Yeah the quiz was really gay. Lots of lateral thinking required, and lots of other stuff that you probably forgot. Review chapters to remember crap.
9.1 Radicals
Well I’m just going to do examples. You might want to know some notation before you read on though.
(200)^1/2=10(2)^1/2
5(18)^1/2=15(2)^1/2
1/(2)^1/2=(2)^1/2 /2
4(3)^1/2+7(3)^1/2=11(3)^1/2
x^2=25; x=5 or -5
x^2+16=25; x=3 or -3
9.2 Circles (the joy of a figure whose points are equidistant from the center…)
So first of all parts of a circle (as if you didn’t know this XD)
RADII=line from the center to any point on the circle
DIAMETER=line between any two points on a circle that crosses the center of the circle
CIRCUMFERENCE= the measure of the total length of the line that forms the circle (sorry this is a really baad definition but by golly, I’m not a professor)
ARC= part of a circumference
AREA= amount of room the circle occupies
Sector= part of the circle bounded by two radii
Chord= any random line that connects two points of a circle
So for arcs, to find the LENGTH, you find the DIAMETER, multiply that by Pi, and then multiply by the amount of the circumference that it takes up. Usually the give you some sort of degree to work with. Just remember its degree that they somehow manage to give you/360 degrees
Ex. Arc around a 90 degree thingy of a circle with a diameter of 4.
16Pi-> 4Pi= LENGTH
Measure= (degree that they somehow manage to give you/360 degrees) * 360
for the previous one, (90/360)*360=90 degrees
Area of sector is found by finding the area and then multiplying that by degree that they somehow manage to give you/360 degrees.
SUMMARY: DONT FORGET (degree that they somehow manage to give you/360 degrees)
Part two of this lesson talks about inscribed angles of a circle. Just note that the inscribed angle is half the measure of its intercepted arc. That’s all you need for this chapter.
9.3 Alt-Hyp theorems (Or the stuff thats probably why people fainted on the quiz. lets just hope that I remember this when I take it)
So image triangle ABCD or heck ill draw points and you imagine the triangle
C
A D B
There you can see the altitude right?… Anyways… The three triangles you see here are all similar…
AB/AC=AC/AD as such-> AB/CB=CB/DB
So from this it means that the ratio between the hyp of two triangles is equal to ratio between the same side (opp or adj) of the triangles.
And why not just say that if the ratio between the same side (opp, hyp, or adj) of two right triangles equal the ratio between the other side (opp, hyp, or adj) of the triangles
Therefore from the above triangle, we can do means-extremes and get something like AC^2=AB*AD and so on and so forth for the rest of the formulas.
Anyways the quick theorems to remember.
CD^2=AD*DB
CB^2=AB*DB
AC^2=AB*AD
BE SURE TO NOTE THAT this is only true if an altitude is drawn to the hypotenuse of a right triangle. But for the quiz purpose, screw formalities and just memorize the theorems.
9.4 Pyth Theorem (not to sound like a loser and a stuckup guy but did we not learn this in like 6th grade? Anyways…)
Anyways… in a triangle ABC where Side C is the Hypothenuse, the A^2+B^2=C^2.
From the converse, we can find that if:
a^2+b^2>c^2 then acute
a^2+b^2=c^2 then right
a^2+b^2<c^2 then obtuse
So as an easy reminder a^2+b^2 is the feather of Maat. If its acute than the heart (or biggest angle) is lightweight and the feather rises (thus C^2 is less than the feather). If its obtuse, than the heart (or biggest angle) is heavyweight and the feather sinks (thus C^2 is more than the feather). and if its equal they are equal weight and the dog like animal is cheated.
Anyways. Just remember the formulas again.
Finally 9.5: Distance Formula.
(Once again, another review)
Such a review that im only gonna do examples again.
Distance between (4,0) and (6,0)
{[(6-4)^2]+[(0-0)^2]}^1/2-> [(2^2)+(0^2)]^1/2-> (4+0)^1/2-> 4^1/2->2
#7. 36/8=AD
Bc is can be solved after Ac is solved.
Anyways, that is all for the quiz, ill update again in about a week for the test. So yeah wish me luck and so long an so forth.
Stuff to remember: Similar triangles, Radii, angle rules, Supplementary rules, etc.
9.6-7 Families
Just remember the 30, 60 90 and the 45, 45, 90 ones the rest, just hope you have a decent calculator.
30′s opposite side: x
60′s opposite side: x(3)^1/2
90′s opposite side: 2x
45′s opposite side: x
90′s opposite side: x(2)^1/2
9.8 Space crap.
REC. To find the diagonal its L^2+W^2+H^2
Square pyramid: Slant height is the perpendicular to a side of a base.
Arg. you know this stuff. Circles are 360 degrees btw.
9.9-10 Law of (Co)sines
Sines: A/sin a=B/sin b=C/sin c
Cosines: C^2=A^2+B^2-2AB (cos C)
And yeah… G2g now. bb.
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