𝐒𝐂𝐈𝐄𝐍𝐂𝐄 𝐒𝐏𝐄𝐂𝐓𝐑𝐔𝐌

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58. Area of Triangle:    • Area =  ½ × base × height 59. Area of Circle:    • Area =  πr² ▎Volume Formulas 60. Volume of Cube:    • Volume = side³ 61. Volume of Rectangular Prism:    • Volume = length × width × height 62. Volume of Cylinder:    • Volume = πr²h 63. Volume of Sphere:    • Volume =  4/3πr³ ▎Surface Area Formulas 64. Surface Area of Cube:    • Surface Area = 6 × side² 65. Surface Area of Rectangular Prism:    • Surface Area = 2(lw + lh + wh) 66. Surface Area of Sphere:    • Surface Area = 4πr² ▎Coordinate Geometry 67. Distance Between Two Points (Pythagorean Theorem):    • Distance = √((x₂-x₁)²+(y₂-y₁)²) ▎Basic Functions 68. Linear Function:    • Form: f(x) = mx + b 69. Quadratic Function:    • Form: f(x) = ax² + bx + c 70. Exponential Function:    • Form: f(x) = ab^x ▎More on Inequalities 71. Graphing Inequalities on Number Line 72. Compound Inequalities 73. Absolute Value Inequalities ▎Mathematical Induction 74. Base Case for Induction 75. Inductive Step for Induction ▎Factorization Techniques 76. Factoring Quadratics 77. Factoring by Grouping 78. Difference of Cubes ▎Miscellaneous Formulas 79. Euler's Formula for Complex Numbers 80. Pythagorean Identity in Trigonometry ▎Additional Concepts in Sets and Logic 81. De Morgan's Laws 82. Cartesian Product ▎Functions and Their Properties 83. Even Function Definition 84. Odd Function Definition 85. One-to-One Function Definition ▎Graphing Basics 86. X-Intercept and Y-Intercept 87. Slope-Intercept Form ▎Probability Rules 88. Addition Rule for Probability 89. Multiplication Rule for Probability ▎Combinatorics Basics 90. Permutations Formula 91. Combinations Formula ▎Limits in Calculus (Introductory) 92. Definition of Limit 93. Limit Properties ▎Basic Derivatives (Introductory) 94. Power Rule for Derivatives 95. Sum Rule for Derivatives ▎Basic Integration (Introductory) 96. Indefinite Integral Formula 97. Definite Integral Properties Join us for more Omo Academy: Your Pathway to Success! ✨ ╔═══════════╗ https://t.me/omo_academy ♨️ https://t.me/omo_academy ♨️ https://t.me/omo_academ♨️ ╚═══════════╝

