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目錄 Table of Content
誤差公式 Estimation and Error Formula
百分比公式 Percentage Formula
比率與比例公式 Rate and Ratio Formula
恆等式公式 Identities Formula
指數定律公式 Law of Indices Formula
求積法公式 Mensuration Formula
反射及旋轉公式 Reflection and Rotation Formula
N邊形公式 N-sides Polygon Formula
統計學公式 Statistics Formula
三角恆等式公式 Trigonometry Identities Formula
坐標幾何公式 Coordinate Geometry Formula
幾何演繹公式 Geometry Reasons Formula
二次方程公式 Quadratic Equation Formula
複數公式 Complex Number Formula
對數函數公式 Logarithmic Function Formula
等差數列公式 Arithmetic Sequences Formula
等比數列公式 Geometry Sequences Formula
高中三角學公式 Senior Trigonometry Formula
概率公式 Probability Formula
圓形方程公式 Equation of Circle Formula
誤差公式 Estimation and Error Formula
1. 最大誤差 = [準確度/2]
Maximum Error = [Precision/2]
2. 相對誤差 = [最大誤差/ 量度值] 或 [最大誤差/ 真實值]
Relative Error = [Maximum Error/ Measured Value] or [Maximum Error/ True Value]
3. 百分誤差 = [相對誤差 × 100%] 或 [最大誤差/ 量度值 × 100%]
Percentage Error = [Relative Error × 100%] or [Maximum Error/ Measured Value × 100%]
4. 上限 = [量度值 ＋ 最大誤差]
Upper Limit = [Measured Value + Maximum Error]
5. 下限 = [量度值 － 最大誤差]
Lower Limit = [Measured Value － Maximum Error]
6. 可能範圍 = 下限 至 上限 之間
Range = Lower Limit to Upper Limit
百分比公式 Percentage Formula
1. 增值 = [新值 － 原值]
Value Increased = [New Value － Original Value]
減值 = [原值 － 新值]
Value Decreased = [Original value － New value]
2. 百分數增加 = [增值 / 原值] = [(新值 － 原值)/ 原值]
Percentage Increased = [Value Increased / Original Value] = [(New value －Original value)/ Original value]
3. 百分數減少 = [減值 / 原值] = [(原值 － 新值)/ 原值]
Percentage Decreased = [Value Decreased / Original Value] = [(Original value －New value)/ Original value]
4. 新值 = [原值 × (1 + 增加%)]
New Value = [Original Value × (1 + % Increase)]
新值 = [原值 × (1 － 減少%)]
New Value = [Original Value × (1 － % Decrease)]
5. 折扣 = [標價 － 售價]
Discount = [Marked Price － Selling Price]
6. 折扣% = [折扣/ 標價 × 100%]
Discount% = [Discount/ Marked Price × 100%]
7. 售價 = [標價 × (1 － 折扣%)]
Selling Price = [Marked Price × (1 － Discount%)]
8. 盈利 = [售價 － 成本]
Profit = [Selling Price － Cost]
虧蝕 = [成本 － 售價]
Loss = [Cost － Selling Price]
9. 售價 = [成本 × (1 + 盈利%)]
Selling Price = [Cost × (1 + Profit%)]
比率與比例公式 Rate and Ratio Formula
速率 = [距離/ 時間]
Speed = [Distance/ Time]
恆等式公式 Identities Formula
指數定律公式 Law of Indices Formula
求積法公式 Mensuration Formula
三角形面積 = [底 × 高/ 2] 或 [ab sinθ] 或 [√(s(s－a)(s－b)(s－c))]
Area of Triangle = [Base × Height/ 2] or
[ab sinθ] or [√(s(s－a)(s－b)(s－c))]
梯形面積 = [(上底 + 下底) × 高/ 2]
Area of Trapezium = [Sum of parallel sides × Height/ 2]
圓形面積Area of Circle = [πr²]
扇形的面積Area of a Sector = [πr² × θ/360°]
弧長Length of an Arc = [(2πrθ)/360° + 2r]
體積Volume =
反射及旋轉公式 Reflection and Rotation Formula
| 反射平面Plane of Reflection |
旋轉對稱軸Axis of Rotation |
|
|
正面體Regtagular Tetrahegon |
6 | 7 |
| 正四方體Cube | 9 | 13 |
| 正八面體Regular Octahedron | 9 | 13 |
N邊形公式 N-sides Polygon Formula
內角和Sum of Interior Angles = [(n－2) × 180°]
外角和Sum of Exterior Angles = 360°
N邊形對角線Numbers of Diagonal of N-sides Polygon = [n(n－3)/2]
統計學公式 Statistics Formula
平均值Mean = 
中位數Median = 第[(n+1)/2]項
