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#### Pre-U Pure Mathematics

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Pre-U Pure Mathematics is a textbook which is specifically aimed at the international students in the pre-university foundation school of Jiangsu University. It has been developed following an extensive period of research and consultation with a large number of teachers and students, several of its chapters being already tried and tested in the foundation school, and it is intended to be usable both as a classroom resource and as a textbook to support self-motivated learners away for classroom.
This textbook covers all the requirements for Pure Mathematics from the laiest pre-university level specifications and course requirements for the international students studying in China. From the very beginning, it has been conceived to be as clear and helpful as possible. It uses a concrete approach, introducing new concepts or revisiting older ones via extensive sets of worked examples and clear figures and diagrams, aiming at diminishing the discomfort which is often caused at this level by a more abstract approach and at developing a solid concept.ual basis on which deeper understanding can be built upon.
The presentation builds on a minimal amount of required knowledge, attempting to provide comprehensive explanations of all topics covered in a friendly, conversational style. The presentation is split into smaller units or modules, clearly labeled as such, each dealing with a single aspect, in clear progression. This makes for easier knowledge assimilation, one step at a time, and helps the reader proceed at a steady pace, while isolating the possible difficulties.
Chapter l Algebra I
1．1 Sets and numbers
1．1．1 Set theory
1．1．2 Rational and irrational numbers
1．1．3 Real numbers
1．2 Indices
1．2．1 Laws of indices
1．2．2 Properties of indices
1．2．3 Exponential equations
1．3 Polynomials
1．4 Factorization
1．6 Simultaneous equations
1．6．1 Simultaneous linear equations
1．6．2 Simultaneous equations: linear and non-linear
1．7 Summary
1．8 Further problems
Chapter 2 Coordinate Geometry
2, 1 Introduction
2．1．1 The distance between two points
2．1．2 The midpoint of a line segment
2．1．3 The slope of a line joining two points
2．2 Equations of a straight line
2．3 Inequalities
2．3．1 Symbols
2．3．2 Properties
2．3．3 Solving linear inequalities involving one variable
2．3．4 Solving linear inequalities involving two variables
2．4 The equation of a circle
2．4．1 Terminology
2．4．2 Cartesian coordinates
2．5 Summary
2．6 Further problems
Chapter 3 Functions
3．1 Mappings and functions
3．1．1 Relations and mappings
3．1．2 Functions
3．1．3 Four ways to represent a function
3．1．4 Injective, surjective and bijective functions
3．1．5 Piecewise-defined functions
3．2 Inverse functions
3．2．1How to find the inverse of a function
3．2．2 How to graph the inverse of a function
3．3 Composite functions
3．3．1 Arithmetic combinations of functions
3．3．2 Composition of functions
3．4 Transformation of graphs and functions
3．5 Odd, even and periodic functions
3．6 Exponentials
3．6．1 Graphs of exponential functions
3．6．2 Transformations of graphs of exponential functions
3．6．3 The natural base e
3．6．4 Properties of exponential functions
3．7 Logarithms
3．7．1 Graphs of logarithmic functions
3．7．2 Natural logarithmic functions
3．7．3 Properties of logarithmic functions
3．8 Summary
3．9 Further problems
……
Chapter 4 Algebra II
Chapter 5 Trigonometry
Chapter 6 Vectors
Chapter 7 Mathematical arguments and proofs

\$9.07