IGCSE maths - random

f(x) + a

move the graph of f(x) UP/DOWN by ‘a’ units

f(x+a)

move the graph of f(x) LEFT (+a) or RIGHT (-a)

af(x)

stretches the graph of f(x) in the y direction by scale factor ‘a’

(x, y) → (x,ay)

f(ax)

stretches the graph of f(x) in the x direction by scale factor 1/'a’

(x, y) → (x/a, y)

f(-x)

reflects the graphs of f(x) in y-axis

change to coordinate point:

(x, y) → (-x, y)

-f(x)

reflects the graph of f(x) in the x-axis

change to coordinate point:

(x, y) → (x, -y)

domain

the list of possible input values

range

the list of possible output values

sin graphs

max = 1

min = -1

repeats every = 360 degrees

0 degrees = 0

cosine graphs

max = 1

min = -1

repeats every = 360 degrees

0 degrees = 1

tangent

max = infinity

min = infinity

repeats every = 180 degrees

0 degrees = 0

equation for the sum of interior angles

(n-2)x180

n = number of sides

sine rule for finding sides

a/sinA = b/sinB = c/sinC

sine rule for finding angles

sinA/a = sinB/b = sinC/c

cosine rule for finding angle

cosA = b²+c²-a²/2bc

equation for Nth term

U_n=a+(n-1)d

n = term number

U_n = Nth term

a = first term

d = difference