國小、國中、高中英文版數學課本

國小、國中、高中英文版數學課本

國小、國中、高中英文版數學課本

筆者有時候會遇到一些學生，需要學習國小、國中、高中程度的數學，但這些學生只懂英文，或是要參加的考試是用英文出題。下面幾本免費的OpexStax開放教科書網站出的書籍，就是很好的教學資源。下面將書籍按照難易排序，但其實這個難度排序並不是很精確。後面附註對照的台灣數學程度，但這個對照表也不是很精確。

如果是要比較簡單，按照年級編排的參考書，可以參考IXL Learning的The Ultimate Math Workbook。

  • Prealgebra（國小）
  • Elementary Algebra（國中）
  • Intermediate Algebra（國中）
  • College Algebra（高中）
  • College Algebra with Corequisite Support（高中）
  • Algebra and Trigonometry（高中）
  • Precalculus（高中）

注意到，這些內容雖然是小學、國中、高中數學，但預設讀者是已經成年的大學生，所以讀者是要有一些基本的閱讀能力的，就如書籍在Preface裡面提到的：

Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes.

因為這些書籍的章節重疊性很高，所以下表將章節的對照列出來，方便老師查找。雖然有時候章節名稱相同，但可能討論的深度及習題難度會不相同。

PrealgebraElementary AlgebraIntermediate AlgebraCollege AlgebraCollege Algebra CorequisiteAlgebra TrigonometryPrecalculus
Whole Numbers 7Foundations 5Foundations 51 Prerequisites 71 Prerequisites 71 Prerequisites 71 Functions 7
1.1 Introduction to Whole Numbers 71.1 Introduction to Whole Numbers 51.1 Use the Language of Algebra 51.1 Real Numbers: Algebra Essentials 71.1 Real Numbers: Algebra Essentials 71.1 Real Numbers: Algebra Essentials 71.1 Functions and Function Notation 7
1.2 Add Whole Numbers 241.2 Use the Language of Algebra 211.2 Integers 241.2 Exponents and Scientific Notation 241.2 Exponents and Scientific Notation 271.2 Exponents and Scientific Notation 241.2 Domain and Range 34
1.3 Subtract Whole Numbers 401.3 Add and Subtract Integers 411.3 Fractions 431.3 Radicals and Rational Exponents 391.3 Radicals and Rational Exponents 451.3 Radicals and Rational Exponents 391.3 Rates of Change and Behavior of Graphs 56
1.4 Multiply Whole Numbers 551.4 Multiply and Divide Integers 641.4 Decimals 571.4 Polynomials 501.4 Polynomials 571.4 Polynomials 501.4 Composition of Functions 73
1.5 Divide Whole Numbers 731.5 Visualize Fractions 791.5 Properties of Real Numbers 741.5 Factoring Polynomials 591.5 Factoring Polynomials 681.5 Factoring Polynomials 591.5 Transformation of Functions 89
The Language of Algebra 1011.6 Add and Subtract Fractions 951.6 Rational Expressions 681.6 Rational Expressions 801.6 Rational Expressions 681.6 Absolute Value Functions 121
2.1 Use the Language of Algebra 1011.7 Decimals 1112 Equations and Inequalities 832 Equations and Inequalities 992 Equations and Inequalities 831.7 Inverse Functions 133
2.2 Evaluate, Simplify, and Translate Expressions 1211.8 The Real Numbers 1302.1 The Rectangular Coordinate Systems and Graphs 832.1 The Rectangular Coordinate Systems and Graphs 992.1 The Rectangular Coordinate Systems and Graphs 83
2.3 Solving Equations Using the Subtraction and Addition Properties of Equality 1361.9 Properties of Real Numbers 1462.2 Linear Equations in One Variable 982.2 Linear Equations in One Variable 1162.2 Linear Equations in One Variable 98
2.4 Find Multiples and Factors 1501.10 Systems of Measurement 1652.3 Models and Applications 1152.3 Models and Applications 1362.3 Models and Applications 115
2.5 Prime Factorization and the Least Common Multiple 1642.4 Complex Numbers 1252.4 Complex Numbers 1482.4 Complex Numbers 125
Integers 1832.5 Quadratic Equations 1342.5 Quadratic Equations 1612.5 Quadratic Equations 134
3.1 Introduction to Integers 1832.6 Other Types of Equations 1492.6 Other Types of Equations 1782.6 Other Types of Equations 149
3.2 Add Integers 2012.7 Linear Inequalities and Absolute Value Inequalities 1612.7 Linear Inequalities and Absolute Value Inequalities 1902.7 Linear Inequalities and Absolute Value Inequalities 161
