Konsep Dasar dan Operasi Aljabar Panduan Lengkap untuk Pemahaman Aljabar 1. Pengertian dan Komponen Aljabar Komponen Utama Aljabar: Variabel (x, y, z) Koefisien (angka di depan variabel) Konstanta (angka tanpa variabel) Suku (term) Contoh Bentuk Aljabar: 3x² + 4x - 5 3x² 4x -5 2. Operasi Dasar Aljabar a. Penjumlahan dan Pengurangan Aturan Dasar: Hanya suku sejenis yang dapat dijumlahkan/dikurangkan Perhatikan tanda positif dan negatif Contoh: (5x² + 3x - 2) + (2x² - 4x + 1) = 7x² - x - 1 b. Perkalian Aljabar Rumus-rumus Penting: (a + b)² = a² + 2ab + b² (a - b)² = a² - 2ab + b² (a + b)(a - b) = a² - b² Visualisasi (a + b)² a² ab ab b² 3. Pemfaktoran Metode Pemfaktoran: Faktor Persekutuan Terbesar (FPB) 6x² + 12x = 6x(x + 2) Selisih Kuadrat x² - 25 = (x + 5)(x - 5) Kua...

Comprehensive Trigonometry Guide for A/AS Level Pure Mathematics Trigonometry, a crucial branch of mathematics, explores the relationships between triangle sides and angles. This guide covers essential concepts, formulas, and applications for A/AS level students. 1. Fundamental Trigonometric Ratios In a right-angled triangle with angle θ, the primary trigonometric ratios are defined as: Sine: sin θ = opposite / hypotenuse = y / r Cosine: cos θ = adjacent / hypotenuse = x / r Tangent: tan θ = opposite / adjacent = y / x 2. Critical Trigonometric Identities Key identities include: Tangent identity: tan θ = sin θ / cos θ (when cos θ ≠ 0) Pythagorean identity: sin²θ + cos²θ = 1 3. Precise Trigonometric Function Values Angle θ sin θ cos θ tan θ 30° = π/6 1/2 √3/2 1/√3 45° = π/4 1/√2 1/√2 1 60° = π/3 √3/2 1/2 √3 4. Understanding Positive and Negative Angles Positive angles are measured counterclockwise from the positive x-axis, while negative angles are me...

Surface Area, Volume, and Capacity: Comprehensive Guide 1. Surface Area Surface area is the total area of all faces or surfaces of a three-dimensional object. Common Shapes and Their Surface Area Formulas: Cube Surface Area = 6s², where s = length of side Rectangular Prism Surface Area = 2(lw + lh + wh), where: l = length w = width h = height Sphere Surface Area = 4πr², where r = radius Cylinder Surface Area = 2πr² + 2πrh, where: r = radius of base h = height 2. Volume Volume is the amount of three-dimensional space enclosed by a closed surface. Cube Volume = s³, where s = length of side Rectangular Prism Volume = l × w × h Sphere Volume = (4/3)πr³ Cylinder Volume = πr²h 3. Capacity Capacity refers to the maximum amount that something can contain, usually measured in units of volume. Common Conversions: 1 m³ = 1000 liters 1 liter = 1000 ml 1 cm³ = 1 ml 4. Practical Applica...

Mechanical Energy Problems An object with a mass of 5 kg is at a height of 10 meters above the ground. Given that the acceleration due to gravity is g = 10 m/s², determine the mechanical energy of the object. A ball with a mass of 2 kg falls freely from a height of 30 meters. If g = 10 m/s², when the ball reaches a height of 10 meters from the ground, calculate: Its velocity Its kinetic energy Its potential energy An object falls from a height of 6 meters above the ground. What is the velocity of the object when it reaches a height of 1 meter from the ground, if the acceleration due to gravity is 10 m/s²? A bullet with a mass of 100 grams is fired vertically upward from the ground with a velocity of 80 m/s. If g = 10 m/s², calculate: The maximum height reached by the bullet The energy of the bullet at its highest point The kinetic energy of the bullet at a height of 40 m from the ground ...

Soal Transformasi Geometri Soal Transformasi Geometri 1. Tentukan persamaan bayangan dari fungsi linear \( f(x) = \frac{3}{2}x + \frac{5}{2} \) oleh pergeseran ke kiri sejauh 2 satuan dan ke atas sejauh 4 satuan. 2. Jika fungsi \( f(x) = 2x + 4 \) ditransformasikan terhadap translasi \( T = \begin{pmatrix} 2 \\ 5 \end{pmatrix} \), tentukan persamaan peta (bayangan) dari fungsi tersebut. 3. Sebuah fungsi linear \( f(x) = \frac{7}{5}x - 7 \) ditranslasi, sehingga bayangannya adalah \( g(x) = \frac{7}{5}x + 5 \). Tentukan matriks translasi fungsi tersebut. 4. Diketahui fungsi \( f(x) = x^2 + 4x - 12 \) ditranslasi oleh \( T = \begin{pmatrix} 3 \\ -5 \end{pmatrix} \). Tentukan persamaan peta dari fungsi tersebut. 5. Sebuah fungsi \( f(x) = -x^2 - 4x + 5 \) ditranslasi, sehingga bayangannya adalah \( g(x) = -x^2 - 8x - 8 \). Tentukan matriks translasi fungsi tersebut. 6. Parabola yang me...