General Knowledge Flashcards
What does GCF stand for?
Greatest Common Factor
What does LCM stand for?
Least Common Multiple
How do you find the GCF of large complex numbers ?
Find the prime factorization of all numbers and stack them in columns.
See what prime factors they have in common
And multiply the column of what they have in common to get the GCF
(In common means the number must be in the row of all the numbers)
How do you find the LCM of large complex numbers ?
Find the prime factorization of all numbers and stack them in columns.
See what is the largest prime factors they have in common
And multiply the largest ones from each column together and thats the LCM
(You will have a number from each column
Definition of a Trapezoid?
A quadrilateral with two sides that are parallel.
Formula to find a Trapezoid area?
½(sum of bases)(height)
Formula to find sum of all interior angles in polygons?
(n-2)*180
where n is the number of sides
In 45º - 45º - 90º triangles, the lengths of the sides are in the ratio of:
1:1:√2
In 30º - 60º - 90º triangles, the lengths of the sides are in the ratio:
1:√3:2
In triangles, the lengths of the sides that are in the ratio
1:1:√2
produce what angles?
45º - 45º - 90º
In triangles, the lengths of the sides that are in the ratio
1:√3:2
produce what angles?
30º - 60º - 90º
Area of a triangle?
(Altitude x Base) /2
What is the altitude of a triangle?
The altitude of a triangle is the segment drawn from a vertex perpendicular to the side opposite that vertex.
Circumference of a circle?
2πr
Area of a circle?
πr^2
Quadratic equations: Shortcut to two solutions?
X1 = ( -b - Root( b^2 - 4ac )) / 2a X2 = ( -b - Root( b^2 - 4ac )) / 2a
Tangent-Secant theorem?
UV2=UX⋅UY
Diagonal of a cube? (formula)
x√3
where x is a side of the cube
Volume of a cone? (formula)
Pi x r^2 x (h/3)
= Base area x h/3
Arithmetic Sequence?
A(n) = A(n-1) + Rate
= A(1) + Rate*(n-1)
Geometric Sequence?
A(n) = A(n-1) * R
= A(1) * R^(n-1)
In which case |x| + |y| > |x+y|
If xy<0 which means X or Y is negative.
= other cases
Result of the Sums?
1) odd + odd
2) even + even
3 odd + even
1) even
2) even
3 odd
Result of the factors?
1) odd x odd
2) even x even
3 odd x even
1) Odd
2) Even
3) Even
Result of the divisions? 1) odd / odd 2) even / even 3 odd / even 4) even / odd
1) Odd or N/A
2) Even or N/A
3) N/A (not a prime ie: 7/2)
4) Even or N/A
7 Properties of Consecutive Integers?
- Terms are evenly spaced
- Arithmetic mean and median are equal
- Arithmetic mean and median= (1st term + last term) /2
- Sum of elements= n x Average
- Number of consecutive numbers = ( (Last + First)/ Increment) + 1
- Average of odd N number = Integer
- Average of even N numbers = Integer
How many solutions to an even exponent?
Any number to an even power has two roots: positive and negative. eg: 4 = 2^2 or -2^2
Product of GCF(a,b) and LCM(a,b) ?
a x b