3.3 Subtract Integers 2163 Functions 1813 Functions 2093 Functions 181
3.4 Multiply and Divide Integers 2363.1 Functions and Function Notation 1813.1 Functions and Function Notation 2093.1 Functions and Function Notation 181
3.5 Solve Equations Using Integers; The Division Property of Equality 2503.2 Domain and Range 2053.2 Domain and Range 2373.2 Domain and Range 205
Fractions 2733.3 Rates of Change and Behavior of Graphs 2233.3 Rates of Change and Behavior of Graphs 2583.3 Rates of Change and Behavior of Graphs 223
4.1 Visualize Fractions 2733.4 Composition of Functions 2393.4 Composition of Functions 2773.4 Composition of Functions 239
4.2 Multiply and Divide Fractions 2973.5 Transformation of Functions 2553.5 Transformation of Functions 2953.5 Transformation of Functions 255
4.3 Multiply and Divide Mixed Numbers and Complex Fractions 3173.6 Absolute Value Functions 2873.6 Absolute Value Functions 3333.6 Absolute Value Functions 287
4.4 Add and Subtract Fractions with Common Denominators 3303.7 Inverse Functions 2953.7 Inverse Functions 3433.7 Inverse Functions 295
4.5 Add and Subtract Fractions with Different Denominators 3424 Linear Functions 3234 Linear Functions 3754 Linear Functions 3232 Linear Functions 163
4.6 Add and Subtract Mixed Numbers 3644.1 Linear Functions 3234.1 Linear Functions 3754.1 Linear Functions 3232.1 Linear Functions 164
4.7 Solve Equations with Fractions 3804.2 Modeling with Linear Functions 3604.2 Modeling with Linear Functions 4154.2 Modeling with Linear Functions 3602.2 Graphs of Linear Functions 186
Decimals 4074.3 Fitting Linear Models to Data 3744.3 Fitting Linear Models to Data 4324.3 Fitting Linear Models to Data 3742.3 Modeling with Linear Functions 211
5.1 Decimals 4072.4 Fitting Linear Models to Data 225
5.2 Decimal Operations 4265 Polynomial and Rational Functions 3995 Polynomial and Rational Functions 4595 Polynomial and Rational Functions 3993 Polynomial and Rational Functions 251
5.3 Decimals and Fractions 4455.1 Quadratic Functions 4005.1 Quadratic Functions 4605.1 Quadratic Functions 4003.1 Complex Numbers 252
5.4 Solve Equations with Decimals 4595.2 Power Functions and Polynomial Functions 4195.2 Power Functions and Polynomial Functions 4835.2 Power Functions and Polynomial Functions 4193.2 Quadratic Functions 262
5.5 Averages and Probability 4685.3 Graphs of Polynomial Functions 4385.3 Graphs of Polynomial Functions 5065.3 Graphs of Polynomial Functions 4383.3 Power Functions and Polynomial Functions 283
5.6 Ratios and Rate 4815.4 Dividing Polynomials 4605.4 Dividing Polynomials 5305.4 Dividing Polynomials 4603.4 Graphs of Polynomial Functions 302
5.7 Simplify and Use Square Roots 4945.5 Zeros of Polynomial Functions 4715.5 Zeros of Polynomial Functions 5445.5 Zeros of Polynomial Functions 4713.5 Dividing Polynomials 325
Percents 5175.6 Rational Functions 4845.6 Rational Functions 5595.6 Rational Functions 4843.6 Zeros of Polynomial Functions 336
6.1 Understand Percent 5175.7 Inverses and Radical Functions 5085.7 Inverses and Radical Functions 5865.7 Inverses and Radical Functions 5083.7 Rational Functions 350
6.2 Solve General Applications of Percent 5345.8 Modeling Using Variation 5215.8 Modeling Using Variation 6035.8 Modeling Using Variation 5213.8 Inverses and Radical Functions 376
6.3 Solve Sales Tax, Commission, and Discount Applications 5463.9 Modeling Using Variation 389
6.4 Solve Simple Interest Applications 5606 Exponential and Logarithmic Functions 5416 Exponential and Logarithmic Functions 6256 Exponential and Logarithmic Functions 5414 Exponential and Logarithmic Functions 409
