Year 1 Pure Flashcards
(21 cards)
a^(m/n) can be rewritten as what?
n√(a^m)
√(ab) can be rewritten as what?
√a*√b
What happens to asymptotes when a function is translated?
They are translated as well.
What is y = f(x+a) to the graph y = f(x)
And translation of -a in the x axis.
What is y = f(ax) to the graph y = f(x)
A stretch of 1/a in the x axis.
Given the circle x^2 + y^2 + 2fx + 2gy + c = 0, what is the centre and radius of the circle?
Centre: (-f,-g)
Radius: √(f^2 + g^2 - c)
How do you find the centre of a circle given 3 points on it?
Find the equations of the perpendicular bisectors of two different chords, then find the coordinates of the intersection of the two.
What different methods of proof are there?
Deduction
Identity
Exhaustion
Counter-example
What is the choose function (nCr)?
n!/( r!(n-r)! )
What is the cosine rule?
cosA = b^2+c^2-a^2 / 2bc
What is sinX also equal to?
sin(180 - X)
CAST diagrams?
Idk something about them? maybe???
Exact Trig Values?
Go Study them!!!
Formula for a unit vector of a?
a /|a|
Point P divides line AB in the ratio x:y, what is OP equal to?
OP = OA + x/x+y * AB
OP = OA + x/x+y * (OB - OA)
How Find stationary points is maximum?
f’‘(x) < 0
How Find stationary points is minimum?
f’‘(x) > 0
How Find stationary points is inflection?
f’‘(x) = 0 could be one, test either side to determine its nature.
What is the graph y = ln x similar to?
It is a reflection of y = e^x in the line y=x
If y=ax^n what will the graph of log y against log x look like?
Straight line with gradient n and vertical intercept log a.
If y=ab^x what will the graph of log y against x look like?
A straight line with gradient log b and vertical intercept log a.
