Theory - Quant Flashcards
(53 cards)
How to create a perpendicular line to another line?
-1/m
How can we mirror points at axes and how at slope 45° and -45°?
45°: P1 (x,y) –> P2(y,x)
-45°: P1 (x,y) –> P3 (-y,-x)
x-axis: P1(x,y) –> P4(x,-y)
x-axis: P1(x,y) –> P5(-x,y)
Area of an isosceles right triangle? In terms of leg and hypothenuse
A= (leg^2)/2 A= (hy^2)/4
Relationship of legs to hypothenuse in an isosceles right triangle?
leg=hy/squr(2)
hy= leg * sqr(2)
Area of an equilateral triangle? In terms of s
A= squr(3) / 4* s^2
Area of 90 - 60 - 30 triangle?
in terms of hyp, 2nd largest, and the smallest side
A= hyp^2 * squr(3)/8 A= (2nd leg*2/squr(3)^2 * squr(3)/8= 2nd leg^2/(squr(3) *2) A= (smL * 2)^2*squr(3)/8= smL^2 * squr(3)/2
Relationships of 90 - 60 - 30 triangle?
hypothenuse to legs
smallest legs to others
2nd largest legs to others
hy=2smL = 2/sqr(3) * 2ndL smL = 1/2 hyp = 1/sqr(3)*2ndL 2ndL = srq(3)/2 hy = smL*sqr(3)
What are the four quadratic triplets?
(3, 4, 5)
(5, 12, 13)
(8, 15, 17)
(7, 24, 25)
The formula of angle sum of polygons
( n − 2 ) × 180
How can you calculate the diagonal length of a square cube? How can you do that for a rectangular solid?
space diagonal of a square cube: sqr(3) s
space diagonal of rectangular solid: length = srq(a^2 + b^2 + c^2)
How is the relationship between the angle of triangle from the center to one at the sides (and both share one side)
winkel in der Mitte ist doppelt so groß wie auf der Seite
Is zero even or odd?
even
What are the squares from 10 to 20?
121, 144, 169. 196, 225, 256, 289, 324, 361, 400
How do you calculate the numbers of factors of a number? How do you calculate the number of even and odd factors?
Prime factors –> take the exponents add one to each one of them and multiply with each other
odd –> do the some just for the off prime factors
Three ways to compare fractions?
add things to the denominator and nominator
close fractions
multiply the denominators
10^-4 how many 0, and 0?
0.0001 –> n-1 zeros between first number and ,
What are the percentages of 1 std, 2 std, 3std?
34%, 13.5%, 2,5%
What happens to the std. if you multiple all numbers of a set by k?
std *k
10 dice rows probability that exactly 2 show a five?
10C2 * (1/6)^2 * (2/6)^8
10!/(8! * 2!) = 10*9/2
What should be done with an answer with a square root?
In Gleichung wieder einsetzen um zu schauen, dass es funktionert und nicht +-2=-2 rauskommt
Units, ten, hundred, tenth, hundredth digit?
ten, unit, tenth, hundreths
15,23
What is sqr(2), sqr(3), sqr(5)
1.4, 1.7, 2.2
8?
2^3
16?
2^4
