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Flashcards in C2 Deck (78):
0

5^-2 =

1/5^2

1

(2/3)^-2 =

(3/2)^2

2

A^2/3 =

3sqrrtA^2

3

Sin graph starts at

0

4

Sinx +2 starts at

2, jut 2 higher than normal sinx

5

Sin(x+90d)

Moves 90 to the left (negatively)

6

3sinx

The crests extend up to 3 instead of 1

A stretch in the y direction factor 3

7

Sin3x

The crests(positive + negative) are 3 times as small

Stretched in the x direction by a factor of 1/3

8

Y=f(x) becomes y= -f(x)

The line has been reflected at the x axis

9

Y=f(x) becomes y= f(-x)

Reflected on the y axis

10

Sin1/3x

The crests are 3 times as big
Stretch in the x direction factor 3

11

Y= sinx crosses x axis at

0, 180, 360

12

When it wants you to evaluate a series

Substitute in the "r"s (1,2,3,4) for given number of terms
Add the terms to find Ur

13

Number on top of sigma
Number on bottom (r=1)

Number of terms
First number substituted in

14

Recurrence relation

Type given value of x1=
Then put in equation have ANS instead of Xn
Keep pressing equal sign
(The value for the equation is hen fed back in as the next X1)

15

Find the limit (convergence) of a sequence

Replace Xn+1 and Xn by L
And find the two limits compare with actual values to find which is right

16

Un(nth term 1,2,3...)(can be used to find last term) =

a + (n - 1)d

a= first term
d=common difference

17

(Sum of first n terms) Sn =

n/2 (2a + (n-1)d)

18

(Sum of first n terms if you know first and last term) Sn =

n/2 (a+l)

19

Sum of the first n natural numbers (taken from sigma notation) r=

n(n + 1) /2

If r is not 1 you will have to do
[top sigma number]-[bottom -1]

20

What is n on sigma notation

Number on top

21

You are given two terms and their values
How to find the common difference

A + (n-1)d

A+ (term-1)difference=value

-simultaneous equation them

22

Geometric series for Un

Un = ar^n-1

r - common ratio
n- nth term

23

Sum of the first n terms of a geometric series
Sn

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

24

Sum to infinity

a/ 1-r

25

Sum to infinity is not possible if

R<1

26

What to do when you see a cubic

Find a factor 1 /. -1 first
Then divide by x = 1/ -1

27

Binomial expansion

A decreases by a power as b increases
Use Pascal's triangle or nCr to find the number for the front

28

nCr

n- the power
r- number along (first number is 0)

29

How to find the sum of integers between two numbers

N/2(a + l) - n/2(a +l)

30

Sine rule

a/sinA = b/sinB = c/sinC

31

Cosine rule length

a^2 = b^2 + c^2 -2bc CosA

32

Cosine rule Angle

CosA= b^2 + c^2 - a^2 /2bc

33

Area of triangle

1/2 ab sinC

34

Pi radians =

180d

35

Radians to degrees

X 180/pi

36

Degrees to radians

Pi/180

37

40degrees in radians

40 x pi/180 =2/9 pi radians

38

Area of circle using radians

A= 1/2 r^2@

@- theta

39

Arc length

r@

@- theta

41

When dealing with circles make sure

You are working in radians

42

y= sinx graph

starts at 0, crosses x axis at 180 then 360

43

y= cosx graph

starts at 1 crosses x axis at 90 then 270

44

y= tanx graph

crosses x axis at 0-180-360, waves up and down to 90 degrees outwards from its crossing point

45

tan@=

sin@/cos@

46

equation linking cos and sin ^2@

sin^2@ + cos^2@ = 1

47

if tan^2x = 3 then x is

tan^-1 sqrrt3

48

cos2x = 0.5 what does the two do

the boundaries are doubled 0<720
all the numbers are divided by 2 AT THE END

49

sin(x-20) =0.2 what happens to the -20

the boundaries change from 0<340
-20 is then minused from each number AT THE END

50

loga(x) +loga(y) =

loga(xy)

51

loga(x) -loga(y)=

loga(x/y)

52

kloga(x)=

loga(x^k)

53

loga(a)=

1 (a^1=a)

54

loga(1)

0 (a^0=1)

55

loga(a^x)=

xloga(a)= 1x

56

loga(1/x)=

loga(x^-1) = -loga(x)

57

a^b = c (explain using logs)

loga(c) =b

58

log3(81) =x (what is x)

3^x =81 (must be 4)

59

if the angle of a triangle is obtuse then

you find the angle the normal way
but then you do PI-angle

60

dy/dx has a minimum stationary point

d^2y/dx^2 >0

61

dy/dx has a maximum stationary point

d^2y//dx^2 <0

62

surface area of a cylinder

2πrh+2πr^2

63

volume of a cylinder

πr^2h

64

Volume of cone

πr^2h/3

65

Area of cone

πr(r+h^2+r^2)

66

to find area under a curve

you always integrate first
UNLESS using trapezium rule

67

how to integrate

up power, then divide by new power
AND ADD C

68

given gradient (dy/dx)
given two points
how to find equation

integrate dy/dx
put two points in to find +C
y=mx +c

69

how to find h (for trapezium rule)

h= b-a/n

70

trapezium rule

1/2h [(y0+yn) +2(inter y's)]

71

how to make a more accurate estimate

split trapezium into more strips

72

do you look at "strips" or "ordinates"

strips

73

If logK(x+2)=1 what is K

logK(x+2)=LogkK
(x+2) =K

74

If logK(x+2)=2 what is K

logK(x+2)=2LogkK
(x+2)=k^2

75

y=sinX
to y=2sinx

stretch in y direction scale factor 2

76

y=sinX
to y= -sinX

reflection in x axis

77

y=sinX
to y=sin(X-30)

translation (30, 0) <- write one on top of the other

78

when finding the first n terms by factorization
you will always get two answers

the positive one is correct (only one can be correct)