Geometry Flashcards
Isoleces right triangle hypotenuse
SQRT(2) * side
30-60-90 triangle base form
x | SQRT(3)x | 2XC
Area of equilaterals
[ Side² * SQRT(3) ] / 4
What are the 5 types of quadrilaterals
Paralellogram, Rhombus, Rectangle, Square, Trapezoid
How to calculate the hight of the equilateral triangle?
h = (side * sq3)/2
Descibre the properties presented in a equilateral triangle and a inscribed and circunscribed circle
Inscribed cicle: radius is h/3
What does the diagonals of trapezoid create
It creates two SIMILAR triangles
What is the approach to geometry questions?
Draw the figure with every info you have. Look at the whole figure (from specific to general level) Infere everything you can.
Then, take each assumption and evaluate how you can use it
What is the result of an odd divided by X?
The result is odd if it’s an integer
How to quickly solve fractions divided by 25 and 125?
Multiply by 4 to get to 100 or by 8 to get to 1000
What is the approach for test cases?
1) note what is obvious about the constraints (I.e. Must be positive)
2) think of how you could create an alternative case
How to represent a set of consecutive integers?
I.e. A set of 5 elements: S-2, s-1, s, s+1,s+2
Average = Med = S
How to calculate direct and inverse proportions?
Direct: multiply by X
Inverse: multiply by 1/x
Think of D=V*T (directly proportional) and D/V=T (inversely proportional, time increases as speed reduces)
What is one approach to solve a system of inequalities?
Combine inequalities if they have the same direction
What is one approach to visualize and solve inequalities?
Plot a number line to compare numbers, I.e. 4x>3y
What can you Infere from x/y<1?
And from x/y>1?
X/y<1: nothing, as it could be positive or negative, could be greater on top or bottom
X/y>1 either positives with x>y, or negatives with x>y
What did you learn with the exercise about remainder of 20/P?
That if it takes too many calculations to prove/disprove a DS, it’s either 1) not sufficient, 2) a math property, or 3) you should look for a specific case that disproves it
What is the equation of the ovelarpponf sets?
Of three: A+B+C - (AB + BC +CA - d) + E = T [for greater intersection]
Or A+B+C - (x + y + z + 2d) + E = T [for limited intersection]
What did you learn with the DS question asking the value of 9^p * 27^3r?
1) translate the question: simplify the expression
2) make the statements as similar to the question as possible
What is the exception case for SQ(X)?
If 0<x<1, SQ(x) is greater than x
i.e. SQ(0,5) = ~0,7
If SQ(x)>z, doesn’t mean x > z
What is the last check on Absolute equations/inequalities questions?
Plug the value back into the absolute equation and see if it holds true
|1-x| > 0
|1-x| = -5 - 3 doesn’t exist
Given x>y>z, which could be true?
1) x³>y³>z³
2) z>y³>x³
3) x³>z³>y³
First of all, questions like this are always testing the exceptions
2) is true for near decimals, 0,9 > 0,89 > 0,88
3) is not true as signal is not changed and z is always more impacted than y
What is the range of a set of N consecutive integers?
Ragen is n-1
R = (S+n-1)-S = n-1
Note: a set with repeating numbers could also have range=n-1