Ethio Matrics

QUICK REVISION⏰
         FORMULAS

🎯1. Formulas related to force:
🗯F = ma
🗯F = kx
🗯F = m(vf² - vi²/2S)
🗯F = mv/t
🗯F = md/t²
🗯F = m(vf - vi)/t
🗯F = Area × density × velocity²
🗯F = 1/2 mv²/d
🗯F = 1/2 Pv/d
🗯F = Power/velocity
🗯Fc = mv²/r
🗯Fc = mrw²
🗯Fc/2 = mv²/2r
🗯Fc = 2K.E/r
🗯F = Area × Stress
🗯F = pir² × stress
🗯F = YA × Strain
🗯F = YAl/L
🗯F = pressure × area
🗯F = change in momentum × time interval
🗯F = - 2mVx × Vx/2l
🗯F2 = F1/A1 × A2
🗯F = qE
🗯F = kQ/r²
🗯F = ILB sintheta
🗯F = q (v × B)
🗯F = qE + q(v × B)

🎯2. Formulas related to energy and work
👉Fd = k.e
👉mgh = 1/2 mv²
👉E = 1/2 kx²
👉E = Ve
👉E = nhf
👉E = nhc/lambda
👉E = Pc
👉K.e = hf - work function = hf - hf° = hf - hc/w° (here w° is cutt off wavelength)
👉E = 1/2 Pv
👉mv²/2r= Fc/2
👉K.E/r = Fc/2
👉K.E = Fc×/r/2
👉K.e = 1.5 KT
👉E = VQ
👉E = Power × time
👉E = Fvt
👉% loss in K.e = v1² - v2²/v1² × 100
👉% loss in P.e = h1² - h²/h1² × 100
👉Energy lost due to air friction(Fh) = 1/2mv² - mgh (when body is thrown upward)
👉Energy lost due to air friction(FS) = mgh - 1/2mv² (when body is thrown downward)
👉E = 1/2 CV² (capacitor)
👉E = R × hc (R is Rydberg' constant)
J = m-¹ × Js ms-¹
👉hf kalpha x rays = EL - Ek
hf kbeta x rays = EM - Ek
👉Binding energy = mass defect × c²
👉W = Fd Costheta
👉W = nmgh (when person is climbing stairs)
👉W = n(m+m) gh (when person is climbing stairs with some load)
👉W = 0mgh + 1mgh + 2mgh + 3mgh ....... (in case of stacking bricks. For ist brick h=0. For 2nd brick h=1. For 3rd brick h=2 and so on)
👉W = Fd = PA × change in V
👉W = Q - change in U
👉Q = mc × change in T
T/273.16 = Q/Q3 (Thermodynamic scale)
👉W = I²Rt
👉W = emf×charge
👉W = VQ
👉W = 1/2 lF
👉W = YAl²/2L
👉W = StressAl²/2Strain
👉W = PressureAl²/2Strain
👉W = Fl²/2Strain

🎯3. Formulas related to Power
💥P = Fv
💥P = E/t
💥P = n(mgh/t)
💥P = Fd/t
💥P = mv²/2t

🎯4. Formulas related to distance, displacement, velocity and accelration
📝d = vt
📝d = at²
📝d = (vf + vi/2) ×t
📝d = 5t² (for distance in 'n' seconds)
📝d = 5(2tn - 1) (for distance in 'nth' second)
📝d = 1/2 mv²/F
📝d = vit + 5t²
📝d = v × underroot 2H/g
📝d = vt = x°wt = x°2pi/T × t = x°2pift
📝x = x° Sin wt
📝x = x° Sin (underroot k/m) t
vf = vi + at
📝2as = vf² - vi²
📝2as = (vi + at)² - vi²
📝2as = vf² - (vf - at) ²
📝v = underroot Vfx² + Vfy²
📝v = Power/Force
📝v = 2×K.E/momentum (k.e = 1/2 Pv)
📝v² = 2×Power×time/mass (P = mv²/2t)
v = underroot 2as
v = underroot gr (speed at highest point in a verticle circle)
v = underroot 5gr (speed at lowest point in a verticle circle)
📝v² = 2FS/m
📝v² = 2E/m
📝v² = 2Ve/m
📝v = eBr/m (velocity of particle under action of magnetic force along circular path)
📝v² = Force/Area.Density
📝v = w underroot x°² - x²
📝v = underroot k/m × underroot x°² - x²
📝v = x°w (at mean position where x=0)
📝v = x° underoot k/m
📝v = v° underroot 1 - x²/x°² (for determining ratio b/w inst. Velocity and maxi. Velocity)
📝v= x°2pif = x°2pi/T
📝a = x°w² = x°w.w = vw = v.2pif
Common velocity = m1v1/m1+m2
📝vi² = Rg/Sin2theta
📝v = underoot Tension×length/mass
📝V = 2pi ke²/nh (speed of e- in nth orbit)
📝Vn = V/n
📝v = nh/2pimr (lambda = 2pir and lambda=h/p)
📝ma = kx
📝a = kx/m (SHM)
📝a = - gx/l (Simple pendulum)
📝ac = v²/r

