𝕖𝕕𝕦𝕔𝕒𝕥𝕚𝕠𝕟 ️️️𝕗𝕠𝕣 𝕒𝕝𝕝 📚

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ለትምህርት ማህበረሰቡ እና ለተማሪዎች በቀላሉ ትምህርታዊ መረጃዎችን ፣ መፅሃፎችን ፣ ትምህርታዊ ጥያቄዎች ፣ ትምህርታዊ አፕሊኪሽን እና ቻናሎችን ሁሉንም በቀላሉ እንዲያገኙ ታስቦ የተዘጋጀ ቻናል ነው:: ⒶⓀ 𝕖𝕕𝕦𝕔𝕒𝕥𝕚𝕠𝕟

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ESSLCE Mathematics Preparation Guide

2	+1 Mathematics Entrance Exam 2017 (ESSLCE) Question	347
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5	🔢 Math Practice & Solutions Here are the step-by-step solutions for the problems provided: Question 4 Data: 1, 3, 7, 9, 11, 13, 18, 28 Problem: What is the coefficient of mean deviation about the median? ✅ Solution: Find the Median: (9+11)/2 = 10 Calculate the absolute deviations from 10: 9, 7, 3, 1, 1, 3, 8, 18 Sum of deviations = 50 Mean deviation = 50/8 = 6.25 Coefficient of mean deviation = 6.25 / 10 = 0.625 The answer is: 5/8 (Option C) Question 5 Problem: Which of the following is an irrational number? ✅ Solution: A. 3.4000 (Rational - terminating decimal) B. √0.04 = 0.2 (Rational) C. 1.16222... (Rational - repeating decimal) D. √29 (Irrational - because 29 is not a perfect square) The answer is: Option D Question 6 Problem: Which trigonometric function represents the graph shown? ✅ Solution: By looking at the graph, when x=0, y=0; and when x=π/2, y=1. This is the characteristic behavior of the Sine function. sin(0) = 0 sin(π/2) = 1 The answer is: y = sin x (Option B)	542
6	No text...	462
7	25 AI tools you can’t Ignore in 2026: 1. http://Claude.ai – solves anything 2. http://Ranked.ai – rank higher on Google, ChatGPT, Claude, Etc! 3. http://Syllaby.io - create viral AI videos that you can monetize 4. http://Wisprflow.com - AI powered speech-to-text 5. http://Skysnail.io - create perfect YouTube thumbnails 6. http://GetViktor.com – AI employee in your Slack 7. http://Threadmaster.ai - create viral Facebook posts 8. http://Submagic.co – turn long videos into shorts 9. http://Hellowarrant.com – marketing compliance to not get fined 10. http://Gemini.google.com – best ai photo editor 11. http://Fastread.io - create ebooks & audiobooks 12. http://Bibley.io - ai for Bible study 13. http://Manus.im - the ultimate ai agent 14. http://Heygen.com – creates AI avatars 15. http://Webinarkit.com - ai for webinars 16. http://Creatorunlock.com - ai for YouTube 17. http://Getmakerai.com - build and sell software 18. http://Adcreative.ai - ai tool for advertising 19. http://Canva.com - design anything 20. http://Brandbutler.ai - create a perfect brand identity 21. http://Replit.com – the most powerful vibe code tool 22. http://Perplexity.ai - computer, is a powerful AI agent 23. http://V0.dev - create frontend mockups 24. http://suno.com - create ai music 25. http://Notion.AI – your second brain, upgraded with AI 🏏Join Us https://t.me/Aksipspg	1
8	## 1. Understanding Power Functions Question: 1 Which one of the following functions is NOT a power function? * A. f(x) = x^{-3/5} * B. f(x) = \sqrt{2}x^2 * C. f(x) = \pi x^5 * D. f(x) = (\sqrt{3})^x Explanation: A power function is defined as a function of the form f(x) = ax^n, where a and n are fixed real numbers (a is the coefficient, n is the exponent). In a power function, the variable (x) is the base, and the exponent is a constant. * In A, B, and C, the variable x is the base, and the exponent is a constant number. Therefore, they are power functions. * In D, f(x) = (\sqrt{3})^x, the variable x is in the exponent position, not the base. This is defined as an exponential function, not a power function. Correct Answer: D ## 2. Calculating the Derivative Question: Let f(x) = (1 - 2x)^{1/2}. What is the value of f'(x)? * A. \frac{1}{\sqrt{1-2x}} * B. -\frac{1}{2}\sqrt{1-2x} * C. \frac{1}{2}\sqrt{1-2x} * D. \frac{-1}{\sqrt{1-2x}} Explanation: To solve this, we use the Chain Rule. The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) \cdot h'(x). 