本書是為國際文憑課程大學預科項目（IBDP）設計的數學輔導書，內容涵蓋了IB標準難度的所有主題和高難度的前6個主題。全書分為20個模塊，每個模塊由Summary，Examples和Exercises這3部分組成。Summary給出本模塊所用的數學概念；Examples提供大量的例題解法演示Exercises包含的習題有助于復習鞏固數學概念和解題技巧。在本書的最后有6幅思維導圖，可幫助學生明確數學概念，理清數學脈絡。
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 of and
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 of and
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
