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?
What is a function? The domain and the range.
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.
16. The vocabulary of polynomial functions
Variables versus constants.
17. The roots, or zeros, of a polynomial
A polynomial equation. The roots of a polynomial.
18. The slope of a straight line
Definition of the slope. Positive and negative slope. A straight line has only one slope.
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.
10. Quadratics: Polynomials of the second degree
Quadratic equation: Solution by factoring.
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.
Reflection about the x-axis. Reflection about the y-axis. Reflection through the origin.
Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry.
Definition of a translation.
Singularities. The reciprocal function.
Definition of inverses. Constructing the inverse.
The system of common logarithms.
21. Logarithmic and exponential functions
24. Permutations and Combinations
The Fundamental Principle of Counting.
A proof of the binomial theorem.
Copyright © 2021 Lawrence Spector
Questions or comments?