🎯5. Formulas related to wavelength 'w'
💭w = v/f
💭w = 1/wave number
💭w1 = 2l (when pipe is opened at both ends)
💭w1 = 4l (when pipe is opened at one end)
💭Delta w = Us/f (doppler shift)
Wavelength for obs. = w - delta w = v/f - Us/f
💭w = hc/Ve
💭w = hc/E
💭w = h/mv
💭w = h/P as P = underroot 2mE so
💭w = h/underroot 2mE (de Broglie wavelength)
💭w = underroot 150/V A° (short method for de Broglie wavelength. This formula is applicable only for e-)
💭1/w = RH (1/p²-1/n²)
💭Wmaxi/Wmini = n²/n²-p² (for determining ratio b/w maxi. Wavelength to mini. Wave length for series of atomic spectrum)
💭w = 2pir/n (n is no. of loops in a circle)

@Ethiomatrichub

📌 Math Grade 12 

Multiple Choice Questions Collected from Unit 1

1) Which of the following best describes a sequence? 
A) A group of numbers arranged in a specific order 
B) A set of random numbers 
C) Numbers that are not related to each other 
D) A sequence is not a mathematical concept 

Answer: A 
Explanation: A sequence is a list of numbers arranged in a specific order, where each number is related to the others by a defined rule.

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2) What is the common difference in the arithmetic sequence: 3, 7, 11, 15, ...? 
A) 2 
B) 3 
C) 4 
D) 5 

Answer: A 
Explanation: The common difference is found by subtracting any term from the next term (7 - 3 = 4).

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3) In a geometric sequence, if the first term is 2 and the common ratio is 3, what is the second term? 
A) 6 
B) 8 
C) 9 
D) 11 

Answer: A 
Explanation: The second term is found by multiplying the first term by the common ratio (2 × 3 = 6).

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4) What does the sigma notation represent in mathematics? 
A) The sum of a sequence 
B) The product of a sequence 
C) The average of a sequence 
D) The difference of a sequence 

Answer: A 
Explanation: Sigma notation (Σ) is used to denote the sum of a sequence of numbers.

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5) What is the sum of the first 5 terms of the arithmetic sequence: 2, 5, 8, 11, ...? 
A) 30 
B) 33 
C) 35 
D) 40 

Answer: B 
Explanation: The first five terms are 2, 5, 8, 11, and 14. Their sum is 2 + 5 + 8 + 11 + 14 = 40.

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6) Which type of series does not have a finite sum? 
A) Arithmetic series 
B) Geometric series 
C) Infinite series 
D) Convergent series 

Answer: C 
Explanation: Infinite series can continue indefinitely and may not converge to a finite sum.

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7) An arithmetic progression has a first term of 4 and a common difference of 3. What is the 10th term? 
A) 31 
B) 30 
C) 34 
D) 33 

Answer: A 
Explanation: The formula for the nth term is aₙ = a₁ + (n - 1)d. Thus, a₁₀ = 4 + (10 - 1) ⋅ 3 = 31.

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8) In a geometric sequence, if the first term is 5 and the common ratio is 2, what is the fourth term? 
A) 10 
B) 15 
C) 20 
D) 25 

Answer: C 
Explanation: The fourth term can be calculated as a₄ = a₁ ⋅ rⁿ⁻¹ = 5 ⋅ 2³ = 40.

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9) What is the formula to find the nth term of an arithmetic sequence? 
A) aₙ = a₁ + (n - 1)d 
B) aₙ = a₁ × rⁿ⁻¹ 
C) aₙ = a₁ + rd 
D) aₙ = a₁ ÷ rⁿ⁻¹ 

Answer: A 
Explanation: The formula for finding the nth term in an arithmetic sequence is aₙ = a₁ + (n - 1)d.

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10) Which of the following is an example of an arithmetic sequence? 
A) 2, 4, 8, 16, ... 
B) 3, 6, 9, 12, 15 ... 
C) 1, 3, 9, 27, ... 
D) 5, 10, 20, 40, ... 

Answer: B 

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