6.5 Solve Proportions and their Applications 5706.1 Exponential Functions 5426.1 Exponential Functions 6266.1 Exponential Functions 5424.1 Exponential Functions 410
The Properties of Real Numbers 5956.2 Graphs of Exponential Functions 5616.2 Graphs of Exponential Functions 6486.2 Graphs of Exponential Functions 5614.2 Graphs of Exponential Functions 429
7.1 Rational and Irrational Numbers 5956.3 Logarithmic Functions 5756.3 Logarithmic Functions 6656.3 Logarithmic Functions 5754.3 Logarithmic Functions 443
7.2 Commutative and Associative Properties 6036.4 Graphs of Logarithmic Functions 5846.4 Graphs of Logarithmic Functions 6776.4 Graphs of Logarithmic Functions 5844.4 Graphs of Logarithmic Functions 452
7.3 Distributive Property 6156.5 Logarithmic Properties 6066.5 Logarithmic Properties 7046.5 Logarithmic Properties 6064.5 Logarithmic Properties 474
7.4 Properties of Identity, Inverses, and Zero 6276.6 Exponential and Logarithmic Equations 6186.6 Exponential and Logarithmic Equations 7206.6 Exponential and Logarithmic Equations 6184.6 Exponential and Logarithmic Equations 486
7.5 Systems of Measurement 6386.7 Exponential and Logarithmic Models 6316.7 Exponential and Logarithmic Models 7366.7 Exponential and Logarithmic Models 6314.7 Exponential and Logarithmic Models 499
Solving Linear Equations 663Solving Linear Equations and Inequalities 203Solving Linear Equations 996.8 Fitting Exponential Models to Data 6506.8 Fitting Exponential Models to Data 7606.8 Fitting Exponential Models to Data 6504.8 Fitting Exponential Models to Data 518
8.1 Solve Equations Using the Subtraction and Addition Properties of Equality 6632.1 Solve Equations Using the Subtraction and Addition Properties of Equality 2032.1 Use a General Strategy to Solve Linear Equations 997 Systems of Equations and Inequalities 6817 Systems of Equations and Inequalities 7957 The Unit Circle: Sine and Cosine Functions 6815 Trigonometric Functions 549
8.2 Solve Equations Using the Division and Multiplication Properties of Equality 6772.2 Solve Equations using the Division and Multiplication Properties of Equality 2182.2 Use a Problem Solving Strategy 1167.1 Systems of Linear Equations: Two Variables 6827.1 Systems of Linear Equations: Two Variables 7967.1 Angles 6825.1 Angles 550
8.3 Solve Equations with Variables and Constants on Both Sides 6852.3 Solve Equations with Variables and Constants on Both Sides 2322.3 Solve a Formula for a Specific Variable 1357.2 Systems of Linear Equations: Three Variables 7017.2 Systems of Linear Equations: Three Variables 8197.2 Right Triangle Trigonometry 7045.2 Unit Circle: Sine and Cosine Functions 573
8.4 Solve Equations with Fraction or Decimal Coefficients 7032.4 Use a General Strategy to Solve Linear Equations 2422.4 Solve Mixture and Uniform Motion Applications 1527.3 Systems of Nonlinear Equations and Inequalities: Two Variables 7137.3 Systems of Nonlinear Equations and Inequalities: Two Variables 8367.3 Unit Circle 7175.3 The Other Trigonometric Functions 594
2.5 Solve Equations with Fractions or Decimals 2552.5 Solve Linear Inequalities 1717.4 Partial Fractions 7257.4 Partial Fractions 8547.4 The Other Trigonometric Functions 7365.4 Right Triangle Trigonometry 610
2.6 Solve a Formula for a Specific Variable 2662.6 Solve Compound Inequalities 1907.5 Matrices and Matrix Operations 7357.5 Matrices and Matrix Operations 8688 Periodic Functions 7596 Periodic Functions 631