1. Identify the outer function g(u) = u^{1/2} and the inner function u = (1 - 2x). 2. Take the derivative of the outer function: \frac{d}{du}(u^{1/2}) = \frac{1}{2}u^{-1/2} = \frac{1}{2\sqrt{u}}. 3. Take the derivative of the inner function: \frac{d}{dx}(1 - 2x) = -2. 4. Multiply them together: Correct Answer: D ## 3. Scalar vs. Vector Quantities Question: Which of the following statements describes the difference between scalar and vector quantities? * A. Physical quantities that only have direction are scalars, while that have only magnitude are vectors. * B. Physical quantities that only have magnitude are scalars, while that have both magnitude and direction are vectors. * C. Physical quantities that only have magnitude are vectors, while that have both magnitude and direction are scalars. * D. Physical quantities that only have direction are vectors, while that have both magnitude and direction are scalars. Explanation: To distinguish between these two fundamental physical quantities, remember these definitions: * Scalar Quantities: Have only magnitude (size or amount). Examples include mass, time, distance, and temperature. * Vector Quantities: Have both magnitude AND direction. Examples include displacement, velocity, force, and acceleration. Comparing this to the options, Option B correctly matches these definitions. Correct Answer: B የሚቀጥለው ክፍል እንዲለቀቅ 👍 Like እና Share በማድረግ ለጓደኞቻችሁ አጋሩ!	705
9	🎓 የ2017 ዓ.ም የኢንትራንስ ልምምድ (ጥያቄ 1 - 3) ከላይ ያሉት ጥያቄዎች መሰረት ራሳችሁን ለመፈተን ሞክሩ። መልሱን ለማየት ከመቸኮላችሁ በፊት በራሳችሁ ለመስራት ሞክሩ!	558
10	📚 የ10ኛ ክፍል (Grade 10 Mathematics) ማጠቃለያ — ክፍል 2 📚 #አብረን_እናስታውስ #MathsGrade10 🇪🇹 Unit 4: Trigonometric Functions • 🔹 Trigonometric Ratios: For a right-angled triangle: ▫️ sin(θ) = Opposite / Hypotenuse ▫️ cos(θ) = Adjacent / Hypotenuse ▫️ tan(θ) = Opposite / Adjacent • 🔹 The Unit Circle: A circle with a radius of 1 centered at the origin (0,0). For any point (x, y) on the unit circle: ▫️ x = cos(θ) ▫️ y = sin(θ) ▫️ x² + y² = 1 ➡️ ስለዚህ sin²(θ) + cos²(θ) = 1 (Fundamental Identity) • 🔹 Graphs of Sine and Cosine: Both functions are periodic with a period of 360° (or 2π radians). Their maximum value is 1, and minimum value is -1. 🇪🇹 Unit 5: Circles • 🔹 Chords and Arcs: A chord is a line segment connecting two points on a circle. Equal chords subtend equal angles at the center. • 🔹 Angles in a Circle: ▫️ Central Angle: An angle whose vertex is the center of the circle. ▫️ Inscribed Angle: An angle whose vertex is on the circle. The measure of a central angle is twice the measure of the inscribed angle that intercepts the same arc. • 🔹 Tangents and Secants: ▫️ A tangent touches the circle at exactly one point and is perpendicular to the radius at that point. ▫️ A secant is a line that intersects a circle at two points. 🇪🇹 Unit 6: Solid Figures 📌 Prisms and Cylinders: • 📐 Volume: V = A_b × h (Base Area × height) • 📐 Lateral Surface Area (LSA) of Cylinder: LSA = 2πrh 📌 Pyramids and Cones: • 📐 Volume: V = (1/3) × A_b × h • 📐 Volume of a Cone: V = (1/3)πr²h 📌 Spheres: • 📐 Volume: V = (4/3)πr³ • 📐 Surface Area: A = 4πr² 📌 Frustum of a Pyramid/Cone: A truncated solid figure formed by cutting off the top with a plane parallel to the base. 