Year 1 Pure Flashcards
Irrational numbers
The square root of any number which is not itself a perfect square
a^m x a^n
a^(m+n)
a^m / a^n
a^(m-n)
(a^m)^n
a^mn
a^-n
1/(a^n)
a^0
1
a^(1/n)
nth root of a
a^(m/n)
nth root of a^m
Describe the shape of a quadratic
Parabola
Discriminant
b^2 - 4ac
b^2 - 4ac
Discriminant
a < x < b
{x:x > a} n {x:x < b}
x > b and x < a
{x:x > b} u {x:x < a}
Equation of a circle
(x - a)^2 + (x - b)^2 = r^2
Where centre (a,b)
Find the midpoint of a circle from 3 points
Find the gradient between two points.
Get the negative reciprocal of this and find the equation from the the midpoint of the two points.
Repeat with two other points
Create a simultaneous equation with this. This is the midpoint.
Sin (theta) using cos
Cos ( 90 - theta )
Cos ( theta ) using sin
Sin (90 - theta)
Trigonometric equation tan (theta)
sin (theta) / cos (theta)
Trigonometric equation 1
Sin^2 (theta) + cos^2 (theta) = 1
Asymptote
A line which is approached by a curve without ever reaching it
y = f(x) + a
Vertical translation
y = f(x - a)
Horizontal translation
y = af(x)
Vertical stretch
y = f(1/a x)
Horizontal stretch
Reflection in the x axis
y = -f(x)
Reflection in the y axis
y = f(-x)
nCr
n! / (r!(n - r)!)
Derivative of kx^n
knx^n-1
Differentiation
The process of finding the gradient function or derivative or derived function
Second derivative
The rate of change of the derivative
At a maximum point
dy/dx = 0
d^2y/dx^2 < 0
At a minimum point
dy/dx = 0
d^2y/dx^2 > 0
Differentiation from first principles
fâ(x) = (f(x-a) -f(x)) / a
a -> lim 0
Integrate kx^n
(kx / (n+1))^n+1 +c
Definite integral
Uses limits to find the area under a portion of a curve
Write (r, theta) in component form
(r cos (theta))
(r sin (theta))
Position vector
A vector which starts at the origin
Unit vector
Has a magnitude of 1
a^x = b
Log (a) b = x
Log(x) + log(y)
Log(xy)
Log(x) - log(y)
Log(x/y)
Log(x^n)
n log(x)
Log(a) a
1
Log(a) 1
0
Derivative of e^kx
ke^kx
