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AS Maths > C2 > Flashcards

C2 Flashcards

0
Q

(2/3)^-2 =

A

(3/2)^2

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1
Q

5^-2 =

A

1/5^2

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2
Q

A^2/3 =

A

3sqrrtA^2

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3
Q

Sin graph starts at

A

0

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4
Q

Sinx +2 starts at

A

2, jut 2 higher than normal sinx

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5
Q

Sin(x+90d)

A

Moves 90 to the left (negatively)

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6
Q

3sinx

A

The crests extend up to 3 instead of 1

A stretch in the y direction factor 3

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7
Q

Sin3x

A

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

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

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8
Q

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

A

The line has been reflected at the x axis

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9
Q

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

A

Reflected on the y axis

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10
Q

Sin1/3x

A

The crests are 3 times as big

Stretch in the x direction factor 3

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11
Q

Y= sinx crosses x axis at

A

0, 180, 360

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12
Q

When it wants you to evaluate a series

A

Substitute in the “r”s (1,2,3,4) for given number of terms

Add the terms to find Ur

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13
Q

Number on top of sigma

Number on bottom (r=1)

A

Number of terms

First number substituted in

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14
Q

Recurrence relation

A

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)

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15
Q

Find the limit (convergence) of a sequence

A

Replace Xn+1 and Xn by L

And find the two limits compare with actual values to find which is right

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16
Q

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

A

a + (n - 1)d

a= first term
d=common difference

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17
Q

(Sum of first n terms) Sn =

A

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

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18
Q

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

A

n/2 (a+l)

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19
Q

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

A

n(n + 1) /2

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

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20
Q

What is n on sigma notation

A

Number on top

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21
Q

You are given two terms and their values

How to find the common difference

A

A + (n-1)d

A+ (term-1)difference=value

-simultaneous equation them

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22
Q

Geometric series for Un

A

Un = ar^n-1

r - common ratio
n- nth term

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23
Q

Sum of the first n terms of a geometric series

Sn

A

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

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24
Q

Sum to infinity

A

a/ 1-r

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25
Q

Sum to infinity is not possible if

A

R<1

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26
Q

What to do when you see a cubic

A

Find a factor 1 /. -1 first

Then divide by x = 1/ -1

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27
Q

Binomial expansion

A

A decreases by a power as b increases

Use Pascal’s triangle or nCr to find the number for the front

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28
Q

nCr

A

n- the power

r- number along (first number is 0)

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29
Q

How to find the sum of integers between two numbers

A

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

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30
Q

Sine rule

A

a/sinA = b/sinB = c/sinC

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31
Q

Cosine rule length

A

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

32
Q

Cosine rule Angle

A

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

33
Q

Area of triangle

A

1/2 ab sinC

34
Q

Pi radians =

A

180d

35
Q

Radians to degrees

A

X 180/pi

36
Q

Degrees to radians

A

Pi/180

37
Q

40degrees in radians

A

40 x pi/180 =2/9 pi radians

38
Q

Area of circle using radians

A

A= 1/2 r^2@

@- theta

39
Q

Arc length

A

r@

@- theta

41
Q

When dealing with circles make sure

A

You are working in radians

42
Q

y= sinx graph

A

starts at 0, crosses x axis at 180 then 360

43
Q

y= cosx graph

A

starts at 1 crosses x axis at 90 then 270

44
Q

y= tanx graph

A

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

45
Q

tan@=

A

sin@/cos@

46
Q

equation linking cos and sin ^2@

A

sin^2@ + cos^2@ = 1

47
Q

if tan^2x = 3 then x is

A

tan^-1 sqrrt3

48
Q

cos2x = 0.5 what does the two do

A

the boundaries are doubled 0<720

all the numbers are divided by 2 AT THE END

49
Q

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

A

the boundaries change from 0<340

-20 is then minused from each number AT THE END

50
Q

loga(x) +loga(y) =

A

loga(xy)

51
Q

loga(x) -loga(y)=

A

loga(x/y)

52
Q

kloga(x)=

A

loga(x^k)

53
Q

loga(a)=

A

1 (a^1=a)

54
Q

loga(1)

A

0 (a^0=1)

55
Q

loga(a^x)=

A

xloga(a)= 1x

56
Q

loga(1/x)=

A

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

57
Q

a^b = c (explain using logs)

A

loga(c) =b

58
Q

log3(81) =x (what is x)

A

3^x =81 (must be 4)

59
Q

if the angle of a triangle is obtuse then

A

you find the angle the normal way

but then you do PI-angle

60
Q

dy/dx has a minimum stationary point

A

d^2y/dx^2 >0

61
Q

dy/dx has a maximum stationary point

A

d^2y//dx^2 <0

62
Q

surface area of a cylinder

A

2πrh+2πr^2

63
Q

volume of a cylinder

A

πr^2h

64
Q

Volume of cone

A

πr^2h/3

65
Q

Area of cone

A

πr(r+h^2+r^2)

66
Q

to find area under a curve

A

you always integrate first

UNLESS using trapezium rule

67
Q

how to integrate

A

up power, then divide by new power

AND ADD C

68
Q 
given gradient (dy/dx)
given two points
how to find equation
A

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

69
Q

how to find h (for trapezium rule)

A

h= b-a/n

70
Q

trapezium rule

A

1/2h [(y0+yn) +2(inter y’s)]

71
Q

how to make a more accurate estimate

A

split trapezium into more strips

72
Q

do you look at “strips” or “ordinates”

A

strips

73
Q

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

A

logK(x+2)=LogkK

(x+2) =K

74
Q

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

A

logK(x+2)=2LogkK

(x+2)=k^2

75
Q

y=sinX

to y=2sinx

A

stretch in y direction scale factor 2

76
Q

y=sinX

to y= -sinX

A

reflection in x axis

77
Q

y=sinX

to y=sin(X-30)

A

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

78
Q

when finding the first n terms by factorization

you will always get two answers

A

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

AS Maths (3 decks)

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