9:18 am
Most materials in Pre-calculus have been covered in Algebra II. However, the content in Pre-calculus is wider and deeper than in Algebra II. In addition, most Pre-calculus books cover introduction to Calculus.
Generally speaking, Pre-calculus is Algebra III. Is that clear?
January 24th, 2011 at 9:21 am
Edited:
My senior year in High School I took a course called Introductory Analysis. It included subjects like combinations and permutations which is what you use to figure out for instance the chance of winning a state or multi-state lottery. It also included the first thing you need to understand in order to comprehend calculus. That is the concept of limits. The formula for the general derivative in calculus is defined as the limit of { [f(x+h) – f(x)]/ h } as h approaches 0 and f(x) is read as f of x and is the function of x. Within the formula for a circle which is r²=x²+y² for instance f(x)=√y²-r². As you should know you cannot divide by zero, so the variable “h” has to be taken out of the denominator and put into the numerator. One simple example is the limit of 1/n as n approaches infinity which is obviously zero since any finite number divided by infinity is zero. But although the limit of 1/n as n approaches zero is infinity, you cannot immediately substitute zero for n, since you cannot divide by zero. It is obvious that as n gets smaller and smaller approaching zero, the ratio of 1 to that decreasing denominator will approach infinity. Therefore infinity is the limit in that case. Another defintion of the derivative in calculus is “the derivative is defined as the instantaeous rate of change”. Its practical purpose is to calculate acceleration and deceleration. Another definition of the derivative is that it is the slope of a single point on a curve which also happens to be the tangent of the curve at that point. You should remember when you studied slopes of lines you needed the x and y coordinates of two of the points on that line in order to calculate the slope, but in calculus you calculate the slope of a single point. The amazing thing to me about derivative calculus is that while measuring the acceleration or deceleration within a zero dimensional point (just like the abstract point in geometry) the implication is that change of velocity is occuring within a point which has no dimension in space or dimension in time. The most important mathematical constant in engineering is the base of the natural logarithm which is called “e”. It is a transcendental number. It is defined as the limit of (1+1/n) raised to the power of n as n approaches infinity. The naive perception is where you substitute infinity for the value of n immediately which would result in (1+0) raised to the power of infinity which would equal 1. However, the actual value of the constant is 2.18281828659. See http://en.wikipedia.org/wiki/Natural_logarithm .