C2 Flashcards by Aneurin Quinn Evans

(2/3)^-2 =

(3/2)^2

How well did you know this?

Not at all

Perfectly

5^-2 =

1/5^2

How well did you know this?

Not at all

Perfectly

A^2/3 =

3sqrrtA^2

How well did you know this?

Not at all

Perfectly

Sin graph starts at

How well did you know this?

Not at all

Perfectly

Sinx +2 starts at

2, jut 2 higher than normal sinx

How well did you know this?

Not at all

Perfectly

Sin(x+90d)

Moves 90 to the left (negatively)

How well did you know this?

Not at all

Perfectly

3sinx

The crests extend up to 3 instead of 1

A stretch in the y direction factor 3

How well did you know this?

Not at all

Perfectly

Sin3x

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

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

How well did you know this?

Not at all

Perfectly

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

The line has been reflected at the x axis

How well did you know this?

Not at all

Perfectly

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

Reflected on the y axis

How well did you know this?

Not at all

Perfectly

Sin1/3x

The crests are 3 times as big

Stretch in the x direction factor 3

How well did you know this?

Not at all

Perfectly

Y= sinx crosses x axis at

0, 180, 360

How well did you know this?

Not at all

Perfectly

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

How well did you know this?

Not at all

Perfectly

Number on top of sigma

Number on bottom (r=1)

Number of terms

First number substituted in

How well did you know this?

Not at all

Perfectly

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)

How well did you know this?

Not at all

Perfectly

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

How well did you know this?

Not at all

Perfectly

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

a + (n - 1)d

a= first term
d=common difference

How well did you know this?

Not at all

Perfectly

(Sum of first n terms) Sn =

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

How well did you know this?

Not at all

Perfectly

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

n/2 (a+l)

How well did you know this?

Not at all

Perfectly

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]

How well did you know this?

Not at all

Perfectly

What is n on sigma notation

Number on top

How well did you know this?

Not at all

Perfectly

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

How well did you know this?

Not at all

Perfectly

Geometric series for Un

Un = ar^n-1

r - common ratio
n- nth term

How well did you know this?

Not at all

Perfectly

Sum of the first n terms of a geometric series

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

How well did you know this?

Not at all

Perfectly

Sum to infinity

a/ 1-r

Sum to infinity is not possible if

R<1

What to do when you see a cubic

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

Binomial expansion

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

nCr

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

How to find the sum of integers between two numbers

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

Sine rule

a/sinA = b/sinB = c/sinC

Cosine rule length

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

Cosine rule Angle

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

Area of triangle

1/2 ab sinC

Pi radians =

180d

Radians to degrees

X 180/pi

Degrees to radians

Pi/180

40degrees in radians

40 x pi/180 =2/9 pi radians

Area of circle using radians

A= 1/2 r^2@ @- theta

Arc length

r@ @- theta

When dealing with circles make sure

You are working in radians

y= sinx graph

starts at 0, crosses x axis at 180 then 360

y= cosx graph

starts at 1 crosses x axis at 90 then 270

y= tanx graph

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

tan@=

sin@/cos@

equation linking cos and sin ^2@

sin^2@ + cos^2@ = 1

if tan^2x = 3 then x is

tan^-1 sqrrt3

cos2x = 0.5 what does the two do

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

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

loga(x) +loga(y) =

loga(xy)

loga(x) -loga(y)=

loga(x/y)

kloga(x)=

loga(x^k)

loga(a)=

1 (a^1=a)

loga(1)

0 (a^0=1)

loga(a^x)=

xloga(a)= 1x

loga(1/x)=

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

a^b = c (explain using logs)

loga(c) =b

log3(81) =x (what is x)

3^x =81 (must be 4)

if the angle of a triangle is obtuse then

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

dy/dx has a minimum stationary point

d^2y/dx^2 >0

dy/dx has a maximum stationary point

d^2y//dx^2 <0

surface area of a cylinder

2πrh+2πr^2

volume of a cylinder

πr^2h

Volume of cone

πr^2h/3

Area of cone

πr(r+h^2+r^2)

to find area under a curve

you always integrate first | UNLESS using trapezium rule

how to integrate

up power, then divide by new power | AND ADD C

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

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

how to find h (for trapezium rule)

h= b-a/n

trapezium rule

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

how to make a more accurate estimate

split trapezium into more strips

do you look at "strips" or "ordinates"

strips

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

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

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

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

y=sinX | to y=2sinx

stretch in y direction scale factor 2

y=sinX | to y= -sinX

reflection in x axis

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

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

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

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

C2 Flashcards

(78 cards)