𝕖𝕕𝕦𝕔𝕒𝕥𝕚𝕠𝕟 ️️️𝕗𝕠𝕣 𝕒𝕝𝕝 📚

📚 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!