Golden Education

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 ...

Other Source Ringkasan Teori & Rumus Variabel Acak Kontinu 1. Definisi Variabel Acak Kontinu Variabel acak kontinu X dapat memiliki nilai apa pun dalam interval kontinu . Contoh: tinggi badan, waktu tunggu, suhu, laju peluruhan radioaktif. 2. Fungsi Kepadatan Peluang (PDF) Syarat PDF f(x) : 1. f(x) ≥ 0 untuk semua x 2. ∫ -∞ ∞ f(x) dx = 1 (total luas = 1) Grafik PDF f(x) x 3. Menghitung Peluang Karena P(X = a) = 0 , peluang hanya bisa dihitung untuk interval: P(a ≤ X ≤ b) = ∫ a b f(x) dx Untuk grafik sederhana bisa juga dengan geometri (luas segiempat, trapesium, segitiga). 4. Nilai Tengah (Median) Median m adalah nilai yang memenuhi: ∫ -∞ m f(x) dx = 0.5 Intuisi: letak vertikal yang membelah luas kurva menjadi dua bagian sama besar. 5. Persentil Umum Persentil- p (0 < p < 1) adalah q sedemikian hingga: ∫ -∞ q f(x) dx = p 6. Nilai Harapan (Mean) E(X) = μ = ∫ -∞ ∞ x f(x) dx 7. Varia...

Quiz 1: Fullscreen Mode Other Quiz Lines, Angles and Shapes - Theory and Formulas 3.1 Lines and Angles Types of Angles Angles can be classified based on their size: Type Size Example Acute angle Less than 90° 30°, 45°, 70° Right angle Exactly 90° Corner of a book Obtuse angle More than 90° but less than 180° 100°, 120°, 150° Reflex angle More than 180° but less than 360° 200°, 270°, 300° Special Pairs of Angles Complementary Angles: Two angles that add up to 90° . Supplementary Angles: Two angles that add up to 180° . Fundamental Angle Rules Angles on a Straight Line: The sum of angles on a straight line is 180° . ∑ ∠ on line = 180° Angles Around a Point: The sum of all angles around a single point is 360° . ∑ ...

Logarithmic & Exponential Functions All-in-One Theory Sheet 2.1 Logarithms to Base 10 Definition: If 10 x = y , then log 10 y = x (written log y for short). ┌-----┐ │ 10 │ │ ^ │ ← Exponent │ y │ └-----┘ log 1000 = 3 because 10³ = 1000 log 0.01 = –2 because 10 –2 = 0.01 2.2 Logarithms to Any Base a Definition: If a x = y with a > 0 and a ≠ 1 , then log a y = x . log₂ 32 = 5 because 2⁵ = 32 log₅ 1 = 0 because 5⁰ = 1 2.3 The Three Laws of Logarithms ┌-------┐ │ Laws │ └-------┘ Product: log a (xy) = log a x + log a y Quotient: log a (x / y) = log a x – log a y Power: log a (x n ) = n log a x 2.4 Solving Logarithmic Equations Golden Rule: Logs only exist for positive numbers. Use the laws to get a single log on each side. Drop the log...

Scientific Notation Quiz Scientific Notation By Mr Agus Salim Score: 0 / 100 Question 1 of 20 Convert the following number to scientific notation: 23500 Answer in format: a.bc × 10^n Enter each digit and exponent separately below: First digit (a): Second digit (b): Third digit (c): ...