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BIO 2017 G12 UNIT 2 SHORT NOTES by T.Marta_compressed.pdf
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ODA SBS BIO 2017 G12 UNIT 2 SHORT NOTES by T.Marta_compressed
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BIO 2017 G12 UNIT 2 WORKSHEET.pdf
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ODA SBS BIO 2017 G12 UNIT 2 WORKSHEET
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MATH WORKSHEET G12 UNIT 1&2 G11 UNIT 1&2.pdf
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ODA SBS MATH WORKSHEET G12 UNIT 1&2 G11 UNIT 1&2
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ENGLISH G12 2017 FIRST WORKSHEET.pdf
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ODA SBS ENGLISH G12 2017 FIRST WORKSHEET


🎯አንድ 12ኛ ክፍል ተፈታኝ ተማሪ የግድ ሊያውቃቸው የሚገቡ የማትስ ፎርሙላወች!!!


1. Pythagorean theorem: a² + b² = c²

2. Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

3. Distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)

4. Slope-intercept form of a line: y = mx + b

5. Point-slope form of a line: y - y₁ = m(x - x₁)

6. Midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)

7. Law of sines: a/sin A = b/sin B = c/sin C

8. Law of cosines: c² = a² + b² - 2ab cos C

9. Sum of angles in a triangle: A + B + C = 180°

10. Area of a triangle: A = (1/2)bh

11. Volume of a sphere: V = (4/3)πr³

12. Volume of a cylinder: V = πr²h

13. Volume of a cone: V = (1/3)πr²h

14. Surface area of a sphere: A = 4πr²

15. Surface area of a cylinder: A = 2πr² + 2πrh

16. Surface area of a cone: A = πr² + πrs, where s is the slant height

17. Binomial theorem: (a + b)ⁿ = Σ(n choose k)a^(n-k)b^k, where Σ is the sum from k=0 to n, and (n choose k) is the binomial coefficient

18. Fundamental theorem of calculus: ∫a^b f(x) dx = F(b) - F(a), where F is the antiderivative of f

19. Derivative of a constant: d/dx(c) = 0

20. Power rule for derivatives: d/dx(xⁿ) = nx^(n-1)

21. Product rule for derivatives: d/dx(fg) = f'g + fg'

22. Quotient rule for derivatives: d/dx(f/g) = (f'g - fg')/g²

23. Chain rule for derivatives: d/dx(f(g(x))) = f'(g(x))g'(x)

24. Mean value theorem: if f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that f'(c) = (f(b) - f(a))/(b-a)

25. Intermediate value theorem: if f is continuous on [a,b], then for any y between f(a) and f(b), there exists c in [a,b] such that f(c) = y

26. Rolle's theorem: if f is continuous on [a,b] and differentiable on (a,b), and if f(a) = f(b), then there exists c in (a,b) such that f'(c) = 0

27. Integration by substitution: ∫f(g(x))g'(x) dx = ∫f(u) du, where u = g(x)

28. Integration by parts: ∫u dv = uv - ∫v du

29. L'Hopital's rule: if lim(x → a) f(x)/g(x) = 0/0 or ∞/∞, then lim(x → a) f(x)/g(x) = lim(x → a) f'(x)/g'(x)

30. Taylor series: f(x) = Σ(n=0 to ∞) f^(n)(a)/n!(x-a)^n, where f^(n) is the nth derivative of f

31. Euler's formula: e^(ix) = cos(x) + i sin(x)

32. De Moivre's theorem: (cos x + i sin x)^n = cos(nx) + i sin(nx)

33. Fundamental trigonometric identities: sin² x + cos² x = 1, 1 + tan² x = sec² x, 1 + cot² x = csc² x

34. Double angle formulas: sin 2x = 2sin x cos x, cos 2x = cos² x - sin² x, tan 2x = (2tan x)/(1 - tan² x)

35. Half angle formulas: sin(x/2) = ±√((1 - cos x)/2), cos(x/2) = ±√((1 + cos x)/2), tan(x/2) = ±√((1 - cos x)/(1 + cos x))

36. Sum-to-product formulas: sin A + sin B = 2sin((A+B)/2)cos((A-B)/2), cos A + cos B = 2cos((A+B)/2)cos((A-B)/2), sin A - sin B = 2cos((A+B)/2)sin((A-B)/2), cos A - cos B = -2sin((A+B)/2)sin((A-B)/2)

37. Product-to-sum formulas: cos A cos B = (1/2)(cos(A-B) + cos(A+B)), sin A sin B = (1/2)(cos(A-B) - cos(A+B)), sin A cos B = (1/2)(sin(A+B) + sin(A-B)), cos A sin B = (1/2)(sin(A+B) - sin(A-B))

38. Hyperbolic functions: sinh x = (e^x - e^-x)/2, cosh x = (e^x + e^-x)/2, tanh x = sinh x/cosh x

39. Inverse trigonometric functions: arcsin x, arccos x, arctan x

40. Logarithmic identities: log(xy) = log x + log y, log(x/y) = log x - log y, log x^n = n log x

41. Exponential identities: e^x+y = e^x e^y, (e^x)^n = e^(nx), e^0 = 1

42. Binomial coefficients: (n choose k) = n!/(k!(n-k)!)


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. Wavelength for series of atomic spectrum)
💭w = 2pir/n (n is no. of loops in a circle)

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EUEE ENGLISH 2009-2015 WRITTING PART ONLY.pdf
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EUEE ENGLISH 2009-2015 WRITTING PART ONLY




ODA and IFA BOARDING ACADEMY

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🐱 Tip of the day


I Vs Me


⚡I የምንጠቀመው እንደ Subject ሲመጣ ነው (ድርጊት ፈፃሚዎቹ እኛ ስንሆን)

Eg:
✔️ My friend and I went to the narket.
❌ My friend and me went to the market.
እዚ ላይ I ነው መጠቀም ያለብን ምክንያቱም ድርጊት ፈፃሚዎቹ ጓደኛዬ እና እኔ ስለሆንን።

✔️ Sara and I are working on the project.
❌ Sara and me are working on the project.