IMPORTANT MATHEMATICS FORMULA FOR BEGINNERS ▎Number System 1. Natural Numbers (N):  N = {1, 2, 3, …} 2. Whole Numbers (W):  W = {0, 1, 2, 3, …} 3. Integers (Z):  Z = {…, -3, -2, -1, 0, 1, 2, 3, …} 4. Rational Numbers (Q):  Q = ({p/q ∣ p, q ∈ Z, q ≠ 0)} 5. Irrational Numbers: Numbers that cannot be expressed as a fraction (e.g.,  √(2), π ) 6. Real Numbers (R):  R = Q ∪ (irrational numbers) 7. Complex Numbers (C):  C = a + bi  where  a, b ∈ R  and  i = √(-1) ▎Sets 8. Union of Sets:  A ∪ B = {x | x ∈ A  or  x ∈ B} 9. Intersection of Sets:  A ∩ B = {x | x ∈ A  and  x ∈ B} 10. Difference of Sets:  A - B = {x | x ∈ A  and  x ∉ B} 11. Complement of a Set:  A' = U - A  where  U  is the universal set. 12. Subset:  A ⊆ B  means every element of  A  is in  B . 13. Proper Subset:  A ⊂ B  means  A  is a subset of  B  but not equal to  B . 14. Power Set: The set of all subsets of a set  A , denoted as  P(A) . 15. Cardinality of a Set: The number of elements in a set  A , denoted as  |A| . ▎Solutions of Equations 16. Linear Equation:  ax + b = 0  → Solution:  x = -b/a 17. Quadratic Equation:  ax² + bx + c = 0  → Solutions:    •  x = (-b + √(b² - 4ac))/2a    •  x = (-b - √(b² - 4ac))/2a 18. Sum of Roots of Quadratic Equation:  r₁ + r₂ = -b/a 19. Product of Roots of Quadratic Equation:  r₁ r₂ = c/a 20. Cubic Equation: General form is  ax³ + bx² + cx + d = 0 ▎Inequalities 21. Linear Inequality:  ax + b > 0  → Solution:  x > -b/a 22. Quadratic Inequality: Solve by finding roots and testing intervals. 23. Transitive Property: If  a < b < c, then  a < c. 24. Addition Property of Inequality: If  a < b, then  a + c < b + c. 25. Multiplication Property of Inequality (positive): If  a < b and  c > 0, then  ac < bc. ▎Additional Formulas 26. Absolute Value: ( |x| = x  x ≥ 0 -x  x < 0    ) 27. Distance Formula (between two points):    •  d = √((x₂ - x₁)² + (y₂ - y₁)²) 28. Midpoint Formula:    •  M = (( (x₁ + x₂)/2, (y₁ + y₂)/2 )) 29. Slope Formula:    •  m = (y₂ - y₁)/(x₂ - x₁) ▎Properties of Numbers 30. Commutative Property of Addition:  a + b = b + a 31. Associative Property of Addition:  (a + b) + c = a + (b + c) 32. Distributive Property:  a(b + c) = ab + ac ▎Basic Algebraic Identities 33. Square of a Sum:    •  (a + b)² = a² + 2ab + b² 34. Square of a Difference:    •  (a - b)² = a² - 2ab + b² 35. Difference of Squares:    •  a² - b² = (a + b)(a - b) ▎Exponents and Radicals 36. Product of Powers Rule:    •  aᵐ ⋅ aⁿ = aᵐ⁺ⁿ 37. Quotient of Powers Rule:    •  aᵐ / aⁿ = aᵐ⁻ⁿ 38. Power of a Power Rule:    •  (aᵐ)ⁿ = aᵐⁿ 39. Square Root Definition:    • If  x² = a, then  x = ±√(a) ▎Logarithmic Functions 40. Definition of Logarithm:    • If  bʸ = x, then  y = logᵦ(x) 41. Logarithm Product Rule:    •  logᵦ(xy) = logᵦ(x) + logᵦ(y) 