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