Dasar-dasar Aljabar
| Nama | Rumus |
|---|---|
| Rumus kuadrat | x = (-b ± √(b²-4ac)) / 2a |
| Formula Vieta | x₁ + x₂ = -b/a, x₁x₂ = c/a |
| Diskriminatif | Δ = b² - 4ac |
| Anjak Piutang | a² - b² = (a+b)(a-b) |
| Persegi sempurna | (a±b)² = a² ± 2ab + b² |
| Jumlah / perbedaan kubus | a³ ± b³ = (a±b)(a² ∓ ab + b²) |
| Teorema binomial | (a+b)ⁿ = Σ C(n,k)aⁿ⁻ᵏbᵏ |
Urutan
| Nama | Rumus |
|---|---|
| Urutan aritmatika | aₙ = a₁ + (n-1)d |
| Jumlah aritmatika | Sₙ = n(a₁+aₙ)/2 = na₁ + n(n-1)d/2 |
| Urutan geometris | aₙ = a₁ · rⁿ⁻¹ |
| Jumlah geometris | Sₙ = a₁(1-rⁿ)/(1-r), r≠1 |
| Geometris tak terbatas | S = a₁/(1-r), |r|<1 |
Fungsi
| Nama | Rumus |
|---|---|
| Aturan eksponen | aᵐ · aⁿ = aᵐ⁺ⁿ, aᵐ/aⁿ = aᵐ⁻ⁿ |
| Aturan logaritma | log(xy) = logx + logy |
| Perubahan basis | logₐb = logₓb / logₓa |
| Hubungan exp-log | y = aˣ ⟺ x = logₐy |
| Fungsi komposit | (f∘g)(x) = f(g(x)) |
| Fungsi terbalik | f(f⁻¹(x)) = x |
Trigonometri
| Nama | Rumus |
|---|---|
| Identitas dasar | sin²θ + cos²θ = 1 |
| Tangen | tanθ = sinθ/cosθ |
| Rumus penjumlahan (sin) | sin(α±β) = sinαcosβ ± cosαsinβ |
| Rumus penjumlahan (cos) | cos(α±β) = cosαcosβ ∓ sinαsinβ |
| Sudut ganda (sin) | sin2θ = 2sinθcosθ |
| Sudut ganda (cos) | cos2θ = cos²θ - sin²θ |
| Hukum sinus | a/sinA = b/sinB = c/sinC = 2R |
| Hukum kosinus | c² = a² + b² - 2ab·cosC |
Kalkulus
| Nama | Rumus |
|---|---|
| Definisi turunan | f'(x) = lim[h→0] (f(x+h)-f(x))/h |
| Aturan daya | (xⁿ)' = nxⁿ⁻¹ |
| Eksponensial | (eˣ)' = eˣ, (aˣ)' = aˣlna |
| Logaritma | (lnx)' = 1/x |
| Turunan trigonometri | (sinx)' = cosx, (cosx)' = -sinx |
| Aturan produk | (fg)' = f'g + fg' |
| Aturan hasil bagi | (f/g)' = (f'g - fg')/g² |
| Aturan rantai | (f(g(x)))' = f'(g(x))·g'(x) |
Geometri Analitik
| Nama | Rumus |
|---|---|
| Rumus jarak | d = √((x₂-x₁)² + (y₂-y₁)²) |
| Rumus titik tengah | M = ((x₁+x₂)/2, (y₁+y₂)/2) |
| Kemiringan | k = (y₂-y₁)/(x₂-x₁) |
| Bentuk kemiringan titik | y - y₁ = k(x - x₁) |
| Bentuk umum | Ax + By + C = 0 |
| Jarak titik-garis | d = |Ax₀+By₀+C| / √(A²+B²) |
| Persamaan lingkaran | (x-a)² + (y-b)² = r² |
| Persamaan elips | x²/a² + y²/b² = 1 |
| Persamaan hiperbola | x²/a² - y²/b² = 1 |
| Persamaan parabola | y² = 4px 或 x² = 4py |
Vektor & Bilangan Kompleks
| Nama | Rumus |
|---|---|
| Penambahan vektor | a⃗ + b⃗ = (a₁+b₁, a₂+b₂) |
| Produk titik | a⃗·b⃗ = |a⃗||b⃗|cosθ = a₁b₁+a₂b₂ |
| Besaran vektor | |a⃗| = √(a₁² + a₂²) |
| Sudut antara vektor | cosθ = a⃗·b⃗ / (|a⃗||b⃗|) |
| Penambahan yang kompleks | (a+bi) + (c+di) = (a+c) + (b+d)i |
| Perkalian kompleks | (a+bi)(c+di) = (ac-bd) + (ad+bc)i |
| Modulus kompleks | |a+bi| = √(a² + b²) |
Probabilitas & Statistik
| Nama | Rumus |
|---|---|
| Probabilitas klasik | P(A) = n(A) / n(S) |
| Aturan penambahan | P(A∪B) = P(A) + P(B) - P(A∩B) |
| Aturan perkalian | P(A∩B) = P(A)·P(B|A) |
| Masalah bersyarat. | P(B|A) = P(A∩B) / P(A) |
| Permutasi | P(n,r) = n! / (n-r)! |
| Kombinasi | C(n,r) = n! / (r!(n-r)!) |
| Berarti | x̄ = Σxᵢ / n |
| Varians | s² = Σ(xᵢ-x̄)² / n |
| Standar deviasi | s = √(s²) |