🎓 Matematika Master
Platform Pembelajaran Matematika Terlengkap & Interaktif
📚 Rumus Aljabar Lengkap 50+ Rumus
🔢 Persamaan Kuadrat
Bentuk umum: $ax^2 + bx + c = 0$
Rumus ABC: $x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$
Diskriminan: $D = b^2 – 4ac$
✨ Identitas Aljabar
$(a + b)^2 = a^2 + 2ab + b^2$
$(a – b)^2 = a^2 – 2ab + b^2$
$(a + b)(a – b) = a^2 – b^2$
📊 Logaritma
$\log_a(xy) = \log_a x + \log_a y$
$\log_a(\frac{x}{y}) = \log_a x – \log_a y$
$\log_a(x^n) = n \log_a x$
📈 Eksponen
$a^m \cdot a^n = a^{m+n}$
$\frac{a^m}{a^n} = a^{m-n}$
$(a^m)^n = a^{mn}$
🔄 Deret & Barisan
Aritmatika:
$U_n = a + (n-1)b$
$S_n = \frac{n}{2}(2a + (n-1)b)$
🎮 Quiz Interaktif Skor: 0
🧮 Kalkulator Persamaan Kuadrat
ax² + bx + c = 0
📐 Rumus Geometri Lengkap
⭕ Lingkaran
Luas: $A = \pi r^2$
Keliling: $K = 2\pi r = \pi d$
Luas juring: $A_{juring} = \frac{\theta}{360°} \times \pi r^2$
Panjang busur: $s = \frac{\theta}{360°} \times 2\pi r$
🔺 Segitiga
Luas: $A = \frac{1}{2} \times alas \times tinggi$
Luas (Heron): $A = \sqrt{s(s-a)(s-b)(s-c)}$
dimana $s = \frac{a+b+c}{2}$
Pythagoras: $c^2 = a^2 + b^2$
📦 Bangun Ruang
Kubus:
Volume: $V = s^3$
Luas permukaan: $L = 6s^2$
Bola:
Volume: $V = \frac{4}{3}\pi r^3$
Luas permukaan: $L = 4\pi r^2$
🧮 Kalkulator Geometri
📊 Rumus Trigonometri
📐 Fungsi Dasar
$\sin \theta = \frac{depan}{miring}$
$\cos \theta = \frac{samping}{miring}$
$\tan \theta = \frac{depan}{samping}$
$\sin^2 \theta + \cos^2 \theta = 1$
🔄 Identitas Trigonometri
$\tan \theta = \frac{\sin \theta}{\cos \theta}$
$1 + \tan^2 \theta = \sec^2 \theta$
$\sin(90° – \theta) = \cos \theta$
$\cos(90° – \theta) = \sin \theta$
➕ Rumus Jumlah
$\sin(A + B) = \sin A \cos B + \cos A \sin B$
$\cos(A + B) = \cos A \cos B – \sin A \sin B$
$\tan(A + B) = \frac{\tan A + \tan B}{1 – \tan A \tan B}$
🧮 Kalkulator Trigonometri
∫ Rumus Kalkulus
📉 Turunan
$\frac{d}{dx}(c) = 0$ (konstanta)
$\frac{d}{dx}(x^n) = nx^{n-1}$
$\frac{d}{dx}(e^x) = e^x$
$\frac{d}{dx}(\ln x) = \frac{1}{x}$
$\frac{d}{dx}(\sin x) = \cos x$
📈 Integral
$\int k dx = kx + C$
$\int x^n dx = \frac{x^{n+1}}{n+1} + C$
$\int \frac{1}{x} dx = \ln|x| + C$
$\int e^x dx = e^x + C$
$\int \sin x dx = -\cos x + C$
🧮 Kalkulator Turunan
📈 Rumus Statistika
📊 Ukuran Pemusatan
Mean: $\bar{x} = \frac{\sum x_i}{n}$
Median: nilai tengah data terurut
Modus: nilai yang paling sering muncul
📏 Ukuran Penyebaran
Range: $R = x_{max} – x_{min}$
Varians: $s^2 = \frac{\sum (x_i – \bar{x})^2}{n-1}$
Standar Deviasi: $s = \sqrt{s^2}$
📊 Kalkulator Statistik
🔢 Rumus Matriks
➕ Operasi Matriks
Penjumlahan: $(A + B)_{ij} = a_{ij} + b_{ij}$
Perkalian: $(AB)_{ij} = \sum_{k=1}^n a_{ik} \cdot b_{kj}$
Transpose: $(A^T)_{ij} = a_{ji}$
🔍 Determinan
Matriks 2×2:
$\det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad – bc$
Invers 2×2:
$A^{-1} = \frac{1}{\det(A)} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$