2.7 Solve Linear Inequalities 2762.7 Solve Absolute Value Inequalities 2017.6 Solving Systems with Gaussian Elimination 7487.6 Solving Systems with Gaussian Elimination 8848.1 Graphs of the Sine and Cosine Functions 7596.1 Graphs of the Sine and Cosine Functions 631
Math Models and Geometry 719Math Models 3017.7 Solving Systems with Inverses 7627.7 Solving Systems with Inverses 9018.2 Graphs of the Other Trigonometric Functions 7796.2 Graphs of the Other Trigonometric Functions 651
9.1 Use a Problem Solving Strategy 7193.1 Use a Problem-Solving Strategy 3017.8 Solving Systems with Cramer's Rule 777 (Determinants)7.8 Solving Systems with Cramer's Rule 9198.3 Inverse Trigonometric Functions 8006.3 Inverse Trigonometric Functions 672
9.2 Solve Money Applications 7343.2 Solve Percent Applications 3188 Analytic Geometry 8018 Analytic Geometry 9459 Trigonometric Identities and Equations 8217 Trigonometric Identities and Equations 693
9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem 7473.3 Solve Mixture Applications 3378.1 The Ellipse 8028.1 The Ellipse 9469.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions7.1 Solving Trigonometric Equations with Identities 693
9.4 Use Properties of Rectangles, Triangles, and Trapezoids 7663.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem 3548.2 The Hyperbola 8188.2 The Hyperbola 9669.2 Sum and Difference Identities 8327.2 Sum and Difference Identities 704
9.5 Solve Geometry Applications: Circles and Irregular Figures 7953.5 Solve Uniform Motion Applications 3788.3 The Parabola 8358.3 The Parabola 9889.3 Double-Angle, Half-Angle, and Reduction Formulas 8477.3 Double-Angle, Half-Angle, and Reduction Formulas 719
9.6 Solve Geometry Applications: Volume and Surface Area 8073.6 Solve Applications with Linear Inequalities 3928.4 Rotation of Axes 8518.4 Rotation of Axes 10099.4 Sum-to-Product and Product-to-Sum Formulas 8607.4 Sum-to-Product and Product-to-Sum Formulas 732
9.7 Solve a Formula for a Specific Variable 8288.5 Conic Sections in Polar Coordinates 8668.5 Conic Sections in Polar Coordinates 10279.5 Solving Trigonometric Equations 8687.5 Solving Trigonometric Equations 740
Graphs 953Graphs 413Graphs and Functions 2279 Sequences, Probability, and Counting Theory 8859 Sequences, Probability, and Counting Theory 10457.6 Modeling with Trigonometric Functions 755
11.1 Use the Rectangular Coordinate System 9534.1 Use the Rectangular Coordinate System 4133.1 Graph Linear Equations in Two Variables 2279.1 Sequences and Their Notations 8859.1 Sequences and Their Notations 104510 Further Applications of Trigonometry 8938 Further Applications of Trigonometry 787
11.2 Graphing Linear Equations 9764.2 Graph Linear Equations in Two Variables 4333.2 Slope of a Line 2569.2 Arithmetic Sequences 9009.2 Arithmetic Sequences 106310.1 Non-right Triangles: Law of Sines 8938.1 Non-right Triangles: Law of Sines 787
11.3 Graphing with Intercepts 9944.3 Graph with Intercepts 4543.3 Find the Equation of a Line 2819.3 Geometric Sequences 9129.3 Geometric Sequences 107910.2 Non-right Triangles: Law of Cosines 9118.2 Non-right Triangles: Law of Cosines 805
11.4 Understand Slope of a Line 10114.4 Understand Slope of a Line 4683.4 Graph Linear Inequalities in Two Variables 2989.4 Series and Their Notations 9219.4 Series and Their Notations 109210.3 Polar Coordinates 9258.3 Polar Coordinates 819
4.5 Use the Slope-Intercept Form of an Equation of a Line 4973.5 Relations and Functions 3179.5 Counting Principles 9359.5 Counting Principles 110910.4 Polar Coordinates: Graphs 9398.4 Polar Coordinates: Graphs 833
