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math > prior knowledge topics > Flashcards

prior knowledge topics Flashcards

1
Q

natural numbers

A

N: 0, 1, 2, …

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2
Q

Integers

A

Z: …, -2, -1, 0, 1, 2, …

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3
Q

positive integers

A

Z+: 1, 2, 3, 4, …

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4
Q

rational numbers

A

Q: a/b (a,bєZ, b≠0)
finite decimal representation or infinite aperiodic decimal representation

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5
Q

irrational numbers

A

infinite aperiodic decimal representation (π, e, surds, …)

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6
Q

surd

A

= root, the result of which is irrational

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7
Q

real numbers

A

R = Q U irrational numbers

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8
Q

complex numbers

A

C: a+bi
(a-bi)(a+bi) = a2+b2

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9
Q

circumcircle

A

triangle inside a circle
circumcenter => perpendicular bisectors

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10
Q

inscribed circle

A

circle inside a triangle
incenter => angle bisectors

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11
Q

orthocenter

A

meeting of all altitudes

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12
Q

centroid

A

= meeting of medians

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13
Q

central and inscribed angle subtend the same angle ⇒

A

central angle = 2 x inscribed angle

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14
Q

Thales’ theorem

A

an inscribed angle, that subtends the diameter of a circle, is equal to 90°

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15
Q

circumference and area of a circle

A

C = 2πr
A = πr^2

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16
Q

surface area and volume of a sphere

A

A = 4πr^2
V = (4/3) πr^3

17
Q

GCD, LCM, LCD

A

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

18
Q

trapezoid area

A

h(a+b)/2

19
Q

cube surface area and volume

A

A = 6a^2
V = a^3

20
Q

cuboid surface area and volume

A

A = 2h(l+b)
V = lhb

21
Q

cone surface area and volume

A

A = πr(r + l)
V = (πhr^2)/3

22
Q

probability

A
  • = number of favorable outcomes/total number of outcomes
  • P = 0 ⇒ event will never happen
  • P = 1 ⇒ event will certainly happen (100% happen)

math (4 decks)

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