Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode Trigonometri, Peluang dan Statistik 📊 Rangkuman Rumus Matematika SMA Trigonometri, Peluang dan Statistik Oleh: Agus Salim 📈 1. STATISTIK Statistik adalah cabang matematika yang berkaitan dengan pengumpulan, analisis, interpretasi, presentasi, dan organisasi data. Dalam konteks SMA, fokus utama adalah pada ukuran pemusatan data dan ukuran penyebaran data. 🎯 1.1 Ukuran Pemusatan Data 📊 1.1.1 Rata-rata (Mean) a. Data Tunggal x̄ = (Jumlah semua nilai data) / (Banyaknya data) Keterangan: • x̄ = rata-rata • n = banyaknya data b. Data Kelompok x̄ = (Σ(fi × xi)) / (Σfi) Keterangan: • fi = frekuensi kelas ke-i • ...

Frequency Distribution Table - Sturges Method Frequency Distribution Table Generator Sturges Method Enter data values below (separated by semicolons). Maximum 500 values: Calculate Distribution Results New Calculation

Kalkulator Sudut Segitiga Kalkulator Sudut Segitiga Sisi a: Sisi b: Sisi c: Hitung Sudut Hasil Perhitungan Sudut A: derajat Sudut B: derajat Sudut C: derajat Penjelasan Hitung Ulang

Quiz 1:   Fullscreen Mode Gerak Parabola: Teori dan Rumus Lengkap Konsep Dasar Gerak Parabola Gerak parabola merupakan kombinasi dari gerak lurus beraturan (GLB) pada sumbu horizontal dan gerak lurus berubah beraturan (GLBB) pada sumbu vertikal. Fenomena ini terjadi ketika benda diberi kecepatan awal dengan sudut elevasi tertentu terhadap bidang horizontal. Persamaan Fundamental 1. Komponen Kecepatan Awal Kecepatan awal (v 0 ) dapat diurai menjadi: v 0x = v 0 · cosθ v 0y = v 0 · sinθ 2. Waktu Mencapai Titik Tertinggi t maks = (v 0 · sinθ)/g 3. Tinggi Maksimum (H) H = (v 0 2 · sin 2 θ)/(2g) 4. Jarak Jangkauan Maksimum (X) X = (v 0 2 · sin2θ)/g Contoh Soal dan Penyelesaian Sebuah bola dilempar dengan kecepatan awal 20 m/s dan sudut elevasi 37° (sin37°=0,6). Percepatan gravitasi 10 m/s². a. Komponen Kecepatan Awal v 0x = 20 · cos37° = 16 m/s v 0y = 20 · sin37° = 12 m/s b. Kecepatan pada t=0,4s v x = 16 m/s (konstan) v y = ...

Quiz 1:   Fullscreen Mode Geometric Transformations Theory 1. Reflections Definition: Mirror image over a line Key Formulas: - Vertical line x=a: (x,y) → (2a-x,y) - Horizontal line y=b: (x,y) → (x,2b-y) - Line y=x: (x,y) → (y,x) - Line y=-x: (x,y) → (-y,-x) 2. Rotations Definition: Turning around a center point Rotation Matrices: 90° clockwise: \(\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\) 180° rotation: \(\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\) 3. Translations Definition: Sliding without rotation Vector Notation: Translation vector \( \binom{a}{b} \): (x,y) → (x+a, y+b) 4. Enlargements Scale Factor Formula: For center (h,k) and scale factor s: x' = h + s(x - h) y' = k + s(y - k) Combined...

Quiz 1   Fullscreen Mode Persamaan dan Pertidaksamaan Nilai Mutlak Teori Dasar Nilai mutlak (|x|) merupakan jarak bilangan real dari titik 0 pada garis bilangan. Sifat utama: |x| ≥ 0 untuk semua x ∈ ℝ |x| = |-x| √(x²) = |x| Rumus Fundamental Jenis Rumus Persamaan |f(x)| = a ⇨ f(x) = a atau f(x) = -a Pertidaksamaan |f(x)| |f(x)| > a ⇨ f(x) a Contoh Soal Contoh 1: Selesaikan |2x - 3| = 5 Penyelesaian: 2x - 3 = 5 ⇒ x = 4 2x - 3 = -5 ⇒ x = -1 Contoh 2: Selesaikan |x + 2| ≤ 3 Penyelesaian: -3 ≤ x + 2 ≤ 3 ⇒ -5 ≤ x ≤ 1

Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode Exothermic and Endothermic Reactions Exothermic and Endothermic Reactions Chemical reactions can be classified into two main categories based on energy changes: exothermic reactions and endothermic reactions . Exothermic Reactions An exothermic reaction is one that releases energy in the form of heat to the surroundings. During this reaction, the temperature of the surroundings increases due to the energy released. A common example of an exothermic reaction is the combustion of fuels, such as methane (CH₄). The combustion reaction of methane can be written as follows: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) + ΔH Here, ΔH has a negative value, indicating that energy is released during this process. The combustion of methane in oxygen produces carbon dioxide and water, releasing about 728 kJ/mol of energy. Characteristics of Exothermic Reactions: Energy Released: Energy in th...

Audio Podcast Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode  5.2.1 Detection of radioactivity ## Radioactivity Detection Radioactivity is the process of releasing radiation from an unstable atomic nucleus. We are all exposed to radiation from various sources every day. Let's discuss some important things about radioactivity: ## Background Radiation Sources Background radiation comes from a variety of sources, both natural and artificial: - Cosmic rays from the sun - Radon gas in the air - Radon-containing granite rocks - Potassium-40 in food - Medical procedures that use radioisotopes - Nuclear power plants and the rest of the nuclear bomb tests ## Ionization Effect Radiation can cause ionization, which is the process of releasing electrons from atoms or molecules. This can be evidenced by: Electroscope Experiments: - When a fire or radium source is brought close to a charged electroscope, the charge is lost - Fire or radiation causes air molecules...

Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode Fundamentals of Magnets Magnets are objects that have two poles - a north (N) pole and a south (S) pole. Every magnet always has these two poles, and cannot have only one pole (Ruoho & Arkkio, 2008). Properties of Magnets: Like poles repel each other Opposite poles attract each other The strength of the magnetic force decreases as the distance increases Magnetic Field The magnetic field is the region around a magnet where the magnetic force can still be felt. The strength of the magnetic field is shown by the magnetic field lines: The closer the field lines, the stronger the magnetic field The direction of the magnetic field is always from the north pole to the south pole Types of Magnetic Materials Magnetic Materials: Examples are iron, steel, nickel, and cobalt Can be attracted by magnets Can be magnetized Non-magnetic Materials: Examples are aluminum and wood Cannot be attr...