Equations

Question 1

What is the equations of ax^2+bx+c=0?

Answer 1

roots are 𝛂, β
𝛂+β=-a/b
𝛂β=c/a

Question 2

What are the equations of ax^3+bx^2+cx+d=0?

Answer 2

roots are 𝛂, β, γ
𝛂+β+γ=-b/a
𝛂β+βγ+γ𝛂=c/a
𝛂βγ=-d/a

Question 3

What is the pattern of Vieta’s Formula?

Answer 3

-,+,-,+,- 순으로 루트의 모두 덧셈, 두 개씩, 세 개씩, 네 개씩… 끼리끼리 곱해서 더하고 마지막에는 몽땅 곱한다.
ex. 𝛂+β+γ=-b/a
𝛂β+βγ+γ𝛂=c/a
𝛂βγ=-d/a

Question 4

a^2+b^2

Answer 4

=(a+b)^2-2ab

=(a-b)^2+ab

Question 5

a^2-b^2

Answer 5

=(a+b)(a-b)

Question 6

a^3+b^3

Answer 6

=(a+b)^3-3ab(a+b)
=(a+b)(a^2-ab+b^2)
=

Question 7

a^3-b^3

Answer 7

=(a-b)^3+3ab(a-b)
=(a-b)(a^2+ab+b^2)

Question 8

(a+b+c)^2

Answer 8

=a^2+b^2+c^2+2(ab+bc+ca)

Question 9

a^3+b^3+c^3-3abc

Answer 9

=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)

Question 10

11의 배수판별법

Answer 10

각 자리의 digit을 더하고 빼기를 한 결과가 0 또는 11의 배수가 될 때

Question 11

Arithmetic Sequence
an formula

Answer 11

=a+(n-1)d

Question 12

What is an?

Answer 12

an=the nᵗʰ term in the sequence

Question 13

Arithmetic Sum
Sn

Answer 13

=n(a+an)/2

Question 14

Geometric Sequence
an

Answer 14

=ar^(n-1)

Question 15

Geometric Sum
Sn

Answer 15

=a(1-r^n)/1-r

=a(1-r^n)/r-1

Question 16

Infinite Geometric Series
*ONLY USE WHEN COMMON RATIO ARE ALL THE SAME LIKE:
S=a+ar+ar^2+ar^3+…
Sum=

Answer 16

S=a/1-r

Question 17

Difference Sequence

Answer 17

The difference is a sequence - Get it?

Question 18

For difference sequences,
an=

Answer 18

an=a+(b1+b2+b3+b4+b5+…+bn-1)
a is first term

Question 19

How to solve recurrence formula?

Answer 19

input 1,2,3 in n
Find common difference
Use arithmetic sequence

Question 20

What is Permutation?

Answer 20

n개중 r개를 순서있이 일렬로 배열

Question 21

nPr

Answer 21

=n!/(n-r)!

Question 22

What is Combination?

Answer 22

n개중 r개를 순서 없이 random하게 뽑기

Question 23

nCr

Answer 23

=nPr/r!
=n!/r!(n-r)!

Question 24

What is Homogeneous Combination?

Answer 24

n개 중 r개를 중복해서 순서 없이 뽑기

Question 25

nHr

Answer 25

nHr=(n+r=1Cr

Question 26

What is n in nPr, nCr, nHr?

Answer 26

n은 선택할 수 있는 대상이다.

Question 27

What is r in nPr, nCr, nHr?

Answer 27

r은 선택의 개수이다.

Question 28

n≥r가 되는 것들

Answer 28

nPr, nCr

Question 29

n<r 가 되는 것들

Answer 29

nHr

Question 30

probability of event=

P(E)=

Answer 30

number of event/number of sample space

n(E)/n(S)

Question 31

What are the characteristics of Probability

Answer 31

0≤P(E)≤1

Question 32

n(a∪B)=

Answer 32

=n(A)+n(b)-n(AnB)

Question 33

P(A∪B)=

Answer 33

=P(A)+P(B)-P(AnB)

Question 34

P=
같은 행동을 n번 반복하여 r번 실행된 확률

Answer 34

nCrP^r(1-P)^n-r

Question 35

Circumcenter Theorem

Answer 35

외심 공식

Question 36

Angle Bisector Theorem

Answer 36

각의 이등분선
Search when you see this until the image appears on your mind!

Question 37

Converse of the Angle Bisector Theorem

Answer 37

각의 이등분선
Search when you see this until the image appears on your mind!

Question 38

Incenter Theorem

Answer 38

내심 공식

Question 39

Centroid Theorem

Answer 39

무게중심
Search when you see this until the image appears on your mind!

Question 40

Orthocenter

Answer 40

수심

Question 41

Trapezoid midsegment theorem

Answer 41

Search when you see this until the image appears on your mind!

Question 41

intersecting chord angle theorem

Answer 41

Search when you see this until the image appears on your mind!

Question 42

Heron’s Formula
Area of triangle without angles or other distances

Answer 42

When s is the semi-parameter
A=√s(s-a)(s-b)(s-c)
A=1/4√4a^2b^2-(a^2+b^2-c^2)2
A=1/2√a^2c^2-((a^2+c^2-b^2)/2)^2

Question 43

Semi-perimeter

Answer 43

s=(a+b+c)/2
half of the perimeter of the circle

Question 44

Simon’s Favorite Factoring Trick
xy+kx+jy+yk=

Answer 44

(x+j)(y+k)