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-Second Article-
Topics in PRECALCULUS
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11. The formal rules of algebra
12. Rational and irrational numbers
What is a rational number? Which numbers have rational square roots? The decimal representation of irrationals. What is a real number?
13. Functions
What is a function? Functional notation. A function of a function.
14. Introduction to graphs
The graph of a function. Coördinate pairs of a function. The height of the curve at x.
15. Basic graphs
The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function.
16. The vocabulary of polynomial functions
Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial.
17. The roots, or zeros, of a polynomial
The polynomial equation. The roots of a polynomial. The x- and y-intercepts of a graph. The relationship between the roots and the x-intercepts.
18. The slope of a straight line
Definition of the slope. Positive and negative slope. A straight line has only one slope. "Same slope" and "parallel." Perpendicular lines.The slope and one point specify a straight line.
19. Linear functions: The equation of a straight line
The equation of the first degree. The graph of a first degree equation -- a straight line. The slope-intercept form, and its proof.
10. Quadratics: Polynomials of the second degree
Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots.
11. Completing the square
Solving a quadratic equation by completing the square. The quadratic formula.
12. Synthetic division by x − a
The remainder theorem.
13. Roots of polynomials of degree greater than 2
The factor theorem. The fundamental theorem of algebra. The integer root theorem. Conjugate pairs.
14. Multiple roots. Point of inflection.
Concave upward, concave downward.
15. Reflections of a graph
Reflection about the x-axis. Reflection about the y-axis. Reflection through the origin.
16. Symmetry of a graph
Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry. Odd and even functions.
17. Translations of a graph
Definition of a translation. The equation of a circle. The vertex of a parabola. Vertical stretches and shrinks.
18. Rational functions
Singularities. The reciprocal function. Horizontal and vertical asymptotes.
19. Inverse functions
Definition of inverses. Constructing the inverse. The graph of an inverse function.
20. Logarithms
The system of common logarithms. The system of natural logarithms. The three laws of logarithms.
21. Logarithmic and exponential functions
22. Factorials
23. Permutations and Combinations
The Fundamental Principle of Counting. Factorial representations.
24. The binomial theorem
Pascal's triangle.
25. Multiplication of sums
A proof of the binomial theorem.
26. Mathematical induction
To view these pages as intended, it is best to view them with Internet Explorer 6 or Firefox 3, and with Garamond as the font.
11. The formal rules of algebra
12. Rational and irrational numbers
What is a rational number? Which numbers have rational square roots? The decimal representation of irrationals. What is a real number?
13. Functions
What is a function? Functional notation. A function of a function.
14. Introduction to graphs
The graph of a function. Coördinate pairs of a function. The height of the curve at x.
15. Basic graphs
The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function.
16. The vocabulary of polynomial functions
Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial.
17. The roots, or zeros, of a polynomial
The polynomial equation. The roots of a polynomial. The x- and y-intercepts of a graph. The relationship between the roots and the x-intercepts.
18. The slope of a straight line
Definition of the slope. Positive and negative slope. A straight line has only one slope. "Same slope" and "parallel." Perpendicular lines.The slope and one point specify a straight line.
19. Linear functions: The equation of a straight line
The equation of the first degree. The graph of a first degree equation -- a straight line. The slope-intercept form, and its proof.
10. Quadratics: Polynomials of the second degree
Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots.
11. Completing the square
Solving a quadratic equation by completing the square. The quadratic formula.
12. Synthetic division by x − a
The remainder theorem.
13. Roots of polynomials of degree greater than 2
The factor theorem. The fundamental theorem of algebra. The integer root theorem. Conjugate pairs.
14. Multiple roots. Point of inflection.
Concave upward, concave downward.
15. Reflections of a graph
Reflection about the x-axis. Reflection about the y-axis. Reflection through the origin.
16. Symmetry of a graph
Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry. Odd and even functions.
17. Translations of a graph
Definition of a translation. The equation of a circle. The vertex of a parabola. Vertical stretches and shrinks.
18. Rational functions
Singularities. The reciprocal function. Horizontal and vertical asymptotes.
19. Inverse functions
Definition of inverses. Constructing the inverse. The graph of an inverse function.
20. Logarithms
The system of common logarithms. The system of natural logarithms. The three laws of logarithms.
21. Logarithmic and exponential functions
22. Factorials
23. Permutations and Combinations
The Fundamental Principle of Counting. Factorial representations.
24. The binomial theorem
Pascal's triangle.
25. Multiplication of sums
A proof of the binomial theorem.
26. Mathematical induction
~PRECALCULUS~
In mathematics education, Precalculus, an advanced form of secondary school algebra, is a foundational mathematical discipline. It is sometimes considered to be an honors course. Courses and textbooks in precalculus are intended to prepare students for the study of calculus. Precalculus typically includes a review of algebra and trigonometry, as well as an introduction to exponential, logarithmic and trigonometric functions, vectors, complex numbers, conic sections, and analytic geo
In detail, precalculus deals with:
Sets
Real numbers
Complex numbers
Solving inequalities and equations
Properties of functions
Composite function
Polynomial functions
Rational functions
Trigonometry
Trigonometric functions and their inverses
Trigonometric identities
Conic sections
Exponential functions
Logarithmic functions
Sequences and series
Binomial theorem
Vectors
Parametric equations
Polar coordinates
Matrices
Mathematical induction
Limits metry. Equivalent college courses are college algebra and trigonometry
In detail, precalculus deals with:
Sets
Real numbers
Complex numbers
Solving inequalities and equations
Properties of functions
Composite function
Polynomial functions
Rational functions
Trigonometry
Trigonometric functions and their inverses
Trigonometric identities
Conic sections
Exponential functions
Logarithmic functions
Sequences and series
Binomial theorem
Vectors
Parametric equations
Polar coordinates
Matrices
Mathematical induction
Limits metry. Equivalent college courses are college algebra and trigonometry
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