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Math for high school > MATH > Flashcards

MATH Flashcards

1
Q

Ringjoone kaare pikkus

A

l = 2 x Pii x r x alfa / 360

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2
Q

Ringjoone pindala

A

Pii x r^2 x alfa / 360

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3
Q

Heroini valem

A

Ruutjuur p x ( p-a)(p-b)(p-c)

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4
Q

Siinusteoreem

A

a/sinalfa = b/sinbeta = c/singamma

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5
Q

Koosinusteoreem

A

a^2 = b^2 + c^2 - 2x c x b x cosalfa

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6
Q

Vektor AB

A

(x2-x1; y2-y1)

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7
Q

Vektori |a| pikkus

A

Ruutjuur x^2 + y^2

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8
Q

Summavektor

A

(x1+x2; y1+y2)

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9
Q

Vahevektor

A

(x1-x2;y1-y2)

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10
Q

Kollineaarsed vektorid

A

x1/x2 = y1/y2

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11
Q

Nurk vektorite vahel

A

cos f = (X1 x X2)+ (Y1 x Y2) / |a| |b|

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12
Q

Vektorid RISTI

A

X1 x X2 + Y1 x Y2 = 0

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13
Q

Punkti ja tõusuga määratud sirge võrrand

A

y - y1 = k ( x - x1)

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14
Q

k =

A

y2-y1 / x2-x1

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15
Q

Tõusu ja algordinaadiga sirge võrrand

A

y = kx + b

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16
Q

Kahe punktiga määratud sirge võrrand

A

x - x1 / x2 - x1 = y - y1 / y2 - y1

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17
Q

Sirge võrrand telglõikudes

A

x / a + y / b = 1

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18
Q

x- teljega paralleerne sirge võrrand

A

y = a / x = 0

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19
Q

y- teljega paralleerne sirge võrrand

A

x = b / y = 0

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20
Q

Punkti ja sihivektoriga määratud sirge võrrand

A

x - x1 / Sx = y - y1 / Sy

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21
Q

Sirge üldvõrrand

A

Ax + By + C = 0

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22
Q

Sirged on paralleersed kui…

A

A2 / A1 = B2 / B1 ei võrdu C2 / C1

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23
Q

Sirged ühtivad, kui…

A

A2 / A1 = B2 / B1 = C2 / C1

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24
Q

Sirged lõikuvad, kui…

A

A2 / A1 ei võrdu B2 / B1

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25
Q

Sirged on risti, kui…

A

k1 x k2 = -1

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26
Q

Nurk sirgete vahel

A

tan alfa = k2-k1 / 1+k1 x k2

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27
Q

Ringjoone võrrand ( keskpunkt O(a;b) ja r)

A

(x-a)^ 2 + (x-b)^ 2 = r^ 2

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28
Q

Ringjoone võrrand (keskpunkt O(0;0) ja r)

A

x^ 2 + y^ 2 = r^ 2

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29
Q

Parabooli võrrand

A

ax^ 2 + bx + c

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30
Q

Haripunkt

A

Xh = -b/2a

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31
Q

Protsent

A

Osa = terve x osamäär

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32
Q

Muutus %

A

m = lõppväärtus x algväärtus / algväärtus

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33
Q

Tõenäosus

A

p = soodsad võimalused (M) / kõik võimalused (N)

34
Q

Bernouli valem

A

Pn;k = C^ k ^n x p^ k x q^ n-k

35
Q

Kombinatsioonide arv

A

C^ m ^ n = n! / m! (n-m)!

