rules 2.0

trig identities

discriminant

positive?

negative?

0?

b² - 4ac

positive - 2 solutions

negative - 0 solutions - no roots

0 - 1 solution

which one considers the order of the placement in probability
combination? permutation?

permutation = order is important

how to find y intercept + gradient from log graph

log rules

log_xa = b → X^b ₌ a

Binomial probability formula

how to calculate unit vector

how to calculate resultant force with vectors

convert degrees to radians

degree x (180/pi)

equation of line in 3d vector

how to calculate angle with 3D vector and the axis

graph transformation

length of arc with radians

L = radius x angle
angle = radian

area of sector with radians

A = ½ x radius² x angle

angle = radians

midpoint of 2 coordinates

second derivative

negative = maximum = n shape

positive = minimum = u shape

suvat equations

to find centre of circle with perpendicular bisector

estimate for small angles

n Choose r

binomial expansion - normal

binomial expansion - (1+x)ⁿ

e - differentiate, number

trig identities: double angle formulae

trig identities - cot, cosec, sec

acceleration on smooth slope

g(sinθ)

Fmax

Fmax = coefficient of friction x reaction force

harmonic form

partial fractions - normal

partial fractions - quadratic and linear

Method for products to multiples- complex numbers

First start with (z + 1/z)^n

Then binomial expansion

Group like terms together

Convert into trig terms using useful trick

Multiples to products method - complex numbers

(cos a + sin a) ^ n

Expand using binomial

If u want cos - use real parts

Sin - use imaginary

Then use trig formula to simplify into what is necessary

Work done by friction

The frictional force x s

Which is also the change in kinetic energy (if no gpe is involved)

Expected value in stats

Multiply the probability by the X value and add together

differentiate a^x

differentiate lnx

1/x

differentiate log_ax

differentiate arsin x

differentiate arcos x

differentiate arctan x

differentiate tan x

sec²x

differentiate cot x

-cosec²x

differentiate sec x

sec x . tanx

differentiate cosec x

cosec x . cotx

differentiate sin x

cos x

differentiate cos x

-sinx

quotient rule for differentiation

product rule

complex number - useful trick 1

• use this in de moivres theorem - in binomial expansion

complex number - useful trick 2

• use this for sum of series/infinity for complex numbers

• OR MULTIPLY THE DENOMINATOR BY CONJUGATE

complex number - useful trick 3

• use this and multiply with original root when finding nth roots of any complex number

Assume particle - ie car is a particle

• all weight acts from a single point at his centre of gravity

Assume uniform - ie plank is uniform

• weight acts from its midpoint

Assume rod - ie plank is a rod

• ignore its width

Assume light - string is light

• In tension pulley problems = tension is same throughout the system

• Otherwise - no weight is acting

Assume inextensible - ie string is inextensible

• acceleration of masses is the same

Assume smooth - ie pulley is smooth

• no frictional forces acting

Conservation of energy

loss of gpe = gain in ke

ke1 + Gpe1 = ke2 + gpe 2 + work done = when frictional forces are involved

When to use binomial distribution - why use?

• fixed number of trials

• two possible outcomes

• each trial has same probabilities

• the probabilities from trials are independent of each other

BE SPECIFIC TO CONTEXT OF Q

Calculate Var(X) - variance of random variable

Var(X) = E(X²) - (E(X))²

AUB

A or B

A∩B

A and B

A’

Not A

A’∩B

A’ overlap B - also only B

A’UB

A’ combine B

A∩B∩C

A’UB’ - how to convert

(A∩B)’

integrate (cos nθ)

1/n sin (nθ)

what is the dot product formula for vectors and what happens if the vectors are perpendicular (at right angle to each other)

when right angle - cos 90 = 0

• dot product is always zero

if the gradient of a line is a fraction eg - what to do to find f is decreasing, values for x

• make numerator equal zero

• solve for x