advanced maths hsc final boss

loga(x) + loga(y)

loga(xy)

loga(x) - loga(y)

loga(x/y)

loga(x^y)

yloga(x)

loga(1)

0

log(0)

undefined

independent event

events are unaffected

dependent event

events are effected

dx sinx

cos(x)

dx cosx

-sin(x)

dx sin(ax)

acos(ax)

dx cos(x) + c

-sin(x)

f(x) = 0

x intercept

x = 0

y intercept

f'(x) = 0

stationary point

f''(x) = 0

possible point of inflection

f(-x), (-x, y)

reflection in y axis

-f(x), (x, -y)

reflection in x axis

-f(-x), (-x, -y)

reflection in the origin

f(x) + c

up c units

f(x) - c

down c units

f(x - b)

right b units

f(x + b)

left b units

f(kx)

dilated x by 1/k

f(x/k)

dilated x by k

kf(x)

dilated y by k

1/kf(x)

dilated y by 1/k

1/n (2(a+b) and add everything inbetween)

trapezoidal rule

a + d(n-1)

arithmetic term series

n/2(2a + d(n-1))

arithmetic sum series

n/2(a+l) -> (last)

arithmetic sum series

ar^(n-1)

geometric term series

a(1 - r^n)/1 - r

geometric sum series

a/1-r

limited sum series

value x frequency

e(x)

e(x)^2 - e(x^2)

var(x)

(var(x))^1/2

standard deviation

all x values

domain

all y values

range

fixed sum of money occuring on a period

annuity

regular contributions to a loan

write A(0-3)

dx lnx

1/x

sinx (oah)

o/h

cosx (oah)

a/h

tanx (oah)

o/a

sinx > 0

quad 1 and 2

sinx < 0

quad 3 and 4

cosx > 0

quad 1 and 4

cosx < 0

quad 2 and 3

tanx > 0

quad 1 and 3

tanx < 0

quad 2 and 4

area of a sector

0/360 (2pi*r)

product rule

vu'+uv'

quotient rule

vu'-uv'/v^2

integral f'(x)/f(x)

ln(f(x)) + c

P(A|B)

P(A and B)/P(B)

P(A and B)

P(A) x P(B)

P(A or B)

P(A) + P(B) - P(A and B)

difference of two squares (a^2 - b^2)

(a-b)(a+b)

area of triangle

1/2(ab)sinC

arc length

r0

semicircle radius

squared term

circle radius

x^2 + y^2 = r^2

point where two lines intersect (cost-benefit graph)

break-even point

a/sinA = b/sinB

sine rule

c^2 = a^2 + b^2 - 2abcosC

cosine rule

(ax + b)^n+1/a(n+1)

chain law integration

concave down (2nd derivative)

f''(x)<0

concave up (2nd derivative)

f''(x)>0

increasing dx

f(x)>0

decreasing dx

f(x)<0

rationalising surds (root(a) +b)

multiply by root(a) - b

point of inflection (different d^2x)

point of inflection

point of inflection (same d^2x)

horizontal point of inflection

loga(f(x)) dx

f'(x)/f(x)lna

integral of a to b

b - a

Δ>0

2 roots

Δ=0

1 root

Δ<0

0 roots

f(x+h)-f(x)/h

first principles

first term

a

common difference

d

common ratio

r

number of terms

n