⚡Me የምንጠቀመው እንደ Object ሲመጣ ነው (ድርጊት ተቀባዮቹ እኛ ስንሆን ነው።)

✔ She invited my friend and me to the to the party.
❌ She invited my friend and I to the party.
እዚ ላይ me ነው መጠቀም ያለብን ምክንያቱም ድርጊት ፈፃሚዋ (ጋባዧ) እሷ ስትሆን ተጋባዞቹ ጓደኛዬ እና እኔ ነን።

✔️ The gift was meant for my sister and me.
❌ The gift was meant for my sister and I.

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💠 Fluid Mechanics

Fluid mechanics: is an important branch of physics that deals with the study of fluids (both liquids and gases) and their behavior in various situations.
👉 here are some key concepts in Fluid Mechanics:

🔻 Pascal's Law: This law states that a change in pressure applied to an enclosed fluid is transmitted equally in all directions.
👉It helps explain how hydraulic systems work, where a small force can be amplified to produce a larger force.

🔻 Archimedes' Principle: This principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid.
👉It helps determine whether an object will sink or float in a fluid.

🔻 Bernoulli's Principle: According to this principle, as the speed of a fluid increases, its pressure decreases.
👉This principle is used to explain the lift generated by airplane wings and the flow of blood in arteries.

🔻 Viscosity: is a measure of a fluid's resistance to flow.
👉It depends on the internal friction between fluid layers.
👉High viscosity fluids have a thick consistency (e.g., honey), while low viscosity fluids flow easily (e.g., water).

🔻Reynolds Number: is a dimensionless quantity used to predict the flow pattern of a fluid (laminar, turbulent, or transitional).
👉It is calculated based on the fluid's velocity, density, viscosity, and characteristic length scale.

🔻 Fluid Pressure:
Pressure is the force applied per unit area.
In fluid mechanics, pressure is calculated using the relationship
P = F/A, where P is pressure,
F is force, and A is the area over which the force is distributed.

🔻 Fluid Flow: refers to the motion of fluids.
👉It can be described as steady or unsteady, laminar or turbulent, and viscous or non-viscous.
👉Understanding the different types of flow is crucial in various engineering applications.

       

                🎯🎯Our Aim🎯🎯

        To Empower Ethiopian Students

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🏖Biology common Terms for Grade 12 Entrance Examinations

1. Cell: The basic unit of life; the smallest structure capable of performing all life processes.

2. DNA (Deoxyribonucleic Acid): A molecule that carries genetic information in living organisms and is responsible for heredity.

3. Gene: A segment of DNA that contains the instructions for building a specific protein or function.

4. Chromosome: A thread-like structure made of DNA and proteins that contains genetic information; humans typically have 46 chromosomes.

5. Mitosis: A type of cell division that results in two genetically identical daughter cells, used for growth and repair.

6. Meiosis: A specialized form of cell division that reduces the chromosome number by half, producing gametes (sperm and eggs).

7. Protein: A macromolecule made up of amino acids, essential for structure, function, and regulation of the body’s tissues and organs.

8. Enzyme: A protein that acts as a catalyst to speed up chemical reactions in biological processes.

9. Photosynthesis: The process by which green plants and some other organisms convert light energy into chemical energy (glucose) using carbon dioxide and water.

10. Respiration: The biochemical process in which cells convert glucose and oxygen into energy, carbon dioxide, and water.

11. Homeostasis: The maintenance of a stable internal environment within an organism despite external changes.

12. Ecosystem: A community of living organisms interacting with one another and their physical environment.

13. Biodiversity: The variety of life in a particular habitat or ecosystem, including the number of species and genetic diversity.

14. Natural Selection: The process by which organisms better adapted to their environment tend to survive and produce more offspring.

15. Mutation: A change in the DNA sequence that can lead to variations in traits and may affect an organism's ability to survive.

16. Allele: Different forms of a gene that can exist at a specific locus on a chromosome.

17. Phenotype: The observable physical or biochemical characteristics of an organism, determined by its genotype and environment.

18. Genotype: The genetic constitution of an organism, representing the alleles inherited from its parents.

19. Autotroph: An organism that produces its own food from inorganic substances, typically through photosynthesis or chemosynthesis.

20. Heterotroph: An organism that cannot produce its food and must consume other organisms for energy.

21. Cell Membrane: A phospholipid bilayer that surrounds the cell, controlling the movement of substances in and out.

22. Nucleus: The membrane-bound organelle that contains the cell's genetic material (DNA) and controls cellular activities.

23. Cytoplasm: The gel-like substance within the cell membrane that contains organelles and is the site of many metabolic processes.

24. Organelle: Specialized structures within a cell that perform distinct functions (e.g., mitochondria, ribosomes).

25. Vesicle: A small membrane-bound sac within a cell that transports materials to different locations inside the cell.

26. Antibody: A protein produced by the immune system that recognizes and neutralizes foreign objects like bacteria and viruses.

27. Hormone: A chemical messenger produced by glands in the endocrine system that regulates physiological processes in the body.

28. Symbiosis: A close interaction between two different species, which can be mutualistic, commensalistic, or parasitic.

29. Population: A group of individuals of the same species living in a specific area at the same time.

30. Trophic Level: The position an organism occupies in a food chain, determined by its feeding relationships (e.g., producers, primary consumers).

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