PAT Flashcards

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1
Q

solving quadratics

A

factorising
quadratic formula -b±√b²-4ac /2a

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2
Q

reciprocal graph

A
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3
Q

exponential/log graph

A
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4
Q

trig graphs

A
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5
Q

stationary points

A

different and set to 0 to find x
sub back into first equation

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6
Q

transformations of variables

A
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7
Q

solving inequalities

A

same as an equation
if *- then flip sign

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8
Q

basic trig

A

SOHCAHTOA

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9
Q

log rules

A

log(a) + log(b) = log(ab)
log(a) - log(b) = log(a/b)
log(a)^b = blog(a)

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10
Q

arithmetic progressions

A

eg add 4 to each term – common difference
= a + (n-1)d

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11
Q

arithmetic progression sum to n

A

Sn = n/2 (2a + (n-1)d)
n = number of terms, a = first term, d = common difference

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12
Q

geometric progression

A

eg 2*previous term – common ratio
= ar^(n-1)

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13
Q

geometric progression sum to n

A

Sn = a(1-rⁿ)/ 1-r if r<1
or a(rⁿ -1)/1-r if r > 1

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14
Q

geometric progression sum to ∞

A

S∞ = a/1-r if |r|<1
but if |r|>1 the series diverges (has an infinite sum)

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15
Q

binomial expansion

A

(a + b)ⁿ = aⁿ + (n,1) a^n-1 b … (n,r)a^n-r b^r + bⁿ

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16
Q

differentiation

A

ax^n –> nax^n-1
finds rate of change (gradient) - set to 0 for max/min
if 2nd diff >0 = min if <0 = max

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17
Q

integration

A

ax^n –> a/n+1 x^n+1
finds area under a curve

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18
Q

odd/even functions

A
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19
Q

velocity

A

rate of change of distance

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20
Q

acceleration

A

rate of change of velocity

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21
Q

vector

A

has magnitude and direction

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22
Q

scalar

A

has magnitude only

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23
Q

force distance graph

A

area under = work done

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24
Q

distance time graph

A

grad = velocity

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25
Q

velocity time graph

A

grad = acceleration
area under = distance

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26
Q

newtons I

A

– an object remains at rest or at constant velocity unless acted on by a resultant force

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27
Q

newtons II

A

the resultant force is ∝ to rate of change of momentum

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28
Q

newtons III

A

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

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29
Q

weight vs mass

A

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

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30
Q

vector addition

A

add vectors to find the net force

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31
Q

circular motion

A

a centripetal force acts perpendicular to the direction of motion so causes acceleration but no change in velocity and no work done

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32
Q

friction

A

a force that resists motion when two surfaces meet

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33
Q

air resistance

A

the force resisting an objects motion through a fluid∝v²

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34
Q

terminal velocity

A

– 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

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35
Q

hookes law

A

within the elastic limit force applied is directly proportional to the extension produces – F = kx

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36
Q

elastic deformation

A

– returns to original shape –
plastic is permanently deformed

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37
Q

Fx graph

A

area under graph = work/ elastic PE

38
Q

law of conservation of momentum

A

total momentum remains constant unless an external force is applied

39
Q

law of conservation of energy

A

total energy in a system is constant

40
Q

mechanical wave

A

energy is transferred by vibration of particles carrying the wave through a medium

41
Q

longitudinal wave

A

– oscillate parallel to direction of energy transfer

42
Q

transverse wave

A

– oscillate perp to direction of energy transfer

43
Q

amplitude

A
  • max displacement from undisturbed position
    sound = loudness
    light = brightness
44
Q

frequency

A

number of complete oscillations / time
sound = pitch
light = colour

45
Q

T

A

time for one complete oscillation
1/f

46
Q

λ

A

distance between two adjacent points on the same cycle of a wave

47
Q

EM waves

A

radio, micro, IR, visible, UV, Xrays, gamma

48
Q

EM waves λ

A

radio >10cm (10^-1)
micro -10cm-1mm (10^-1 - 10^-3)
IR -1mm - 1μm (10^-3 - 10^-6)
visible - 400-700nm (10^-7)
UV - 10nm (10^-8)
X - 1nm - 0.01nm (10-9 - 10^-11)
gamma <10^-11

49
Q

EM waves freq

A

radio <10^11
micro - 10^11 - 10^13
IR - 10^13 - 10^14
visible - 10^14
UV - 10^15 - 10^17
X - 10^17-10^20
gamma >10^20

