雙重根式：√[(a+b)+2√ab] = √a + √b

1. aᵐaⁿ = aᵐ⁺ⁿ

2. (aᵐ)ⁿ = aᵐⁿ

3. aⁿbⁿ = (ab)ⁿ

4. a⁰ = 1

5. aᵐ ⁄ aⁿ = aᵐ⁻ⁿ

6. a¹⁄ⁿ = ⁿ√a

7. aᵐ⁄ⁿ = (ⁿ√a)ᵐ = ⁿ√aᵐ

log10ⁿ = n

log(x)+log(y) = log(xy)

log(aⁿ) = n log(a)

1. 直線斜率：

m = Δy ⁄ Δx (Δx ≠ 0)

2. 點斜式：

通過A(x₀, y₀)且斜率為m

⇒y−y₀ = m(x−x₀)

3. 斜截式：

斜率為m且y截距為b

⇒y = mx+b

4. 截距式：

x截距為a且y截距為b(a≠0且b≠0)

⇒x ⁄ a + y ⁄ b = 1

5. 當L：ax+by+c=0時

• 若b ≠ 0，m = −a ⁄ b

• 若b = 0，L無斜率

6. 點到直線的距離：

P(x₀, y₀)到L: ax+by+c=0的距離d =|ax₀+by₀=c| ⁄ √(a²+b²)

1. 標準式：M(h, k)為圓心，r為半徑

⇒(x−h)² + (y−k)² = r²

1. 等差數列(d = 公差) an = a₁ + (n−1)d

2. 等比數列(r = 公比) an = a₁rⁿ⁻¹

1. 1+2+…+n = n(n+1) ⁄ 2

2. 1²+2²+…+n² = n(n+1)(2n+1) ⁄ 6

3. 1³+2³+…+n³ = [n(n+1) ⁄ 2]²

sin(α + β) = sinαcosβ + cosαsinβ

sin(α − β) = sinαcosβ − cosαsinβ

cos(α + β) = cosαcosβ − sinαsinβ

cos(α − β) = cosαcosβ + sinαsinβ

tan(α + β) = tanα + tanβ ⁄ [1−tanα tan(−β)]

tan(α − β) = tanα − tanβ ⁄ (1+tanα tanβ)

sin2θ = 2sinθcosθ

cos2θ = cos²θ − sin²θ = 1−2sin²θ = 2cos²θ−1

tan2θ = 2tanθ ⁄ (1−tan²θ)

sin(½θ) = ± √1 − cosθ ⁄ 2

cos(½θ) = ± √1 + cosθ ⁄ 2