4.6 Find the Equation of a Line 5243.6 Graphs of Functions 3329.6 Binomial Theorem 9469.6 Binomial Theorem 112210.5 Polar Form of Complex Numbers 9588.5 Polar Form of Complex Numbers 852
4.7 Graphs of Linear Inequalities 5429.7 Probability 9539.7 Probability 113210.6 Parametric Equations 9698.6 Parametric Equations 863
Systems of Linear Equations 577Systems of Linear Equations 37110.7 Parametric Equations: Graphs 9828.7 Parametric Equations: Graphs 876
5.1 Solve Systems of Equations by Graphing 5774.1 Solve Systems of Linear Equations with Two Variables 37110.8 Vectors 9948.8 Vectors 888
5.2 Solving Systems of Equations by Substitution 5984.2 Solve Applications with Systems of Equations 39311 Systems of Equations and Inequalities 10279 Systems of Equations and Inequalities 921
5.3 Solve Systems of Equations by Elimination 6144.3 Solve Mixture Applications with Systems of Equations 41111.1 Systems of Linear Equations: Two Variables 10289.1 Systems of Linear Equations: Two Variables 922
5.4 Solve Applications with Systems of Equations 6294.4 Solve Systems of Equations with Three Variables 42511.2 Systems of Linear Equations: Three Variables 10479.2 Systems of Linear Equations: Three Variables 941
5.5 Solve Mixture Applications with Systems of Equations 6484.5 Solve Systems of Equations Using Matrices 43811.3 Systems of Nonlinear Equations and Inequalities: Two Variables 10599.3 Systems of Nonlinear Equations and Inequalities: Two Variables 953
5.6 Graphing Systems of Linear Inequalities 6614.6 Solve Systems of Equations Using Determinants 45211.4 Partial Fractions 10719.4 Partial Fractions 965
4.7 Graphing Systems of Linear Inequalities 46611.5 Matrices and Matrix Operations 10819.5 Matrices and Matrix Operations 975
Polynomials 853Polynomials 685Polynomials and Polynomial Functions 49311.6 Solving Systems with Gaussian Elimination 10949.6 Solving Systems with Gaussian Elimination 988
10.1 Add and Subtract Polynomials 8536.1 Add and Subtract Polynomials 6855.1 Add and Subtract Polynomials 49311.7 Solving Systems with Inverses 11089.7 Solving Systems with Inverses 1002
10.2 Use Multiplication Properties of Exponents 8656.2 Use Multiplication Properties of Exponents 7005.2 Properties of Exponents and Scientific Notation 50711.8 Solving Systems with Cramer's Rule 11239.8 Solving Systems with Cramer's Rule 1017
10.3 Multiply Polynomials 8806.3 Multiply Polynomials 7145.3 Multiply Polynomials 53212 Analytic Geometry 114710 Analytic Geometry 1041
10.4 Divide Monomials 8946.4 Special Products 7315.4 Dividing Polynomials 54912.1 The Ellipse 114810.1 The Ellipse 1042
10.5 Integer Exponents and Scientific Notation 9146.5 Divide Monomials 74412.2 The Hyperbola 116410.2 The Hyperbola 1058
10.6 Introduction to Factoring Polynomials 9326.6 Divide Polynomials 76312.3 The Parabola 118110.3 The Parabola 1075
6.7 Integer Exponents and Scientific Notation 77612.4 Rotation of Axes 119710.4 Rotation of Axes 1091
Factoring 807Factoring 57512.5 Conic Sections in Polar Coordinates 121210.5 Conic Sections in Polar Coordinates 1106
7.1 Greatest Common Factor and Factor by Grouping 8076.1 Greatest Common Factor and Factor by Grouping 57513 Sequences, Probability, and Counting Theory 123111 Sequences, Probability and Counting Theory 1125
7.2 Factor Trinomials of the Form x2+bx+c 8216.2 Factor Trinomials 58413.1 Sequences and Their Notations 123111.1 Sequences and Their Notations 1125