🇪🇹 Unit 7: Coordinate Geometry • 🔹 Distance Formula: The distance between two points P₁(x₁, y₁) and P₂(x₂, y₂) is: d = √[(x₂ - x₁)² + (y₂ - y₁)²] • 🔹 Midpoint Formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2) • 🔹 Slope (Gradient) of a Line (m): m = (y₂ - y₁) / (x₂ - x₁) • 🔹 Equation of a Line: ▫️ Slope-Intercept form: y = mx + c (where m is slope, c is y-intercept) ▫️ Point-Slope form: y - y₁ = m(x - x₁) 🇪🇹 Unit 8: Statistics and Probability 📌 Measures of Central Tendency (for Grouped Data): • 📊 Mean (x̄): ∑(f × x) / ∑f (where f is frequency and x is class mark). • 📊 Median & Mode: Found using specific formulas based on the median class and modal class intervals. 📌 Probability: • 🎲 Probability of an Event P(E): P(E) = Number of favorable outcomes / Total number of possible outcomes • 🎲 Range: 0 ≤ P(E) ≤ 1 (0 ማለት የማይሆን/Impossible፣ 1 ማለት ደግሞ እርግጠኛ/Certain). 🏁 የ10ኛ ክፍል ማቲማቲክስ ማጠቃለያ በዚህ ተጠናቋል። ይህ ማጠቃለያ ለፈተና ለሚዘጋጁ ተማሪዎች ጠቃሚ ስለሆነ 👍 Like እና Share በማድረግ ለሌሎችም አጋሩ!	718
11	አስረኛ ክፍል Mathematics ምን ያህል ታስታውሳላቹ ። #አብረን_እናስታውስ 🇪🇹Unit 1: Relations and Function • Relation: A relation is a set of ordered pairs, typically defined as a subset of the Cartesian product of two sets. • Domain: The set of all possible inputs (first elements) for a relation. • Range: The set of all possible outputs (second elements) for a relation. • Function: A special type of relation where each element in the domain is associated with exactly one element in the range. • Notation: A function is often denoted as f(x) , where x is the input variable. • One-to-One Function: A function where each element of the range is mapped by at most one element of the domain. • Onto Function: A function where every element in the range is mapped by at least one element of the domain. • Inverse Function: A function that reverses the mapping of the original function. If f(x) = y , then f⁻¹(y) = x . 🇪🇹 Unit 2: Polynomial Function • Polynomial Function: A function of the form f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ , where aₙ, aₙ₋₁, ..., a₀ are constants and n is a non-negative integer. 📬Operations on Polynomial Functions • Addition: Combining polynomials by adding their corresponding coefficients. • Subtraction: Combining polynomials by subtracting their corresponding coefficients. • Multiplication: Using the distributive property to multiply polynomials. • Division: Dividing polynomials using long division or synthetic division. 📭Theorem on Polynomial Functions • Remainder Theorem: If a polynomial f(x) is divided by x - c , the remainder is f(c) . • Factor Theorem: A polynomial f(x) has a factor x - c if and only if f(c) = 0 . 📭 Zeros of Polynomial Functions • Zero of a Polynomial: A value x = c such that f(c) = 0 . • Multiplicity: The number of times a particular zero occurs as a root. 📭 Graphs of Polynomial Functions • End Behavior: Describes how the graph behaves as x approaches positive or negative infinity. • Turning Points: Points where the graph changes direction, determined by the degree of the polynomial. 🇪🇹Unit 3: Exponential and Logarithmic Functions • Exponent: A number that indicates how many times to multiply a base by itself (e.g., aⁿ = a × a × ... × a (n times)). • Logarithm: The inverse operation to exponentiation, defined as logᵦ(a) = c if and only if bᶜ = a . 