PAT Flashcards
solving quadratics
factorising
quadratic formula -b±√b²-4ac /2a
reciprocal graph
exponential/log graph
trig graphs
stationary points
different and set to 0 to find x
sub back into first equation
transformations of variables
solving inequalities
same as an equation
if *- then flip sign
basic trig
SOHCAHTOA
log rules
log(a) + log(b) = log(ab)
log(a) - log(b) = log(a/b)
log(a)^b = blog(a)
arithmetic progressions
eg add 4 to each term – common difference
= a + (n-1)d
arithmetic progression sum to n
Sn = n/2 (2a + (n-1)d)
n = number of terms, a = first term, d = common difference
geometric progression
eg 2*previous term – common ratio
= ar^(n-1)
geometric progression sum to n
Sn = a(1-rⁿ)/ 1-r if r<1
or a(rⁿ -1)/1-r if r > 1
geometric progression sum to ∞
S∞ = a/1-r if |r|<1
but if |r|>1 the series diverges (has an infinite sum)
binomial expansion
(a + b)ⁿ = aⁿ + (n,1) a^n-1 b … (n,r)a^n-r b^r + bⁿ
differentiation
ax^n –> nax^n-1
finds rate of change (gradient) - set to 0 for max/min
if 2nd diff >0 = min if <0 = max
integration
ax^n –> a/n+1 x^n+1
finds area under a curve
odd/even functions
velocity
rate of change of distance
acceleration
rate of change of velocity
vector
has magnitude and direction
scalar
has magnitude only
force distance graph
area under = work done
distance time graph
grad = velocity
velocity time graph
grad = acceleration
area under = distance
newtons I
– an object remains at rest or at constant velocity unless acted on by a resultant force
newtons II
the resultant force is ∝ to rate of change of momentum
newtons III
if an object A exerts a force on object B then object B exerts a force of equal magnitude and opposite direction of the same type on object A
weight vs mass
W – the measure of the gravitational force acting on a mass –
m – an objects resistance to change in motion or a measure of the amount of matter in an object
vector addition
add vectors to find the net force
circular motion
a centripetal force acts perpendicular to the direction of motion so causes acceleration but no change in velocity and no work done
friction
a force that resists motion when two surfaces meet
air resistance
the force resisting an objects motion through a fluid∝v²
terminal velocity
– when an objects at a constant speed free falling through a fluid – ball is released a=g, as v^ drag^ but mg>drag so Rf is less so acceleration is less but v still ^ so drag ^ until mg= drag
hookes law
within the elastic limit force applied is directly proportional to the extension produces – F = kx
elastic deformation
– returns to original shape –
plastic is permanently deformed