7.3 Factor Trinomials of the Form ax2+bx+c 8346.3 Factor Special Products 60313.2 Arithmetic Sequences 124611.2 Arithmetic Sequences 1140
7.4 Factor Special Products 8526.4 General Strategy for Factoring Polynomials 61713.3 Geometric Sequences 125811.3 Geometric Sequences 1152
7.5 General Strategy for Factoring Polynomials 8696.5 Polynomial Equations 62713.4 Series and Their Notations 126711.4 Series and Their Notations 1161
7.6 Quadratic Equations 88013.5 Counting Principles 128111.5 Counting Principles 1175
Rational Expressions and Equations 903Rational Expressions and Functions 65313.6 Binomial Theorem 129211.6 Binomial Theorem 1186
8.1 Simplify Rational Expressions 9037.1 Multiply and Divide Rational Expressions 65311.7 Probability 1193
8.2 Multiply and Divide Rational Expressions 9207.2 Add and Subtract Rational Expressions 67012 Introduction to Calculus 1215
8.3 Add and Subtract Rational Expressions with a Common Denominator 9337.3 Simplify Complex Rational Expressions 68512.1 Finding Limits: Numerical and Graphical Approaches 1215
8.4 Add and Subtract Rational Expressions with Unlike Denominators 9427.4 Solve Rational Equations 69712.2 Finding Limits: Properties of Limits 1227
8.5 Simplify Complex Rational Expressions 9567.5 Solve Applications with Rational Equations 71212.3 Continuity 1237
8.6 Solve Rational Equations 9697.6 Solve Rational Inequalities 73512.4 Derivatives 1252
8.7 Solve Proportion and Similar Figure Applications 984
8.8 Solve Uniform Motion and Work Applications 1000
8.9 Use Direct and Inverse Variation 1010
Roots and Radicals 1033Roots and Radicals 757
9.1 Simplify and Use Square Roots 10338.1 Simplify Expressions with Roots 757
9.2 Simplify Square Roots 10438.2 Simplify Radical Expressions 773
9.3 Add and Subtract Square Roots 10568.3 Simplify Rational Exponents 792
9.4 Multiply Square Roots 10668.4 Add, Subtract, and Multiply Radical Expressions 808
9.5 Divide Square Roots 10798.5 Divide Radical Expressions 821
9.6 Solve Equations with Square Roots 10938.6 Solve Radical Equations 834
9.7 Higher Roots 11118.7 Use Radicals in Functions 848
9.8 Rational Exponents 11278.8 Use the Complex Number System 857
Quadratic Equations 1155Quadratic Equations and Functions 883
10.1 Solve Quadratic Equations Using the Square Root Property 11559.1 Solve Quadratic Equations Using the Square Root Property 883
10.2 Solve Quadratic Equations by Completing the Square 11679.2 Solve Quadratic Equations by Completing the Square 896
10.3 Solve Quadratic Equations Using the Quadratic Formula 11839.3 Solve Quadratic Equations Using the Quadratic Formula 911
10.4 Solve Applications Modeled by Quadratic Equations 11979.4 Solve Quadratic Equations in Quadratic Form 925
10.5 Graphing Quadratic Equations in Two Variables 12089.5 Solve Applications of Quadratic Equations 933
9.6 Graph Quadratic Functions Using Properties 947
9.7 Graph Quadratic Functions Using Transformations 973
9.8 Solve Quadratic Inequalities 994
Exponential and Logarithmic Functions 1015
10.1 Finding Composite and Inverse Functions 1015
10.2 Evaluate and Graph Exponential Functions 1033
10.3 Evaluate and Graph Logarithmic Functions 1049
10.4 Use the Properties of Logarithms 1066
10.5 Solve Exponential and Logarithmic Equations 1079
Conics 1103
11.1 Distance and Midpoint Formulas; Circles 1103
11.2 Parabolas 1118
11.3 Ellipses 1139
11.4 Hyperbolas 1156
11.5 Solve Systems of Nonlinear Equations 1170
Sequences, Series and Binomial Theorem 1197
12.1 Sequences 1197
12.2 Arithmetic Sequences 1210