42. Logarithm Quotient Rule:    •  logᵦ(x/y) = logᵦ(x) - logᵦ(y) 43. Logarithm Power Rule:    •  logᵦ(xᵏ) = k logᵦ(x) ▎Sequences and Series 44. Arithmetic Sequence Formula:    • General term:  aₙ = a₁ + (n-1)d 45. Sum of Arithmetic Series:    •  Sₙ = n/2(a₁ + aₙ) 46. Geometric Sequence Formula:    • General term:  aₙ = a₁ rⁿ⁻¹ 47. Sum of Geometric Series (finite):    •  Sₙ = a₁(1-rⁿ)/(1-r) (if  r ≠ 1) ▎Probability Basics 48. Probability of an Event:    •  P(E) = (Number of favorable outcomes)/(Total number of outcomes) ▎Basic Statistics 49. Mean (Average):    • Mean =  (∑ᵢ₌₁ⁿ xᵢ)/n 50. Median:    • Middle value when data is ordered. 51. Mode: • Most frequently occurring value in the data set. ▎Miscellaneous Concepts 52. Factorial Definition:    •  n! = n(n-1)(n-2)⋯(3)(2)(1), where  n > 0. 53. Binomial Theorem:    •  (a+b)ⁿ = ∑ₖ₌₀ⁿ n\choose k aⁿ⁻ᵏbᵏ ▎Basic Trigonometry 54. Sine Function:    • In right triangle,  sin(θ) = opposite/hypotenuse 55. Cosine Function:    • In right triangle,  cos(θ) = adjacent/hypotenuse 56. Tangent Function:    • In right triangle,  tan(θ) = opposite/adjacent ▎Geometry Basics 57. Area of Rectangle:    • Area = length × width

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NEWTON’S LAW OF GRAVITATION 𝑲𝒆𝒚 𝑰𝒅𝒆𝒂𝒔 ● 𝑨𝒏𝒚 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆 𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒗𝒆𝒓𝒔𝒆 𝒂𝒕𝒕𝒓𝒂𝒄𝒕𝒔 𝒂𝒏𝒚 𝒐𝒕𝒉𝒆𝒓 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆 𝒘𝒊𝒕𝒉 𝒂 𝒈𝒓𝒂𝒗𝒊𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒍 𝒇𝒐𝒓𝒄𝒆 𝒘𝒉𝒐𝒔𝒆 𝒎𝒂𝒈𝒏𝒊𝒕𝒖𝒅𝒆 𝒊𝒔 (𝑵𝒆𝒘𝒕𝒐𝒏’𝒔 𝒍𝒂𝒘 𝒐𝒇 𝒈𝒓𝒂𝒗𝒊𝒕𝒂𝒕𝒊𝒐𝒏), 𝒘𝒉𝒆𝒓𝒆 𝒎1 𝒂𝒏𝒅 𝒎2 𝒂𝒓𝒆 𝒕𝒉𝒆 𝒎𝒂𝒔𝒔𝒆𝒔 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆𝒔, 𝒓 𝒊𝒔 𝒕𝒉𝒆𝒊𝒓 𝒔𝒆𝒑𝒂𝒓𝒂𝒕𝒊𝒐𝒏, 𝒂𝒏𝒅 𝑮 (- 6.67 1011 𝑵𝒎2 /𝒌𝒈2 ) 𝒊𝒔 𝒕𝒉𝒆 𝒈𝒓𝒂𝒗𝒊𝒕𝒂- 𝒕𝒊𝒐𝒏𝒂𝒍 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕. 𝑭 - 𝑮 𝒎1𝒎2 𝒓2 ● 𝑻𝒉𝒆 𝒈𝒓𝒂𝒗𝒊𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒍 𝒇𝒐𝒓𝒄𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒆𝒙𝒕𝒆𝒏𝒅𝒆𝒅 𝒃𝒐𝒅𝒊𝒆𝒔 𝒊𝒔 𝒇𝒐𝒖𝒏𝒅 𝒃𝒚 𝒂𝒅𝒅𝒊𝒏𝒈 (𝒊𝒏𝒕𝒆𝒈𝒓𝒂𝒕𝒊𝒏𝒈) 𝒕𝒉𝒆 𝒊𝒏𝒅𝒊𝒗𝒊𝒅𝒖𝒂𝒍 𝒇𝒐𝒓𝒄𝒆𝒔 𝒐𝒏 𝒊𝒏𝒅𝒊𝒗𝒊𝒅𝒖𝒂𝒍 𝒑𝒂𝒓- 𝒕𝒊𝒄𝒍𝒆𝒔 𝒘𝒊𝒕𝒉𝒊𝒏 𝒕𝒉𝒆 𝒃𝒐𝒅𝒊𝒆𝒔. 𝑯𝒐𝒘𝒆𝒗𝒆𝒓, 𝒊𝒇 𝒆𝒊𝒕𝒉𝒆𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒃𝒐𝒅𝒊𝒆𝒔 𝒊𝒔 𝒂 𝒖𝒏𝒊𝒇𝒐𝒓𝒎 𝒔𝒑𝒉𝒆𝒓𝒊𝒄𝒂𝒍 𝒔𝒉𝒆𝒍𝒍 𝒐𝒓 𝒂 𝒔𝒑𝒉𝒆𝒓𝒊𝒄𝒂𝒍𝒍𝒚 𝒔𝒚𝒎𝒎𝒆𝒕𝒓𝒊𝒄 𝒔𝒐𝒍𝒊𝒅, 𝒕𝒉𝒆 𝒏𝒆𝒕 𝒈𝒓𝒂𝒗𝒊𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒍 𝒇𝒐𝒓𝒄𝒆 𝒊𝒕 𝒆𝒙𝒆𝒓𝒕𝒔 𝒐𝒏 𝒂𝒏 𝒆𝒙𝒕𝒆𝒓𝒏𝒂𝒍 𝒐𝒃𝒋𝒆𝒄𝒕 𝒎𝒂𝒚 𝒃𝒆 𝒄𝒐𝒎𝒑𝒖𝒕𝒆𝒅 𝒂𝒔 𝒊𝒇 𝒂𝒍𝒍 𝒕𝒉𝒆 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒉𝒆𝒍𝒍 𝒐𝒓 𝒃𝒐𝒅𝒚 𝒘𝒆𝒓𝒆 𝒍𝒐𝒄𝒂𝒕𝒆𝒅 𝒂𝒕 𝒊𝒕𝒔 𝒄𝒆𝒏𝒕𝒆𝒓. GRAVITATION NEAR EARTH’S