C2 Flashcards
(2/3)^-2 =
(3/2)^2
5^-2 =
1/5^2
A^2/3 =
3sqrrtA^2
Sin graph starts at
0
Sinx +2 starts at
2, jut 2 higher than normal sinx
Sin(x+90d)
Moves 90 to the left (negatively)
3sinx
The crests extend up to 3 instead of 1
A stretch in the y direction factor 3
Sin3x
The crests(positive + negative) are 3 times as small
Stretched in the x direction by a factor of 1/3
Y=f(x) becomes y= -f(x)
The line has been reflected at the x axis
Y=f(x) becomes y= f(-x)
Reflected on the y axis
Sin1/3x
The crests are 3 times as big
Stretch in the x direction factor 3
Y= sinx crosses x axis at
0, 180, 360
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
Number on top of sigma
Number on bottom (r=1)
Number of terms
First number substituted in
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)
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
Un(nth term 1,2,3…)(can be used to find last term) =
a + (n - 1)d
a= first term
d=common difference
(Sum of first n terms) Sn =
n/2 (2a + (n-1)d)
(Sum of first n terms if you know first and last term) Sn =
n/2 (a+l)
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]
What is n on sigma notation
Number on top
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
Geometric series for Un
Un = ar^n-1
r - common ratio
n- nth term
Sum of the first n terms of a geometric series
Sn
Sn = a(1-r^n) /1-r
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)