12.3 Geometric Sequences and Series 1221
12.4 Binomial Theorem 1238
對話式StewartPearson Algebra 2
第一冊
第一章 數與式
1-1（上） 乘法公式與有理數
1. 三次的乘法公式"1.3 Algebraic Expressions
■ Special Product Formulas
■ Special Factoring Formulas"
2. 有理數與分式（小數化為有理數，數線上的分點坐標）"11.3 Geometric Sequences
p.849, exa.7, Writing a Repeated Decimal as a Fraction
數線上的分點坐標"
1-1（下） 根式運算與實數
1. 根式的運算與化簡（根式的分母有理化，雙重根號的化簡）"1.2 Exponents and Radicals
■ Rationalizing the Denominator
雙重根號的化簡"
2. 實數與數線（無理數，數系及其代號，算幾不等式）"1.1 Real Numbers
■ Real Numbers
p.91, exe.139, Arithmetic-Geometric Mean Inequality (proof only)
無理數"
1-2 絕對值
1. 絕對值的定義與性質"1.1 Real Numbers
■ Absolute Value and Distance"
2. 絕對值方程式與不等式"1.5 Equations
p.55, exa.14, An Absolute-Value Equation
1.8 Inequalities
■ Absolute-Value Inequalities"
3. 絕對值函數及其圖形（補充）"2.2 Graphs of Functions
p.162, exa.5, Graph of the Absolute-Value Function"
1-3 指數與常用對數
1. 指數符號的拓展與指數律1.2 Exponents and Radicals
2. 科學記號與常用對數"1.2 Exponents and Radicals
■ Scientific Notation
常用對數"
第二章 直線與圓
2-1 坐標平面與直線方程式
1. 點的移動與直線的斜率1.10 Lines
2. 直線方程式1.10 Lines
2-2 直線方程式的應用
1. 點對直線的投影點、對稱點與點線距
2. 三角形的四心定義及求法
3. 二元一次不等式9.1 Systems of Linear Equations In Two Variables
2-3 圓方程式
1. 圓方程式"1.9 The Coordinate Plane; Graphs of Equations; Circles
■ Circles"
2. 圓內、圓外與半圓
2-4 圓與直線的關係
1. 圓與直線的關係
2. 作圓的切線"1.10 Lines
p.115, exe.86, Tangent Line to a Circle"
3. 圓系方程式
第三章 多項式
3-1 多項式的除法
1. 多項式的概念與運算
2. 除法及餘式定理、因式定理3.3 Dividing Polynomials
3. 求餘式的進階問題
3-2 多項式函數
1. 線型函數2.5 Linear Functions and Models
2. 二次函數的圖形與極值3.1 Quadratic Functions and Models
3. 三次函數的圖形
4. 多項式函數的大域特徵與局部特徵
3-3 多項式不等式3.7 Polynomial and Rational Inequalities
1. 圖解不等式
2. 解二次不等式1.8 Inequalities
3. 高次不等式"3.7 Polynomial and Rational Inequalities
■ Polynomial Inequalities"
第二冊
第一章 數列與級數
1-1 數列與遞迴關係
1. 等差數列與等比數列"11.2 Arithmetic Sequences
11.3 Geometric Sequences"
2. 遞迴關係
3. 數學歸納法1.4 Mathematical Induction
1-2 級數求和
1. 等差級數與等比級數"11.2 Arithmetic Sequences
11.3 Geometric Sequences"
2. 級數性質與求和公式
第二章 排列組合與古典機率
2-1 邏輯、集合與計數原理
1. 敘述的否定、且與或、充分與必要
2. 集合的表法與相關符號"1.1 Real Numbers
■ Sets and Intervals"
3. 集合的運算與圖解"1.1 Real Numbers
■ Sets and Intervals"
4. 計數原理
2-2 排列11-1 Permutations
1. 階乘與相異物的直線排列
2. 重複排列
3. 有相同物的排列
2-3 組合與二項式定理
1. 組合C^n_r的定義與性質11-1 Combinations
2. 巴斯卡定理與二項式定理11.5 The Binomial Theorem5-7 The Binomial Theorem
2-4 古典機率與期望值
1. 樣本空間與事件、機率的定義與性質"11-2 Probability
11-3 Probability of Multiple Events
"
2. 試驗的期望值11-6 Analyzing Data
第三章 數據分析
3-1 一維數據分析
1. 未分組資料求均量與差量"11-6 Analyzing Data
11-7 Standard Deviation"
2. 資料的平移伸縮及標準化
3. 圖表判讀與百分位數
3-2 相關係數與迴歸直線
1. 數對的散步圖
2. 相關係數及迴歸直線
3. 資料的平移伸縮與標準化
第四章 三角比的性質與應用
4-1 極坐標與三角比的定義
1. 有向角與極坐標"8.1 Polar Coordinates
6.1 Angle Measure"
2. 三角比sin、cos、tan的定義"6.2 Trigonometry of Right Triangles
6.3 Trigonometric Functions of Angles"
4-2 三角比的性質
1. 商數關係與平方關係7.1 Trigonometric Identities
2. 角度變換---餘角、補角、角變號、加減180°
4-3 正弦定理與餘弦定理
1. 三角形面積基本公式與正弦定理"6.3 Trigonometric Functions of Angles
■ Areas of Triangles
6.5 The Law of Sines"
2. 正射影與餘弦定理6.6 The Law of Cosines
3. 三角形面積海龍公式與中線定理"6.6 The Law of Cosines
p.535, Heron's Formula"
4-4 反三角與三角測量
1. 鋭角三角比的查表與內插估計
2. 反三角的定義與性質"5.5 Inverse Trigonometric Functions and Their Graphs
6.4 Inverse Trigonometric Functions and Right Triangles"
3. 三角測量的名詞定義與解題步驟"6.6 The Law of Cosines
■ Navigation: Heading and Bearing"
第三冊
第一章
1-1 弧度、扇形與三角比
1. 弧度與扇形6.1 Angle Measure
2. 三角比cot、sec、csc及其關係"6.2 Trigonometry of Right Triangles
6.3 Trigonometric Functions of Angles"
1-2 和差角與倍半角公式
1. 和角公式與差角公式7.2 Addition and Subtraction Formulas
2. 二倍角與半角公式7.3 Double-Angle, Half-Angle, and Product-Sum Formulas
1-3 三角函數的圖形與正餘弦疊合