SURFACE ● The gravitational acceleration ag of a particle (of mass m) is due solely to the gravitational force acting on it. When the particle is at distance r from the center of a uniform, spheri- cal body of mass M, the magnitude F of the gravitational force on the particle is given by Eq. 13-1. Thus, by Newton’s second law, F=mag, which gives . ● Because Earth’s mass is not distributed uniformly, because the planet is not perfectly spherical, and because it rotates,the actual free-fall acceleration of a particle near Earth differs slightly from the gravitational acceleration , and the particle’s weight (equal to mg) differs from the magnitude of the gravitational force on it.    Join us for more Omo Academy: Your Pathway to Success! ✨ ╔═══════════╗ https://t.me/omo_academy ♨️ https://t.me/omo_academy ♨️ https://t.me/omo_academ♨️ ╚═══════════╝

ፎርሙላን ወደ ጎን ለመፃፍ ስለማይመች ወደ ታች ነው የፃፍኩት።😔😔      ➡️ Neither of      ➡️ Either of      ➡️ Each of      ➡️ Every one of                +      Plural noun (subject)                +      Singular Verb. ያው እንደነገርኳችሁ ፎርሙላውን ወደ ጎን ለመፃፍ ስለማይመች ወደ ታች ነው የፃፍኩት ። እስኪ እናብራራው😁😁       #1⏭ Neither of Neither of  ካልን በሗላ የሚመጣው subject መሆን ያለበት plural subject ነው። ከ plural subject ቱ ቀጥሎ የሚመጣው verb ደግሞ singular Verb ነው።🤗🤗 በአጭሩ ከ Neither of ቀጥሎ plural subject እንጠቀማለን ፡ verb ቡ ግን 🙊 singular Verb ነው የሚሆነው።         🤔 Examples Neither of the students....... disturbing now. A) is       B) are ☹️😕 መልሱ ምንድን ነው የሚሆነው?? እንግዲህ ቅድም እንደነገርኳችሁ፡ ከ Neither of ቀጥሎ የሚመጣው plural subject ነው። ከ plural subject ቀጥሎ ደግሞ singular Verb ነው።😇 ስለዚህ በዚህ ጥያቄ መሰረት Neither of + the students ( plural subject) + is ( singular Verb ) ይሆናል። ስለዚህ መልሱ 🤗 Neither of the students is disturbing now. 😳😳🤣🤣 አይገርምም ግን The students ተብሎ is ን መጠቀም። ህግ ህግ ነው አለ ባሻ🥺🥺        #2⏭ Either of Either of ካልን በሗላ የሚመጣው plural subject ሲሆን ከ plural subject ቱ ቀጥሎ የሚመጣው verb ደግሞ singular Verb ነው። በ አጭሩ 🤗 ከ Either of በሗላ plural subject ን እንጠቀማለን፡ ከ plural subject ቱ በሗላ ደግሞ  singular Verb እንጠቀማለን።        😁😁Example Either of the workers....... to take the blame. A) has        B) have 😢😢 መልሱ??? ፈታ በሉ😁😁 ቅድም እንደነገርኳችሁ ከ Either of ቀጥሎ plural subject እንጠቀማለን ። ከ plural subject ቀጥሎ ደግሞ singular Verb እንጠቀማለን። ስለዚህ ፡ በዚህ ጥያቄ መሰረት ከ Either of ቀጥሎ ያለው the workers የሚለው plural subject ነው። ስለዚህ ከ plural subject ቱ ቀጥሎ የሚመጣው ደግሞ singular Verb ነው ። ስለዚህ መልሱ Has  ወይስ have ?? ተናገሩ እንጅ😂😂 በቃ እሱን ስትገረፍ ታወራዋለህ።😢 ከ has እና ከ have የቱ ነው singular Verb?