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Other note source PDF Source 📐 Perimeter, Area and Volume Complete Guide for Grade 7 - Cambridge Curriculum 📏 Section 1: Perimeter and Area in Two Dimensions 1.1 Understanding Perimeter Perimeter is the total distance around the outside of a shape. To find the perimeter, add up the lengths of all sides. For any polygon: Perimeter = Sum of all sides Circle - Circumference The perimeter of a circle is called circumference . r d C = πd or C = 2πr where π ≈ 3.14 or 22/7 Example 1: Circle Circumference Find the circumference of a circle with radius 7 cm. Solution: C = 2πr C = 2 × 3.14 × 7 C = 43.96 cm 1.2 Understanding Area Area is the total space contained...

Other note source NUMERICAL SOLUTIONS OF EQUATIONS Concise Theory & Formula Guide Cambridge AS & A Level Mathematics 1. INTRODUCTION Numerical methods find approximate solutions to equations that cannot be solved algebraically. Examples include x³ + x - 4 = 0 , eˣ = 2x + 1 , and sin(x) = x - 1 . Historical Fact: Quintic equations (degree 5 and higher) generally have no algebraic solutions, making numerical methods essential. 2. LOCATING ROOTS (Section 6.1) Root Definition α is a root of f(x) = 0 if f(α) = 0 Method 1: Graphical Approach Rearrange equation as g(x) = h(x) , sketch both graphs, and find intersection points. Each intersection represents a root. Method 2: Change of Sign Method Change of Sign Principle: If f(x) is continuous and f(a) · f(b) If f(a) 0 → Root exists between a and b Example: Change of Sign Problem: Show f(x) = x⁵ + x - 1 = 0 has a root between 0 ...

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Algebra Guide: Equations, Factors & Formulae 📐 Algebra Essentials: Equations, Factors & Formulae Welcome! This guide covers fundamental algebra concepts: solving equations (finding unknowns), factorization (breaking expressions into factors), and rearranging formulae (changing the subject). These skills apply to real-world problems from cooking times to physics calculations. 1️⃣ Solving Equations Linear Equations A linear equation has variables with power ≤ 1 (e.g., 3x + 1 = 13 ). Golden Rule: Whatever you do to one side, do to the other side to keep it balanced. Method 1: Function Machine x → [×3] → 3x → [+1] → 3x+1 = 13 ↓ Work backwards ↓ 4 ← [÷3] ← 12 ← [-1] ← 13 Result: x = 4 Method 2: Algebraic Steps Solve: 3x + 1 = 13 Step 1: 3x + 1 - 1 = 13 - 1 → 3x = 12 Step 2: 3x ÷ 3 = 12 ÷ 3 → x = 4 Type 1: Variable on ...

Other note source 📐 INTEGRATION - Theory & Formulas Cambridge AS & A Level Mathematics - Pure Mathematics 2 1. Introduction to Integration Integration is the reverse process of differentiation . Symbol: ∫ f(x) dx means "integrate f(x) with respect to x" ⚠️ Always add + c for indefinite integrals (constant of integration) Example: • Differentiate x² → get 2x • Integrate 2x → get x² + c 2. Integration of Exponential Functions Basic Rules ∫ e x dx = e x + c ∫ e (ax+b) dx = (1/a) e (ax+b) + c Example 1: ∫ e (3x) dx a = 3, so answer = (1/3)e (3x) + c Example 2: ∫ 6e (3x) dx = 6 × (1/3)e (3x) + c = 2e (3x) + c Example 3: Evaluate ∫₀² e (3x) dx Step 1: Integrate: [(1/3)e (3x) ]₀² Step 2: Upper limit: (1/3)e⁶ Step 3: Lower limit: (1/3)e⁰ = 1/3 Answer: (1/3)(e⁶ - 1) 3. Integration of 1/(ax+b) Basic Rules ∫ (1/x) dx = ln|x| + c ∫ 1/(ax+b) dx = (1/a) ln|ax+b| + c ⚠️ Always use |x| (absolute value) b...

Differentiation - Cambridge AS & A Level Mathematics 📐 DIFFERENTIATION Cambridge AS & A Level Mathematics - Pure Mathematics 2 📚 Apa yang Akan Anda Pelajari: Mendiferensiasikan produk dan hasil bagi Menggunakan turunan dari e x , ln(x), sin(x), cos(x), tan(x) Mencari turunan dari fungsi implisit dan parametrik Menerapkan diferensiasi untuk menyelesaikan masalah nyata 4.1 ATURAN PRODUK (PRODUCT RULE) Apa itu Aturan Produk? Ketika kita perlu mendiferensiasikan fungsi yang dikalikan bersama , kita menggunakan Aturan Produk. Contoh: y = (x + 1)⁴ × (3x - 2)³ 📌 RUMUS ATURAN PRODUK Jika y = u × v, maka: dy/dx = u(dv/dx) + v(du/dx) 💡 Dalam Kata-kata: Fungsi pertama × turunan kedua + Fungsi kedua × turunan pertama y = u × v | _________|_________ | | | | u(dv/dx) v(du/dx) | | |_______TAMBAH______| ...

Quiz 1:   Fullscreen Mode Fractions, Percentages and Standard Form - Complete Guide 📐 FRACTIONS, PERCENTAGES AND STANDARD FORM 📊 Complete Theory and Formulas for Cambridge IGCSE Grade 9 Mathematics 1️⃣ EQUIVALENT FRACTIONS 📌 Definition Equivalent fractions are fractions that represent the same value but have different numerators and denominators. They are created by multiplying or dividing both the numerator and denominator by the same non-zero number. Key Formula: a b = a × k b × k where k is any non-zero number 1 2 = 2 4 = 3 6 = 4 8 🔍 Cross Multiplication Method To find a missing value in equivalent fractions, use cross multiplication: If a b = c d Then: a × d = b × c Example: Find x if 2 5 ...