50
Q

all EM waves

A

transverse
speed of light in a vacuum
reflect, refract, diffract

51
Q

law of reflection

A

i = r

52
Q

refractive index

A

ratio of the speed of light in a vacuum to the speed of light in a material

53
Q

n (glass)

A

1.52

54
Q

snells law

A

n1sinθ1 = n2sinθ2

55
Q

TIR

A

if i>C
and light is going from more dense to less

56
Q

interference

A

superposition of coherent waves
– constructive = in phase causes reinforcement (antinode)
– destructive = antiphase causes cancellation (node)

57
Q

diffraction

A

waves bending when going through a gap
– bigger aperture = less diffraction
– max is when gap = λ

58
Q

standing waves

A

– two wave in opposite direction with same f, v and amp are superposed
– distance between nodes is λ/2
– on a string L=nλ/2 where n is no. antinodes

59
Q

transformer

A

– steps up/down an ac voltage using electromagnetic induction
– ac through a coil creates changing field in the iron core which induces an ac of the same freq in the second coil

60
Q

step up transformer

A
  • means voltage is increased – second coil has greater voltage by having more turns Vp/Vs = Np/Ns – opposite with step down – when V ^ I decreases as P = IV and power remains constant (if 100% efficient)
61
Q

use of transformers

A

step up - transmit at low I to reduce energy losses
atep down - reduce voltage to safe household use levels

62
Q

transformer efficiency

A

= IsVs/IpVp

63
Q

V, I and R in series /parallel

A

I - same in series, splits in parallel
V - splits in series, same in parallel
R - adds in series 1/Rt = 1/R1 + 1/R2 in parallel

64
Q

photoelectric effect

A

photoelectrons are emitted if they are given sufficient energy to overcome the work function of the material

65
Q

capacitor

A

an electrical component that stores charge on 2 separated metallic plates with an insulator between to prevent charge travelling across

66
Q

capitance

A

charge stored per unit pd – C = Q/V (measured in Farads)
series 1/Ct = 1/C1 +1/C2
parallel Ct = C1 + C2

67
Q

capitance eq

A

C = Q/V

68
Q

capacitor connected to dc

A

there’s a current as the power supply draws electrons from one plate and deposits on the other
– leaving them with +Q and -Q charge - these are equal and opposite due to the conservation of charge
– current flows until pd between plates = emf

69
Q

storing energy in a capacitor

A

work is done to put electrons to the negative plate or remove them from the positive plate
– as the charge stored increases the voltage increases
– work done is the area under the VQ graph – W = ½ QV = ½ V^2C = ½ Q^2/C

70
Q

discharging capacitor

A
  • by disconnecting the power supply and connecting it to another component
    – electrons are no longer held by emf so repel and flow dissipating electrical energy as heat
    – once the plates have equilibrated V = 0 as Q = 0 so current stops flowing
    – the time taken is related to the charge and the resistance of the discharging circuit C = Q/V ∝Q/I which goes as t
71
Q

ions

A

charged atom

72
Q

isotopes

A

same no protons diff no neutrons

73
Q

atomic number

A

– no protons in an atom

74
Q

alpha

A
75
Q

beta

A
76
Q

gamma

A
77
Q

bohr model

A

+ nucleus surrounded by revolving – electrons in fixed orbits

78
Q

planets

A

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune
– orbit a star

79
Q

moons

A

– orbit a planet

80
Q

comets

A

– orbits a star elliptical orbit

81
Q

asteroids

A

orbits a star in elliptical orbits – made of metals or rock

82
Q

phases of moon

A
83
Q

eclipse

A

when celestial bodies are aligned

84
Q

centripetal acceleration

A

acceleration by an object moving in a circular path (towards the centre of the object) changes direction not speed

85
Q

gravitational centripetal force

A

net force that acts perp to velocity towards the centre of a circular orbit

86
Q

geostationary orbit

A

satellites orbital period = earths rotation period (24h) – 35,800 km above the equator

87
Q

polar orbits

A

– satelites travel as low as 200km above sea level very close to the Earth at high speeds – follows Earths meridian lines – tends to have a period of 12h

88
Q

flux density

A
89
Q

images

A
90
Q

angular size

A
91
Q

mechanical advantage

A
92
Q

upthrust

A