分佈域 = 最大值 － 最小值
Range = Maximum Value － Minimum Value
四分位間距 = 上四分位數 － 下四分位數
Interquartile Range = Upper Quartile － Lower Quartile
標準差Standard Deviation = 
方差Variance = 
標準分Standard Score = 
三角恆等式公式 Trigonometry Identities Formula
1. sin² θ + cos² θ = 1
2. tan θ = sin θ / cos θ
3. sin (90° − θ) = cos θ
4. cos (90° − θ) = sin θ
5. tan (90° − θ) = 1 / tan θ
6. sin (90° + θ) = cos θ
7. cos (90° + θ) = − sin θ
8. tan (90° + θ) = − 1 / tan θ
9. sin (180° − θ) = sin θ
10. cos (180° − θ) = − cos θ
11. tan (180° − θ) = − tan θ
12. sin (180° + θ) = − sin θ
13. cos (180° + θ) = − cos θ
14. tan (180° + θ) = tan θ
15. sin (270° − θ) = − cos θ
16. cos (270° − θ) = − sin θ
17. tan (270° − θ) = 1 / tan θ
18. sin (270° + θ) = − cos θ
19. cos (270° + θ) = sin θ
20. tan (270° + θ) = − 1 / tan θ
21. sin (360° − θ) = − sin θ
22. cos (360° − θ) = cos θ
23. tan (360° − θ) = − tan θ
24. sin (360° + θ) = sin θ
25. cos (360° + θ) = cos θ
26. tan (360° + θ) = tan θ
坐標幾何公式 Coordinate Geometry Formula
兩點距離Distance Between Two Points = √((x1 − x2)² + (y1 − y2)²)
斜率Slope (m) = (y1 − y2) / (x1 − x2) = tan θ
中點Mid-point = 
平行與垂直Parallel and Perpendicular
- If L1 ⊥ L2, m1 × m2 = − 1
- If L1 // L2, m1 = m2
幾何演繹公式 Geometry Reasons Formula
1. 同頂角(∠s at a pt.)
b + 75° + 135° = 360°
2. 直線上的鄰角(Adj. ∠s on st. line)
a + 47° = 180°
3. 對頂角(Vert. opp ∠)
c = 50°
4. 平行線Parallel Lines
錯角, AB // CD
b = 50°
同位角, AB // CD
a = 40°
同旁內角, AB // CD
c + 150° = 180°
內角和
a + b + c = 180°
外角
c = a + b
中點定理(Mid-pt. Thm.)
If AD = DB and AE = EC, 2DE = BC, DE // BC
截線定理(Intercept Thm.)
If CG // BF // AE, CB:BA = GF:FE
畢氏定理(Pyth. Thm.)
In △ABC, if ∠C = 90° , a² + b² = c²;
if a² + b² = c², ∠C = 90° (Converse of Pyth. thm.)
二次方程公式 Quadratic Equation Formula
判別式Discriminant = Δ = b² − 4ac
| Δ > 0 | Δ = 0 | Δ < 0 |
| 兩相異根2 Distinct Real Roots | 二重根1 Double Real Root | 沒有實根No Real Roots |
根的和Sum of Roots = α + β = − a / b
根的積Product of Roots = αβ = c / a
頂點Vertex = 
複數公式 Complex Number Formula
對數函數公式 Logarithmic Function Formula
等差數列公式 Arithmetic Sequences Formula
1. 如A, B, C為一等差數列 If A, B, C is an arithmetic sequence
→ A + C = 2B
2. 一般式General Term = an = a1+ (n − 1) d
*a1為首項，d為公差 *a1 is first term, d is common difference
3. 等差數列求和法General Term of Summation
等比數列公式 Geometry Sequences Formula
1. 如A, B, C為一等比數列 If A, B, C is a geometry sequence
→ A × C = B²
2. 一般式General Term = 
*a1為首項，r為公比 *a1 is first term, r is common ratio
3. 等比數列求和法General Term of Summation
4. 無限項之和Sum to infinity
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高中三角學公式 Senior Trigonometry Formula
正弦公式Sine Formula
餘弦公式Cosine Formula
c² = a² + b² − 2ab cos C
概率公式 Probability Formula
1. A ∪ B 即 A or B
2. A ∩ B 即 A and B
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
3. 獨立事件Independent Event
P(A ∩ B) = P(A) × P(B)
4. 互斥事件Mutually Exclusive Event
P(A ∩ B) = 0
5. 條件概率Conditional Probability
P(A | B) = P(A ∩ B) / P(B)
圓形方程公式 Equation of Circle Formula
1. 標準式Center-radius Form
(x − h)² + (y − k)² = r²
*(h, k) 為圓心， r 為半徑 *(h, k) is center, r is radius
2. 一般式General Form
x² + y² + Dx + Ey + F = 0
圓心Center = 
半徑Radius = 