1. 三角函數的圖形及變化"5.3 Trigonometric Graphs
5.4 More Trigonometric Graphs"
2. 三角函數週期的變化"5.3 Trigonometric Graphs
p.432, Sine and Cosine Curves"
3. 正餘弦的疊合"7.2 Addition and Subtraction Formulas
■ Expressions of the Form A sin x + B cos x"
第二章 指數、對數函數
2-1 指數函數及其圖形
1. 指數函數4.1 Exponential Functions
2. 指數函數的圖形"4.1 Exponential Functions
■ Graphs of Exponential Functions"
3. 指數方程式與不等式"4.5 Exponential and Logarithmic Equations
■ Exponential Equations"
2-2 對數符號與對數律
1. 對數符號4.3 Logarithmic Functions
2. 對數律公式4.4 Laws of Logarithms
2-3 對數函數及其應用
1. 對數函數的圖形"4.3 Logarithmic Functions
■ Graphs of Logarithmic Functions"
2. 對數的方程式、不等式、極值與應用問題"4.5 Exponential and Logarithmic Equations
■ Logarithmic Equations"
第三章 平面向量
3-1 平面向量的加減法與係數積
1. 向量的定義及表法8.5 Vectors
2. 向量的加法與減法8.5 Vectors
3. 向量的係數積與平行向量8.5 Vectors
4. 線性組合、分點公式與共線定理
5. 三分點公式應用在重心與內心
3-2 平面向量的內積
1. 向量內積的定義與性質8.6 The Dot Product
2. 向量內積的應用
3-3 直線的向量性質與二階行列式
1. 坐標平面上直線的參數式與點法式
2. 二階行列式的定義與性質9.6 Determinants and Cramer's Rule
3. 二階行列式的應用
第四冊
第一章 空間向量
1-1 空間概念
1. 空間中點、線、面的關係
2. 三垂線定理與二面角
1-2 空間坐標與向量
1. 空間坐標系與兩點的距離、中點與分點
2. 空間向量的加減法與係數積
1-3 空間向量的內積
1. 內積的計算及其性質
2. 內積的應用
1-4 外積與三階行列式
1. 外積的定義、性質及其應用
2. 三階行列式的定義及性質
3. 三階行列式的應用
第二章 空間中的平面與直線
2-1 空間中的平面
1. 平面方程式
2. 兩平面的關係與點面距公式
2-2 空間中的直線方程式
1. 直線的參數式、比例式與兩面式
2. 空間中直線與點、線、面的關係
第三章 條件機率與獨立事件
3-1 條件機率
1. 條件機率
2. 乘法法則、分割與貝氏定理
3-2 獨立事件
1. 獨立事件的定義及性質
第四章 矩陣
4-1 聯立方程的矩陣表達
1. 加減消去法與三平面的相交情形
2. 聯立方程的增廣矩陣與列運算求解
4-2 矩陣的四則運算
1. 矩陣的表示、加減法與係數積
2. 矩陣的乘法及其性質
4-3 反方陣與轉移方陣
1. 反方陣及其性質
2. 轉移方陣
4-4 平面的線性變換
1. 線性變換
2. 旋轉方陣
3. 三大基本變換---鏡射、伸縮、推移
選修數甲
第一章 極限
1-1 數列的極限
1-2 無窮級數的收斂與發散
1-3 函數及其極限
第二章 多項式函數的微分
2-1 導數與導函數
2-2 函數的增減與凹向
第三章 多項式函數的積分
3-1 積分的意義
3-2 積分的應用
第四章 複數與複數平面
4-1 多項方程式
4-2 複數平面與極式
第五章 二次曲線
5-1 拋物線
5-2 橢圓
5-3 雙曲線
第六章 隨機變數與機率分布
6-1 隨機變數的期望值與標準差
6-2 二項分布與幾何分布
第1冊
第1章 整數的運算
1-1 負數與數線
1-2 整數的加減
1-3 整數的乘除與四則運算
1-4 指數記法與科學記號
第2章 分數的運算
2-1 因數與倍數
2-2 最大公因數與最小公倍數
2-3 分數的四則運算
2-4 指數律
第3章 一元一次方程式
3-1 代數式的化簡
3-2 一元一次方程式
3-3 應用問題
第2冊
第1章 二元一次聯立方程式
1-1 二元一次方程式
1-2 解二元一次聯立方程式
1-3 應用問題
第2章 直角坐標與二元一次方程式的圖形
2-1 直角坐標平面
2-2 二元一次方程式的圖形
第3章 比與比例式
3-1 比例式
3-2 正比與反比
第4章 一元一次不等式
4-1 認識一元一次不等式
4-2 解一元一次不等式
第5章 統計
5-1 統計圖表與資料分析
第6章 生活中的幾何
6-1 垂直、線對稱與三視圖
第3冊
第1章 乘法公式與多項式
1-1 乘法公式
1-2 多項式與其加減運算
1-3 多項式的乘除運算
第2章 平方根與畢氏定理
2-1 平方根與近似值
2-2 根式的運算
2-3 畢氏定理
第3章 因式分解
3-1 利用提公因式與乘法公式做因式分解
3-2 利用十字交乘法做因式分解
第4章 一元二次方程式
4-1 因式分解解一元二灰方程式
4-2 配方法與公式解
4-3 應用問題
第5章 統計資料處理
5-1 資料整理與統計圖表
第4冊
第1章 數列與級數
1-1 等差數列
1-2 等差級數
1-3 等比數列
第2章 函數
2-1 函數與函數圖形
第3章 三角形的基本性質
3-1 三角形與多邊形的內角與外角
3-2 尺規作圖
3-3 三角形的全等性質
3-4 垂直平分線與角平分線的性質
3-5 三角形的邊角關係
第4章 平行與四邊形
4-1 平行
4-2 平行四邊形
4-3 特殊四邊形的性質
第5冊
第1章 相似形
1-1 連比例
1-2 比例線段
1-3 縮放與相似
1-4 相似三角形的應用
第2章 圓
2-1 點、直線與圓之間的位置關係
2-2 圓心角、圓周角與弧的關係
第3章 幾何與證明
3-1 證明與推理
3-2 三角形的外心、內心與重心
第6冊
第1章 二次函數
1-1 二次函數的圖形與最大值、最小值
第2章 統計與機率
2-1 資料的分析
2-2 機率
第3章 生活中的立體圖形
3-1 空間中的線、平面與形體
龍騰數A數B數甲數乙章節對照
數3A數3B
單元01-弧度量單元01-弧度量
單元02-三角函數的圖形單元02-週期性數學模型
單元03-三角的和差角公式
單元04-正餘弦的疊合
單元05-指數函數單元03-指數函數
單元06-對數與對數律單元04-對數
單元07-對數函數單元05-對數函數
單元08-平面向量單元06-平面向量
單元09-平面向量的運算單元07-平面向量的運算
單元10-二元一次聯立方程式
數4A數4B
單元01-空間概念單元01-空間概念
單元02-空間向量的坐標表示法單元02-空間坐標系
單元03-空間向量的運算
單元04-三階行列式
單元05-空間中的平面單元03-平面上的比例
單元06-空間中的直線
單元07-條件機率與貝氏定理單元04-條件機率
單元08-三元一次聯立方程式單元05-貝氏定理
單元09-矩陣的運算單元06-矩陣的運算
單元10-矩陣的應用單元07-矩陣的應用
單元08-圓錐曲線
數甲上數乙上
單元01-數列的極限與無窮等比級數單元01-數列的極限與無窮等比級數
單元02-函數與函數的極限單元02-函數與函數的極限
單元03-微分單元03-微分
單元04-函數性質的判定單元04-函數性質的判定
單元05-積分單元05-積分
單元06-積分的應用單元06-積分的應用
數甲下數乙下
單元01-離散型隨機變數單元01-離散型隨機變數
單元02-二項分布與幾何分布單元02-二項分布
單元03-複數與多項式方程式單元03-複數與複數平面
單元04-複數的幾何意涵單元04-多項式方程式的根
單元05-拋物線單元05-線性規劃
單元06-橢圓
單元07-雙曲線

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