😳 Has ነው እሺ። ስለዚህ መልሱ👇👇 🤗 Either of the workers has to take the blame. 😤😱 አይገርምም ግን?? The workers ተብሎ has ን ስንጠቀም። ህግ ህግ ነው🤓        #3⏭ Each of Each of ካልን በሗላ የሚመጣው plural subject ሲሆን ከ plural subject ቱ ቀጥሎ የሚመጣው verb ደግሞ singular Verb ይሆናል። በአጭሩ ከ Each of በሗላ plural subject ን እንጠቀማለን ፡ ከ plural subject ቱ በሗላ ደግሞ singular Verb እንጠቀማለን።          🤔😋 Example Each of the books ......... stolen yesterday. A) was        B) were 😊 Well እንግዲህ ከ Each of በሗላ the books የሚለውን plural subject ነው የመጣው። ከ the books( ከ plural subject) በሗላ የሚመጣው ደግሞ singular Verb ነው። ስለዚህ was ወይስ were ?? የቱ ነው singular Verb?? Was ነው ኣ ። ስለዚህ መልሱ 😺😺 Each of the books was stolen yesterday. 😥ጉድ እኮ ነው😂 the books ተብሎ was😔 ። ህግ ህግ ነው።        #4⏭ Every one of Every one of ካልን በሗላ የሚመጣው plural subject ሲሆን ከ plural subject ቱ ቀጥሎ ደግሞ የሚመጣው singular Verb ይሆናል።            🤔 Example Every one of the teachers ......... unhappy of his/her monthly salary.    A) is      B) are ከ Every one of በሗላ የመጣው the teachers የሚለው plural subject ነው። the teachers ከሚለው plural subject ቀጥሎ የሚመጣው verb ደግሞ singular Verb ነው። ስለዚህ መልሱ ፡ 😏😒 Every one of the teachers is unhappy of his/her monthly salary. "አይከብድም ወይ በልብ ያለን ሰው መርሳት" አለ ዘፋኙ😂😂 አይከብድም ወይ the teachers ተብሎ is ን መጠቀም።😔😁 ህግ ህግ ነው ብሏል ባሻ😡😡 ግን እዚጋ ማስተዋል ያለብን ነገር Every of አይባልም። በህግ ያስቀጣል 🙆‍♂😳‍ okay😒 Every one of ነው የሚባለው😊 የዛሬው ክላስ በዚህ ይብቃን😢          🙈 ማስታወሻ 🙊 ከላይ የተማርናቸው ህጎች በ British English ብቻ ነው የሚያገለግሉት። በ American English ሲሆን ደግሞ ሌላ ህግ አላቸው። ለ Entrance ጥያቄ ግን መልሳችን የሚሆነው በ British English ስለሆነ ከላይ ያለውን ኖት ተረዱት🤕🤕          🙄 ማስታወሻ 🙆 "None of" ደግሞ የራሱ የሆነ special case አለው። በቀጣይ እናየዋለን።                 𝕁𝕆𝕀ℕ 𝕌𝕊 for more Omo Academy: Your Pathway to Success! ✨ ╔═══════════╗ https://t.me/omo_academy ♨️ https://t.me/omo_academy ♨️ https://t.me/omo_academ♨️ ╚═══════════╝

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ሰላም ተማሪዎች፡ በኢትዮጵያ ካልኩረም መሠረት የወጡ topicችን more ለመረዳት በውጭ አጋዥ መጽሐፍ ማንበብ የምትፈልጉ የNatural science ተማሪዎች ቻነላችንን ሼር እያደረጋችሁ የsubscriber መጠን ከ200+ ስሆን መልቀቅ እንጀምራለን። በተጨማሪም ከ9-11 በቭድዮ መከታተል የምትፈልጉ tutorial ስለተዘጋጀ ለጓደኞቻችሁ (እያንዳንዱ ሰው ለ10 ሰው) ሼር አድርጋችሁ ሼር ያደረጋችሁትን screen shot በማድረግ ወደ @AMBESSA2024 በመላክ tutorial በነፃ ማግኘት የምትችሉ መሆኑን እንገልፃለን። ይሄኛው private class ስሆን በውስጡ 115+ videos 60+pdfs 50+photographs And ........ መልካም የጥናት ጊዜ ! Omo Academy: Your Pathway to Success! ✨ https://t.me/omo_academy ╔═══════════╗ https://t.me/omo_academy ♨️ https://t.me/omo_academy ♨️ https://t.me/omo_academ♨️ ╚═══════════╝

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