euler method
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Mathematics
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math study guide 4 grade
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Math study guide Discrete a point is a dot T geometry a line is a set of dots in a row T a line has no thickness F 2 crossing lines intersect in a point F Synthetic a point is a physical dot F (exact location) Geometry a line is a set of points going in both directions going the shortest paths T A line has no thickness T A line extends 2 directions T Plane coordinate a point is an ordered pair of numbers not a # T Geometry a line is a set of ordered pairs that go with ax+by=c when they are both not 0 T
Geometry Theorems and Postulates for a Midterm
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DEFINITIONS?Def. line segment (segment) - part of a line that has 2 definite endpoints?Def. ray - part of a line that starts with a definite endpoint and extends indefinitely in 1 direction?Def. angle - the union of 2 noncollinear rays with a common endpoint?Def. union - elements belonging in 1 or both sets?Def. intersection - elements that belong to both sets?Def. absolute value - |x| = if x _>_ 0; -x if x _<_ 0?Def. segment length - the distance between the endpoints?Def. congruent segments - segments with the same length?Def. midpoint - a point B is called the midpoint of lineAC if A - B - C and AB = BC?Def. segment bisector - a point, line, ray, segment, or plane that passes through the midpoint of a line?Def.
Geometry Theorems and Postulates
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MATH NOTES PART ONE Geometry- A metric system of measuring the earth Four parts of a mathematics system- undefined terms, defined terms, postulates, theorems Defined terms- postulates, theorems Undefined terms- a point (use capitals), a line (name it with capitals, or name it line l), a plane (adds a new dimension) Zero-dimension- the dimension of a point One-dimension- the dimension of a line Two-dimensional- the dimension of a plane Collinear- when two points are on the same line Non-collinear- when two points are NOT on the same line Non-coplanar- if the point can never be in the plane Postulates- statements accepted without proof Theorem- statements that can be proven with postulates Segment- is part of a line that has two endpoints
Point Slope Formula
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Point-slope refers to a method for graphing a linear equation on an x-y axis. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph. While you could plot several points by just plugging in values of x, the point-slope form makes the whole process simpler. Point-slope form is also used to take a graph and find the equation of that particular line. Point slope form gets its name because it uses a single point on the graph and the slope of the line. Think about it this way: You have a starting point on a map, and you are given a direction to point. You have all the information you need to draw a single line on the map. The standard point-slope equation looks like this:
Zsigmondy
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The Zsigmondy Theorem PISOLVE 7/31/11 Abstract In this paper we will be discussing the uses and applications of Zsigmondy?s Theorem. As some of you may consider the theorem as ?large/ brutal? , it can actually be proved by elementary methods [1] - at the same time, it is applicable in so many Number Theoretic problems(All problems in this article are sourced in AoPS). We see no reasons not to use it. Intro Problem Let p > 3 be a prime. Show that every positive divisor of 2 p+1 3 is in the form 2kp+ 1. Solution: We show that all prime divisors are in this form, then the result readily follows.Let q| 2 p+1 3 . Then: q|22p ? 1 o2(q)|2p If o2(q) 6= 2p, we have 3 cases: o2(q) = 1 Then q|1, clearly impossible. o2(q) = 2
Trig cheat sheet
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? 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 pq< < or 0 90q? < < ? . oppositesin hypotenuseq = hypotenusecsc oppositeq = adjacentcos hypotenuseq = hypotenusesec adjacentq = oppositetan adjacentq = adjacentcot oppositeq = Unit circle definition For this definition q is any angle. sin 1 y yq = = 1csc yq = cos 1 x xq = = 1sec xq = tan yxq = cot x yq = Facts and Properties Domain The domain is all the values of q that can be plugged into the function. sinq , q can be any angle cosq , q can be any angle tanq , 1 , 0, 1, 2,2n nq p ? ?? + = ? ?? ?? ? K
Basic Aglebra
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Basics of Algebra Algebra is a division of mathematics designed to help solve certain types of problems quicker and easier. Algebra is based on the concept of unknown values called variables, unlike arithmetic which is based entirely on known number values. This lesson introduces an important algebraic concept known as the Equation. The idea is that an equation represents a scale such as the one shown on the right. Instead of keeping the scale balanced with weights, numbers, or constants are used. These numbers are called constants because they constantly have the same value. For example the number 47 always represents 47 units or 47 multiplied by an unknown number. It never represents another value.
Logarithms
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Many students in high school and in college have a difficult time with logarithms. In many cases, they memorize the rules without fully understanding them, and they sometimes even manage to squeak by a course. Why waste their time on these archaic entities; they are never going to see them again. Wrong! Just when the student breathes a sigh of relief to be done with logarithms, they encounter them again in another course. They are now in trouble because the second encounter with logarithms is at a more sophisticated level. Without an understanding of the basics, the student is doomed to blindly stumble through and fail the course. You have our sympathy and you have our solution. We at S.O.S. Math want you to succeed.
Pythagorean Theorem
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a^2 + b^2 = c^2
c being the hypotenuse, and a & b being the two other sides of the triangle.
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