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January 27th, 2011, 10:32 PM   #1
Joined: Jan 2011

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Book for recommendation?

Looking for quality textbook(s) that covered all these 17 topics in preparation for an university entrance exam in near future, thanks.

1. Equations and inequalities
(1) Numbers and expressions
1) Real numbers
2) Expansion and factorization of a polynomial
(2) Linear inequalities
(3) Quadratic equations

2. Quadratic functions
(1) Quadratic functions and its graphs
(2) Variation in values of quadratic functions
1) Maximum value and minimum value of a quadratic function
2) Quadratic inequalities

3. Figures and measurements
(1) Trigonometric ratios
1) Sine, cosine, tangent
2) Relations between trigonometric ratios
(2) Trigonometric ratios and figures
1) Sine formulas, cosine formulas
2) Measurement of figures

4. Plane figures
(1) Properties of triangles
(2) Properties of circles

5. Set theory and logic
(1) Sets and the number of elements
(2) Propositions and proofs

6. The number of possible outcomes and probability
(1) Permutations, Combinations
(2) Probability and its fundamental laws
(3) Independent trials and probability

7. Expressions and proofs/Equations of higher degree
(1) Expressions and proofs
1) Division of polynomials, fractional expressions
2) Proofs of equalities and inequalities
(2) Equations of higher degree
1) Complex numbers and quadratic equations
2) Equations of higher degree

8. Figures and equations
(1) Points and lines
1) Coordinates of a point
2) Equation of a line
(2) Circles
1) Equation of a circle
2) Relative position of a circle and a line

9. Various functions
(1) Trigonometric functions
1) General angles
2) Trigonometric functions and their basic properties
3) Addition theorems for trigonometric functions
(2) Exponential and logarithmic functions
1) Expansion of exponents
2) Exponential functions
3) Logarithmic functions

10. The concept of differentiation/integration
(1) The concept of differentiation
1) Differential coefficients and derivatives
2) Applications of the derivative
Tangent lines, increase/decrease in function value
(2) The concept of integration
1) Indefinite integrals and definite integrals
2) Areas of figures

11. Sequences (Progressions) of numbers
(1) Sequences and their sums
1) Arithmetic sequences (Arithmetical progressions) and geometric sequences (geometrical progressions)
2) Various sequences
(2) Recurrence formulae and mathematical induction
1) Recurrence formulae and sequences
2) Mathematical induction

12. Vectors
(1) Vectors in a plane
1) Vectors and their operations
2) Scalar product (Inner product) of vectors
(2) Space coordinates and vectors
Space coordinates and vectors in a space

13. Limits
(1) Limits of sequences
1) Limit of {r n}
2) Sum of an infinite geometric series
(2) Functions and their limits
1) Composite functions and inverse functions
2) Limit of value of a function

14. Differential calculus
(1) Derivatives
1) Derivatives of the sum/difference/product/quotient of two functions
2) Derivatives of composite functions
3) Derivatives of trigonometric functions, exponential functions, logarithmic functions
(2) Applications of the derivative
Tangent lines, increase/decrease in value of functions, velocity, acceleration

15. Integral calculus
(1) Indefinite integrals and definite integrals
1) Integrals and their basic properties
2) Integration by substitution, integration by parts
3) Integrals of various functions
(2) Applications of integration
Area, volume

16. Matrices and their applications
(1) Matrices
1) Matrices and operations on them
Sum, difference, and scalar multiple
2) Product of matrices, inverse matrices
(2) Applications of matrices
1) Systems of linear equations
2) Translation of a point

17. Expressions and curves
(1) Quadratic curves
1) Parabolas
2) Ellipses and hyperbolas
(2) Parametric representations
Parametric representation of a curve
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