《mathematics - hl & sl for the ib diploma》是2016年上海科學技術出版社出版的圖書，作者是Yu Song。
本書涵蓋了高級課程的前六個主題以及標準課程的所有主題，是IB課本和教學大綱的補充，包含了IB考試中*常出現的題型。本書可以幫助IB學生有效地準備IB學業考試。
基本介紹
- 中文名：mathematics - hl & sl for the ib diploma
- 作者：Yu Song
- 出版社：上海科學技術出版社
- ISBN：9787547827260
內容簡介,圖書目錄,作者簡介,
內容簡介
本書主要是為IB文憑項目數學高級課程和標準課程的學生編寫的。IB I SEE的IB是國際文憑組織的縮寫，I代表讀者，SEE代表總結、例題和習題，這也是本書每個單元的主要模組。本書涵蓋了高級課程的前六個主題以及標準課程的所有主題，是IB課本和教學大綱的補充，包含了IB考試中常出現的題型。本書可以幫助IB學生有效地準備IB學業考試。
圖書目錄
1 Function characters
Summary
Examples
A.Domain and range
B.Odd and even functions
C.Composite and inverse functions
Exercises
2 Function transformations
Summary
Examples
A.Dilation, reflection and translation
B.Graphs of1f(x),fx and|fx|
Exercises
3 Exponents and logarithms
Summary
Examples
A.Exponents and exponential equations
B.Logarithms and logarithmic equations
Exercises
4 Basic functions
Summary
Examples
A.Linear and quadratic functions
B.Polynomial and rational functions
C.Exponential and logarithmic functions
Exercises
5 Trigonometric identities
Summary
Examples
A.Definitions of trigonometric ratios
B.Pythagorean identities
C.Compound angle identities
D.Double and half angle formulas
Exercises
6 Trigonometric functions
Summary
Examples
A.Graph of trigonometric functions
B.Trigonometric equations
C.Inverse trigonometric functions
Exercises
7 Lengths and areas in circles and triangles
Summary
Examples
A.Lengths (arc length, radius and perimeter)
B.Areas (area of a sector, area of a triangle and area of a segment)
C.The sine rule and its ambiguous case
D.The cosine rule
Exercises
8 Vectors and their operations
Summary
Examples
A.Using vectors to find area of a triangle
B.Parallel and perpendicular vectors
Exercises
9 Complex numbers
Summary
Examples
A.Operations of complex numbers
B.Modulus and argument of a complex number
C.Cartesian form, Modulus-argument form and Euler’s form
D.Conjugate of a complex number
E.De Moivre’s theorem
F.th roots of a complex number
Exercises
10 Lines and planes
Summary
Examples
A.Lines
B.Planes
Exercises
11 Sequences and series
Summary
Examples
A.Arithmetic sequences and series
B.Geometric sequences and series
C.Compound interests and population
Exercises
12 Differentiation
Summary
Examples
A.Limit, convergence and continuity
B.First principles
C.Simple rules of differentiation
D.Chain rule, product rule and quotient rule
E.& Implicit differentiation
F.The equations of tangents and normals
G.The second and higher derivatives
Exercises
13 Integration
Summary
Examples
A.Simple rules of integration
B.Integral of
C.Integral of trigonometric functions
D.Integral by substitution
E.Integral by parts
Exercises
14 Applications of calculus
Summary
Examples
A.Rate of change and related rate of change
B.Graphical behaviors of a function
C.Optimisation
D.Areas and volumes
E.Kinematics
Exercises
15 Statistics
Summary
Examples
A.Measurement of the center and spread of a data set
B.Frequency distribution table
C.Histogram
D.Cumulative frequency table and graph
E.Boxplot
F.& The relationship between variance and mean
G.T Correlation and linear regression
Exercises
16 Counting principles
Summary
Examples
A.Sum and product principles
B.Permutation and combination
Exercises
17 Probability Calculation
Summary
Examples
A.Tree diagram and Venn diagram
B.2-dimensional table or 2-dimensional grids
C.Independent events and mutually exclusive events
D.Conditional probability
Exercises
18 Binomial expansion
Summary
Examples
A.Pascal triangle and binomial coefficients (binomial theorem)
B.Coefficients and terms in the binomial expansion
C.Coefficients and terms in the product of binomial expansions
Exercises
19 Probability distributions
Summary
Examples
A.Discrete distribution
B.Continuous distribution
C.Binomial distribution
D.Poisson distribution
E.Normal distribution
Exercises
20 Mathematical induction
Summary
Examples
A.Divisibility
B.Sequences and series
C.Differentiation
Exercises
Answers to Exercises
作者簡介
作者吳斌是一位有8年IB數學教學經驗的教師，同時也是IB的助理考官。
作者於嵩有7年的DP數學高級課程和標準課程的教學經驗，同時也是IB高級課程試卷二和探索研究的助理考官，是上海世界外國語中學的DP數學部的主任。
