Easy pts, dumb questions

[101dalmatians]

What are transcendal numbers?

How do you define the following nos:

abundant
lucky
extravagant
sad
unlucky
happy
odious

There are more but these are of my concern as of now.

Also, I found that to get to those high scores, I shouldn't leave easy questions out of the way.
So:

How do you find the following with the coordinates of a triangle:
incenter
orthocenter
circumcenter
centroid

how do you find the other coordinate for:
triangle (all types)
quadrilateral

How do you find the area of a triangle and quadrilateral with its coordinates given (no herons formula for the triangle)

Also, how do you find the following with the trig equation given:
frequency
amplitude
max/min
Also, without graphing a trig function on ur calculator, how can you find out its graph? How bout polars? (equations are ans. choices)

[101dalmatians]

Also, on 2010 Invitational A how do you do:

#33
#43
#59

[darksaber21]

Transcendental numbers are non-algebraic numbers, typically numbers with out a pattern in the decimal.

Examples of transcendental numbers include [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], and even [unparseable or potentially dangerous latex formula]


The whole list I am pretty sure you can look up. If there is one you are having trouble finding you can ask, but I'm sure if you look it up you will come across neat information plus what you are looking for.

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EDIT:
I felt like putting this up here since I am now back on my laptop:

Abundant/Perfect/Deficient numbers:
Suppose you take a positive integer number and add its positive proper divisors (all divisors except itself). The type the number it is depends on the sum of its positive proper divisors:

Deficient Number - The sum is less than itself (first number is 1)
Perfect Number - The sum is equal itself (First number is 6)
Abundant Number - The sum is greater than itself (First Number is 12)

Every Prime number is a Deficient number as the only proper divisor each number has is 1
All multiples of perfect numbers happen to be Abundant numbers (hence all numbers that is multiple of six except 6 itself are abundant).

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Given the trig function [unparseable or potentially dangerous latex formula]

Frequency: [unparseable or potentially dangerous latex formula]

Amplitude: A

Maximum: A + D

Minimum: D - A




To derive a trig function from a graph during is test, you would need to find A, B, C, and D in the equation, for both sine and cosine, or for both tangent and cotangent, or for both secant and cosecant, depending on the graph. Then compare your result to the multiple choice question and take your guess. You need to do some on your own, so you can find your own techniques to doing these. However, I would leave this question for near the end, as it takes a while to do sometimes.

As for polar graphs, you need to memorize the different types of polar graphs, determine which graph it is, then find the amplitude or another information you need to solve it. These are typically less time consuming to do than the actual trig graph problems on the tests, for me anyway.

[darksaber21]

[darksaber21]

[darksaber21]

[darksaber21]

Given lengths [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula], and [unparseable or potentially dangerous latex formula], and the coordinates [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula], and [unparseable or potentially dangerous latex formula].


Incenter coordinates: [unparseable or potentially dangerous latex formula]


Centroid coordinates: [unparseable or potentially dangerous latex formula]



There is no set formula to find the circumcenter or the orthocenter of any triangle, but since each involves perpendicular lines, you can find each, but it would take a while. You have to find the equation of each line (that goes from the vertex to the side the line is perpendicular to for the orthocenter or from the perpendicular bisectors for the circumcenter), then solve for where the three lines intersect.

There are a couple special cases, but I am going to leave that up to you. I will tell you one though, whether you know it or not: All four points are the same in an equilateral triangle.

[101dalmatians]

How do u find reference angle?
how do u rotate about a point?
(these stuff - long back - forgot...)

how do you find the equation of parabola given a few points?

[darksaber21]

Reference angle is basically the angle that connects the terminal side to the x-axis. The reference angle is always between 0° and 90°(or 0 rad and [unparseable or potentially dangerous latex formula] rad). So, depending on which quadrant the terminal side or angle is in:

- Quadrant I : the measure of the angle and the terminal angle are the same
- Quadrant II : the sum of the measures of the angle and the terminal angle equal to [unparseable or potentially dangerous latex formula] or 180°
- Quadrant III: the absolute difference of the measures of the angle and the terminal angle equal to [unparseable or potentially dangerous latex formula] or 180°
- Quadrant IV: the sum of the measures of the angle and the terminal angle equal to 2[unparseable or potentially dangerous latex formula] or 360°


To find out how to rotate about a point, refer to .

Realize that you need to translate to (0,0), and then translate the result back if you use the equation. You can just add x or y at the end of the equation instead if you think you'll forget to do so often.


is an example of finding the equation of a parabola.

[101dalmatians]

District 1 2009 test questions:

#16

#23

#31(what is the geometric principle behind this?)

#41

#42

#48

#50

#51

What does jointly varying mean on #57?

[101dalmatians]

[101dalmatians]

for rotations, is it most of the time like about the origin?

[darksaber21]

[darksaber21]

[darksaber21]

[101dalmatians]

how do classify an odd, eve, neither, one-to-one function?
i dont get it cuz whenever i put odd it is neither and whenever i put even it is odd, etc...

Also how do you do district 1 2009 #11? i dont get it at all!

What is the exact way to do #20 2009 district 1 without wasting time like i did?

What i did was i solved for y nd graphed and found the pts of intersections (approximately and i just found the slope to be like -0.57. then i found the -2/3 in the ans. choices - which was close to -0.57. so i chose tha for my ans...

then how do you convert RPM to RAD?

[darksaber21]

[darksaber21]

[darksaber21]

[darksaber21]

One revolution equals 2[unparseable or potentially dangerous latex formula]. Remember that.

Joint variation just means that multiple variables affects the variable in question. So, in 09D1-57, P is inversely proportional to both Q and R. So the equation is P = QRk, where k is the constant of proportionality.

[101dalmatians]

What are one-to-one functions?
How do you identify them?

[darksaber21]

One-to-One functions
- For every x there is only one y
- For every y there is only one x
[unparseable or potentially dangerous latex formula] - Thus the inverse of the function is indeed a function
[unparseable or potentially dangerous latex formula] - Passes both the horizontal and vertical line tests
- Are strictly monotonic (decreasing or increasing)

[101dalmatians]

Are they like log or ln functions or e^x functions?

[darksaber21]

Those are examples of one-to-one functions.

As [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are inverse functions of each other, both are strictly monotonic, and thus are both one-to-one functions


Same is true for [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], or whatever base the logarithms are in.

[101dalmatians]

Can anyone tell me like ALL they know of theorems relating to CIRCLES like the SECANT/TANGENT THM???
These questions are such easyones but really dumb ones - the reason for which I am posting to continue this thread!