📬 The Exponential Functions and Their Graphs • Exponential Function: A function of the form f(x) = abˣ , where a ≠ 0 and b > 0 . • Graph Characteristics: Exponential functions grow rapidly; they have horizontal asymptotes. 📬 The Logarithmic Functions and Their Graphs • Logarithmic Function: A function of the form f(x) = logᵦ(x) , which is the inverse of the exponential function. • Graph Characteristics: Logarithmic functions increase slowly; they also have vertical asymptotes. 📬 Solving Exponential and Logarithmic Equations • Methods include using properties of exponents and logarithms, such as: – b^(logᵦ(x)) = x – logᵦ(xy) = logᵦ(x) + logᵦ(y) 📬 Relation between Exponential and Logarithmic Functions • The relationship is defined by the equations: – If y = bˣ , then x = logᵦ(y) . – They are inverses of each other, reflecting across the line y = x . ክፍል 2 ይቀጥላል ...	609
12	+1 የ6ኛ እና 8ኛ ክፍል ከተማ አቀፍ መልስ መስጫ ወረቀት አጠቃቀም መመሪያ ለተማሪዎች፣ ➊ የተማሪዎች መለያ ቁጥር እና የትምህርት ዓይነት መለያ ቁጥር ለእያንዳንዳቸው በተቀመጠው ሳጥን ውስጥ ከላይ ወደ ታች መፃፍ አለበት፡፡ ❷ በተፃፈው መለያ ቁጥር ፊት ለፊት የተፃፈውን ቁጥር የያዘውን ክብ ብቻ መጠቆር አለበት፡፡ ➌ ተማሪዎች የመረጡትን መልስ ትይዩ በተሰጠው ክብ ላይ በትክክል ማጥቆር አለባቸው፡፡ ❹ ተማሪዎች ያጠቆሩትን መልስ መቀየር ቢፈልጉ መጀመሪያ ያጠቆሩትን ክብ በደንብ ማጥፋት አለባቸው፡፡ ❺ በአንድ ረድፍ ከአንድ በላይ ክብ ማጥቆር የተከለከለ ነው፡፡ ❻ ለመፃፍ እና ለማጥቆር ከተፈቀደው ቦታ ውጭ ምንም አይነት ፅሁፍም ሆነ ጭረት ማድረግ የተከለከለ ነው፡፡ ❼ ለመፃፍ ከተፈቀደው ቦታ ውጭ ተፅፎ ወይም ትንሽ ጭረት እና ነጥብ ከተገኘ የመልስ መስጫ ወረቀቱ ሙሉ በሙሉ ተቀባይነት አይኖረውም፡፡ ❽ መልስ በሚጠቆርበት ጊዜ እርሳሱ ከተሰጠው የክብ ሳጥን መውጣት የለበትም። ከወጣም በማጥፊያ (Eraser/Rubber) ማጥፋት ይጠበቅባችኋል። ❾ መልስ መስጫ ኮርነር ላይ ያሉትን አራት ጠርዞች መንካትም ፈጽሞ የተከለከለ ነው፡፡ ➓ ተፈታኞች የመልስ መስጫ ወረቀታቸውን በንፅህና መያዝ አለባቸው ማለትም እንዳይቆሽሽ፣ እርጥበት እንዳይነካው፤ እንዳይቀደድ እና እንዳይታጠፍ መጠንቀቅና ሙሉ ኃላፊነት መውሰድ አለባቸው፡፡ ⓫ በእስክሪብቶ መፃፍ አይፈቀድም። ስለዚህ እርሳስ፣ ላጲስ እና መቅረጫ አይለያችሁ ⓬ ፈተና ጨረስኩ ብሎ አላስፈላጊ የሆነ ነገር፤ ስዕል ወይም ሌላ ከጀርባም ይሁን ከፊት አይፃፍበትም። ⓭ በጣም የተቀረፀ ሹል እርሳስ በምንጠቀም ወቅት ወረቀቱ እንዳይቀደድ መጠንቀቅ አለብን።	2 083
13	✨ አንድ ነገር አትርሱ! ጥያቄዎቹን መለሳችሁ ስታበቁ Submit የሚለውን ስትጫኑ ውጤታችሁን በቀጥታ ማየት ትችላላችሁ። በፈተናው ላይ የምትሰሯቸው ስህተቶች ወደ ትክክለኛው ስኬት የሚያደርሷችሁ መማሪያዎች ናቸውና በልበ ሙሉነት ሞክሩት። ታላቅ ውጤት እንደምታመጡ አንጠራጠርም፤ መልካም ዕድል ለሁላችሁም! 🚀 ✅ join 👇 https://t.me/Aksipspg	992
14	🚨 ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን የBiology የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLSeg7WoQNRqQIVSirebRknsopChgKfrz9TEmygSEOKJAjJQrjg/viewform?usp=header	844
15	ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን የEconomics የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLSfSgusaOEVe51if1h-PtGc55BVZcba4VOqUVEVjOqELTfUs4Q/viewform?usp=header	744
16	ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን History የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLSe7gww49YgkWp1R8DXdcauiFPqfwogv4i8gjdN5cNb3PBS7JQ/viewform?usp=header	667
17	ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን የChemistry የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLSdF_vP_dzQHQlMJq2SRq9j-XRgT2XkAhqCwsH27cYm3m3GHbw/viewform?usp=header	677
18	ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን የGeography የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLSe1DrAxldlxQ1aitK6sQkReBvMHdPG8_WvWaxk8AJ8pZweTNQ/viewform?usp=header	523
19	ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን የphysics የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLScIz2lossnsY5IEREFiDItLLyaXWI8meFXH1xmkQnPWUEJ-og/viewform?usp=header	578
20	ለ12ኛ ክፍል ተፈታኞች! በGoogle Form የተዘጋጁትን የAPTITUDE የፈተና ጥያቄዎች ሊንኩን በመንካት ገብታችሁ እንድትሞክሩ እንጋብዛለን። 👇👇👇 https://docs.google.com/forms/d/e/1FAIpQLSdPVG240JA7htRybQACHtiLboIJhrA2iLjvJ4C_xmt276UCXg/viewform?usp=header	539

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