PAT

Question 1

Period vs Freq

Answer 1

Period is the number of seconds per wave
Frequency is the number of waves per second

Question 2

Wave velocity, energy, angular velocity

Answer 2

λf = v
hv/λ = E

Question 3

0 Kelvin in C

Answer 3

To convert from C to Kelvin, add 273

To convert from Kelvin to C, subtract 273

Question 4

Inverse Square Law

Answer 4

Intensity (apparent brightness) = L / 4πr²

Question 5

Lenz’s Law Ratio

Answer 5

Vs/Vp = Ns/Np

The ratio of the voltage over the secondary coil and the voltage over the primary coil is equivalent to the ratio of the number of loops in the secondary and primary coils.

Question 6

sin cos tan approximations

Answer 6

x
1 - (x^2/2)
x

Question 6

Power

Answer 6

Fv = VI = V²/R = I²R = P

Question 7

Energy

Answer 7

mgh = 1/2mv^2 = 1/2 k(deltax)^2

Question 8

specific heat capacity

Answer 8

J = mCdeltaT

how much energy is needed to change 1kg of some material’s temperature by 1K

Question 9

capacitance

Answer 9

Q = cV

capacitors store energy, so current is lost when a capacitor is connected.
current is lost in
Rc = t

c = kA

Question 10

Kepler’s Laws

Answer 10

1st - orbits are ellipses
2nd - orbits sweep equal area at all times (approximate using squares)
3rd - T^2 = kr^3

Question 11

Simple harmonic motion

Answer 11

T = 2pi x sqrt(m/k)
w = vA

Question 12

xuvat

Answer 12

v = u + at

x = ut + at²/2
x = vt - at²/2

v² = u² + 2ax
x = (v-u)/(2) x t

Question 13

coeff of restitution

Answer 13

e = (v1-v2)/(u2-u1)

Question 14

waves between media

Answer 14

flipped
v1/v2 = n2/n1

notflipped
n1sin(thetac) = n2sin(thetar)

Question 15

mechanical advantage

Answer 15

count how many pulleys there are

ratio between the tensions (less force needed to produce more)

Question 16

coulomb’s and newton’s law

Answer 16

F = ke (abs(Q1Q2))/(r²)

F = G (M1M2)/(r²)

Question 17

point charge

Answer 17

point charge produces a force
F = qE

like charges have positive displacement and opposite

Question 18

water displacement

Answer 18

if an object is at rest on the surface: the same WEIGHT of water is displaced

if an object is submerged under the surface: the same VOLUME of water is displaced

Question 19

Derivation techniques

Answer 19

Chain Rule
y = f(g(x)) = f(u)

dy/dx = dy/du x du/dx

Product Rule
y = f(x)g(x) = uv

dy/dx = u(dv/dx) + v(du/dx)

Quotient Rule
y = f(x)/g(x) = u/v

dy/dx = (v(du/dx) - u(dv/dx))/v^2

Question 20

Integration techniques

Answer 20

Substitution
y = f(g(x)) x d(g(x))/dx = f(u) x du/dx

∫ydx = ∫f(u)du

By parts
y = f(x)g(x) = uv

u∫vdx - ∫(du/dx)x∫vdx dx

uxintegral - allintegralderivativexintegral

Question 21

Combinations & Permutations

Answer 21

n!/(n-r)! = permutations
order doesn’t matter

n! = permutations with repeats

n!/r!(n-r)! = combinations
order matters

Question 22

areas/volumes of ball, cone/pyramid, triangle, equilateral

Answer 22

4/3 pir^3
4pir^2

1/3 x pir^2h
pir^2 + pirl

1/2 absinx

xh/2
sqrt(3)/4 x^2

Question 23

trigonometric functions for all values

Answer 23

can be defined by rpi + n2pi (don’t forget there are two y for each x)

Question 24

Resistance/Temperature graphs

Answer 24

Wire
Linear with some intercept

Resistors/filament lamps
Concave quadratic with some intercept [starts horizontal]

Thermistors/LDRs
Concave quadratic approaching zero with some [high] intercept

Question 25

Current/Voltage graphs

Answer 25

Wire
Linear with no intercept

Resistors/filament lamps
Concave quadratic with no intercept [ends horizontal]

Diodes
Current only passes after threshold voltage is reached where shoots up with high gradient

Question 26

General formula for wavelength

Answer 26

y(x,t) = Acos((2pi/lambda)x+wt)

you can use partial derivatives to get max velocity and acceleration

Question 27

max velocity & acceleration in circular motion

Answer 27

v = wA
a = w^2 * A

Question 28

conditional probability

Answer 28

P(A|B) = P(AuB)/P(B)

for P(B), forget about any other conditions, just the probability of that even occuring and the P(AuB) is the probability of both events occuring at the same time.

Question 29

Graph transformations weird

Answer 29

for f(-x+a), the graph moves in the positive direction and otherwise

Question 30

Elastic motion

Answer 30

Ek is fully conserved when changing direction of motion, e=1

Question 31

Function ranges

Answer 31

always multiply by f(x)^2

if not remember that x-a can be -ive or +ive

if applicable, find limits, asymptotes, turning points

Question 32

Summation

Answer 32

Can be manipulated the same as integrals, lay out the start and end points clearly and !!substitute!!

Question 33

Circle arc and sector

Answer 33

theta r

(theta r^2)/2

Question 34

Total energy

Answer 34

ALWAYS equals U + Ek (unless dissapative forces not ignored)

Question 35

Coulomb’s Constant

Answer 35

1/(4pi permittivityconstant)

Question 36

-ive and +ive electrostatic potential energy

Answer 36

If electrostatic energy is negative, it means the system is bound and needs energy to be “broken”

If positive, the system repels.

Question 37

Projectile Trajectories

Answer 37

On level ground, the displacement of a projectile is maximised by a 45 degree angle.

Downhill, the displacement is maximised by <45 degree angle.

Uphill, the displacement is maximised by >45 degree angle.

Question 38

Equation governance

Answer 38

When substituting values into an equation for graphing, check which values will make the biggest difference to the result.

For products and sums, the greater number will always govern the result.

For quotients and differences, it depends on the position of the bigger number but you can figure it out.

Question 39

g

Answer 39

Unless the question specifies it’s on Earth, don’t use g=10ms^-2 DUMMY

Question 40

Half-life questions

Answer 40

ALWAYS start out with equating the number of atoms after the half life time passes in both forms (N(0)/2 and the expression)

Question 41

Mechanical Advantage

Answer 41

For pulleys, the “input” force < weight of the mass because of the multiple segments of the rope.

Same goes for distance, the “input” distance < distance one segment travels because the input distance is the sum of the segments.

Question 42

Gravitational Potential Energy

Answer 42

Use mgh when near the surface of a planet, use -GMm/r when far away.

It’s negative for the same reason as electrostatic potential, energy needs to be put in to break the system.

Question 43

Phase change at reflection

Answer 43

180 degrees

Question 44

Constructive and destructive conditions

Answer 44

Constructive: d = mλ

Destructive d = (2m-1)/2 * λ

Question 45

Q1 ≠ Q2

Answer 45

Q1 = nQ2

Question 46

Circuits

Answer 46

POWER is constant over both sides of a transformer

RESISTANCE is constant for a component (unless temp isn’t)

CURRENT is constant in series and splits in parallel in ratio equal to resistance

PD is constant in parallel and splits over components in ratio equal to resistance