pure november half term test

log_ab=c

a^c=b

cubic graph

quartic graph

y=1/x

y=-1/x

y=1/x²

y=-1/x²

y=2^x

y=lnx vs y=e^x

y=f(-x)

reflection in y-axis

y=-f(x)

reflection in x-axis

y=f(ax)

horizontal stretch by 1/a (BECOMES COMPRESSED INWARDS)

y=af(x)

vertical stretch by a (pulled taller)

y=f(x+a)

move graph a to the left (-a on x-axis)

y=f(x)+a

move graph up by a (+a on y-axis)

y=|f(x)|

reflect negative y-values in x-axis

y=f|x|

reflect the positive x side in y-axis

function types

one-to-one
many-to-one

for function to have an inverse

function must be one-to-one

composite function

fg(x)

self inverse function

f(x) = f^-1(x)
ff(x)=x
it is self-inverse if the curve has y=x as line of symmetry

sine rule

cosine rule

area of triangle rule

1/2absinC

degrees to radians conversion

π radians = 180°

arc length formula in radians

rθ

area of sector in radians

1/2r²θ

area of segment in radians

1/2r²(θ-sinθ)

finding all values of x for sinx=__

degrees: 180-ans

radians: π-ans (gives first pair, then go to next cycle by adding 2π as sin repeats every 2π)

finding all values of x for cosx=__

degrees: 360-ans

radians: 2π-ans (gives first pair, then go to next cycle by adding 2π as cos repeats every 2π)

finding all values of x for tanx=___

degrees: ans +- 180
radians: ans +- π (tan repeats every π not 2π)

sin²x+cos²x =

1

sinx/cosx=

tanx

cosecθ

cosecant

secθ

secant

cotθ

cotangent

y=cosecθ

y=secθ

y=cotθ

cotθ =

cosθ/sinθ

tan²θ+1=

sec²θ

1+cot²θ =

cosec²θ

sin(A+B) =

sinAcosB+sinBcosA

sin(A-B) =

sinAcosB-sinBcosA

cos(A+B) =

cosAcosB - sinAsinB

cos(A-B) =

cosAcosB + sinAsinB

tan(A+B) =

tan(A-B) =

sin2θ =

2sinθcosθ

cos2θ =

cos²θ - sin²θ
1-2sin²θ

2cos²θ-1

tan2θ =

arcsinx =

sin^-1x