36
Q

Funktsiooni uurimine MP

A

murru nimetaja ei saa olla 0

logaritm peab olema positiivne

37
Q

Nullkohad

A

X0 => y = 0

38
Q

Positiivsus ja negatiivsus pk

A

Y + = y >0

Y - = y<0

39
Q

Paaris ja paaritufunktsioon

A 
paaris f(-x) = f(x)
paarity f(-x) = -f(x)
40
Q

Logaritm

A

logaC= b ja a^ b= c

41
Q

Loga(c x d)

A

loga C + loga D

42
Q

Loga(c/d)

A

logaC - logaD

43
Q

LogaC^ d

A

dLoga C

44
Q

Liitprotsendiline kasv. ja kahanemine

A

L = A (1 +- 1/100)^ n

45
Q

Aritmeetiline jada

A

An= A1 + (n-1)x d

46
Q

Aritmeetilise jada summa

A

Sn = 2a1 + (n-1) x d/ 2 x n

47
Q

Geomeetriline jada

A

An= a1 x q^ n-1

48
Q

Geom. jada summa valem

A

Sn = a1 ( q^ n-1)/ q-1

49
Q

Hääbuva jada summavalem

A

Sn= a1/ 1 - q

50
Q

sin x = m

A

x = (-1)^ n x arcsin m + nPII ; n kuulub hulka Z

51
Q

cos x = m

A

x= +- arccos m + 2nPII

52
Q

tan x = m

A

x= arctan m + nPII

53
Q

c’

A

0

54
Q

x’

A

1

55
Q

(1/x)’

A

-1/x^2

56
Q

(ruutjuut x) ‘

A

1/ 2ruutjuur x

57
Q

(e^x)’

A

e^x

58
Q

(lnx)’

A

1/x

59
Q

(loga x) ‘

A

1/ x lna

60
Q

sinx’

A

cosx

61
Q

cosx’

A

-sinx

62
Q

tanx’

A

1/cos^2x

63
Q

f(x) x g(x) ‘

A

f’(x)g(x) + f(x)g’(x)

64
Q

f(x) / g(x) ‘

A

f’(x)g(x) - f(x)g’(x) / g(x)^2

65
Q

Joone puutuja võrrand

A

y- y0 = f’(x0) (x- x0)

66
Q

Funktsiooni nõgusus piirkond

A

f’‘(x) > 0

67
Q

Funktsiooni kumerus piirkond

A

f’‘(x) < 0

68
Q

Ekstreerum Vmax Smax

A

S/V’= 0

S/V’’ <0

69
Q

Vmin Smin

A

S/V’ = 0

S/V’’ > 0

70
Q

Püstprisma

A 
St= 2Sp + Sk
Sk= P x h
V= Sp x h
71
Q

Püramiid

A 
St= Sp + Sk
Sk= P x m / 2 
V = 1/3 x Sp x H
72
Q

Püramiid lõige

A

Sp/Sl = H^2/h^2

73
Q

Kolmnurkne püramiid KORRAPÄRANE

A

Kõrgus langeb mediaanide lõikepunkti
r= 1/3 h
R= 2/3 h

74
Q

Mittekorrapärane kolmnurkne püramiid
ERIKÜLGNE
Kõik nurgad külgtahkude ja põhitahu vahel on võrdsed

A

kõrgus langeb siseringjoone punkti

75
Q

Mittekorrap. kolmn. pürmiid ERIKÜLGNE

Kõik nurgad külgserva ja põhitahu vagel on võrdsed

A

kõrgus langeb ümberringjoone keskpunkti

76
Q

Silinder

A 
St = 2Sp + Sk
Sk= 2pii r x h
Sp = 2pii r ^2
V= Sp x h
77
Q

Koonus

A 
St = Sp + Sk
Sk = pii x r x m
Sp = pii x r ^2
V = 1/3x Sp x h
78
Q

Kera

A 
S = 4 x pii x R ^2
V = 4 x pii x R^3 / 3
79
Q

Integraal sin x

A

-cos x + C

80
Q

Integraal cos x

A

sin x + c

81
Q

Integraal 1/ cos ruut x

A

tan x + c

82
Q

Integraal dx/ ruutjuur x

A

2 ruutjuur x + c

Math for high school (1 decks)

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