Year 2 Pure Flashcards
What form can a rational number be written in
a/b
What are the different types of functions
One to one
Many to one
Not a function
What is the relationship between f(x) and f-1(x)
they are the inverse of each other
What order should fg(x) be done in
Apply g(x) into f(x)
What is y = l f(x) l
It is a reflection in the x-axis
What is y= f(lxl)
Reflection in the y-axis
What is f(x+a)
Horizontal translation of -a
What is f(x) + a
vertical translation of +a
what is f(ax)
horizontal stretch of 1/a
What is af(x)
Vertical stretch of scale factor a
What is f(-x)
refection in the y-axis
What is -f(x)
refection of f(x) in x-axis
What is an arithmetic sequence
The difference between consecutive terms is the same
What is the formula for the nth term in an arithmetic sequence
Un = a + (n-1)d
a=first term
d=common difference
What is an arithmetic series
It is the sum of the terms of an arithmetic sequence
What is the formula for the sum of the first n terms of an arithmetic sequence
Sn = n/2 (2a + (n-1)d)
a=first term
d=common difference
Sn = n/2 (a+l) where l is the last term
What is a geometric sequence
It is a sequence with a common ratio between consecutive terms
What is the formula for nth term of a geometric sequence
Un = ar(n-1)
a=first term
r=common ratio
What is the formula for the sum of the first n terms of a geometric sequence
Sn = a(1-rn)/1-r
a=first term
r=common ratio
What is the formula for the sum to infinity of a convergent geometric series
S = a/1-r
What is a recurrance relation
It defines each term of a sequence as a function of the previous term
What is the recurrence relation formula
Un+1 = f(Un)
What is the formula for binomial expansion of (1+x)n
1+nx+ n(n-1)x2/2! (x2) + n(n-1)(n-2)x3/3! (x3)
What is 2 pi equal to in degrees
360 degrees
what is the equation for arc length
l = r0
r=radius
0=is the angle in radians
What is the equation for area of a sector
A=1/2 r20
r=radius
0=angle in radians
What is sin0, cos0 and tan0 equal to when 0 is small
sin0 = 0
tan0 = 0
cos0 = 1-02/2
What is secx equal to
1/cosx
what is cosecx
1/sinx
What is cotx equal to
1/tanx
cosx/sinx
What does the graph y=secx look like
Symetrical in y axis
vertical asymptotes at -450,-270,-90,90,270 and 450
y is less than or equal to -1
y is greater than or equal to 1
What does the graph y=cosecx look like
Vertical asymptotes at -360,-180,0,180,360
y is less than or equal to -1
y is greater than or equal to 1
What does the graph of y=cotx look like
vertical asymptotes at -360,-180,0,180 and 360
Intersect x-axis at -270, -90, 90 and 270
equal to all value of y
What are the 3 identities
sin2x + cos2x = 1
1+ tan2x = sec2x
1 + cot2x = cosec2x
What is the inverse function of sinx, cosx and tanx
arcsinx
arccosx
arctanx
What does arcsinx look like
domain is -1 < x < 1
Range is -pi/2 < y < pi/2
or -90 < y < 90
Goes through the origin
What does arccosx look like
Domain is -1 < x < 1
Range is 0 < y < pi
or 0 < y < 180
What does arctanx look like
Domain is all values of x
Range is -pi/2 < y < pi/2
with asymptotes at pi/2 and -pi/2
Goes through the origin
What is sin (A + B) equal to
sinAcosB + cosAsinB
What is cos (A + B) equal to
cosAcosB - sinAsinB
What is tan(A+B) equal to
tanA + tanB / 1 - tanAtanB
What is sin(A-B) equal to
sinAcosB - cosAsinB
What is cos(A-B) equal to
cosAcosB + sinAsinB
What is tan(A-B) equal to
tanA - tanB / 1 + tanAtanB
What is sin2A equal to
2sinAcosA
What is cos2A equal to
cos2A - sin2A
2cos2A -1
1 - 2sin2A
What is tan2A equal to
2tanA / 1 - tan^2A
What is asinx +- bcosx equal to
Rsin(x +- c)
What is acosx +- bsinx equal to
Rcos(x -+ c)
What is the rule if a series converges
l r l < 1
How do you find the distance from the origin of the co-ordinate (x,y,z)`
square root(x^2 + y^2 + z^2)
How do you find the distance between to points
Find the difference in points then
(xd^2 + yd^2 + zd^2) ^1/2
Whats the equation for the angle that a vector a = xi + yj + zk makes with the x axis and x,y,z
Cos0x = x / l a l
Cos0y = y / l a l
Cos0z = z / l a l
What happens to 0 when 0 is small
Disregard terms with 0 in them
What is a period sequence
A sequence that repeats numbers
what is a periodic sequence of order 3 mean
The sequences repeats numbers every 3 terms
How do you calculate the shortest distance between 2 points when there is a variable “t”
Form an equation for the distance and then solve the quadratic to find minimum point
Minimum point x coordinate is the value of t and y coordinate is shortest distance
