prior knowledge topics Flashcards
natural numbers
N: 0, 1, 2, …
Integers
Z: …, -2, -1, 0, 1, 2, …
positive integers
Z+: 1, 2, 3, 4, …
rational numbers
Q: a/b (a,bєZ, b≠0)
finite decimal representation or infinite aperiodic decimal representation
irrational numbers
infinite aperiodic decimal representation (π, e, surds, …)
surd
= root, the result of which is irrational
real numbers
R = Q U irrational numbers
complex numbers
C: a+bi
(a-bi)(a+bi) = a2+b2
circumcircle
triangle inside a circle
circumcenter => perpendicular bisectors
inscribed circle
circle inside a triangle
incenter => angle bisectors
orthocenter
meeting of all altitudes
centroid
= meeting of medians
central and inscribed angle subtend the same angle ⇒
central angle = 2 x inscribed angle
Thales’ theorem
an inscribed angle, that subtends the diameter of a circle, is equal to 90°
circumference and area of a circle
C = 2πr
A = πr^2
surface area and volume of a sphere
A = 4πr^2
V = (4/3) πr^3
GCD, LCM, LCD
GCD = greatest common divisor = largest number that divides a set of numbers
LCM = lowest common multiple = the smallest number that is a multiple of a set of numbers
LCD = lowest common denominator = lowest common multiple of the denominators of a set of fractions
trapezoid area
h(a+b)/2
cube surface area and volume
A = 6a^2
V = a^3
cuboid surface area and volume
A = 2h(l+b)
V = lhb
cone surface area and volume
A = πr(r + l)
V = (πhr^2)/3
probability
- = number of favorable outcomes/total number of outcomes
- P = 0 ⇒ event will never happen
- P = 1 ⇒ event will certainly happen (100% happen)
