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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...

Other note source Quiz 1:   Fullscreen Mode ⚡ ELECTROMAGNETIC EFFECTS ⚡ 📖 Section 18.1: Electromagnetic Induction Definition Electromagnetic Induction is the process by which an induced electromotive force (e.m.f.) is produced in a conductor due to a changing magnetic field. Faraday's Discovery (1831) Michael Faraday discovered that a changing magnetic field produces an induced current in a conductor. This was the opposite of what was already known - that current produces a magnetic field. Faraday's Experiment Faraday's Electromagnetic Induction Experiment N S Coil G Bar Magnet Solenoid Galvanometer Observations from Faraday's Experiment Action Galvanometer Reading Magnet moves INTO coil Needle deflects in ONE direction ...

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 ...