SESSION 1: (PAGE 1)
Introduction, understanding definitions, set notation, natural
numbers, whole numbers, integers.
SESSION 2: (PAGE 7)
Rational numbers, irrational numbers, real numbers, subsets.
SESSION 3: (PAGE 13)
Union, intersection, closure, commutative, associative,
identities, distributive, inverses.
SESSION 4: (PAGE 19)
<, >, absolute value, left-right analysis, precedence of
SESSION 5: (PAGE 26)
Exponent laws, Jugular Problem #1.
SESSION 6: (PAGE 35)
Scientific notation, square root, nth roots.
SESSION 7: (PAGE 39)
Rational (fractional) exponents.
SESSION 8: (PAGE 46)
Perfect nth powers, rationalizing denominators, simplified form,
Jugular Problem #2, expressions with radicals.
SESSION 9: (PAGE 50)
Polynomials (add, subtract, multiply), FOILing.
SESSION 10: (PAGE 57)
More rationalizing of denominators, polynomial division including
long division of polynomials.
SESSION 11: (PAGE 62)
Factoring, group then factor, factoring quadratics by limited
trial and error.
SESSION 12: (PAGE 69)
Factoring a quadratic by reduce to “group then factor” method,
Mini-Jugular Problem #3, formulas for multiplying and
SESSION 13: (PAGE 74)
Factor completely, reducing rational expressions.
SESSION 14: (PAGE 78)
Least common multiple, smallest common denominator, adding
rational expressions, complex fractions, Jugular Problem #4.
SESSION 15: (PAGE 86)
Complex numbers (add, subtract, multiply), complex conjugate.
SESSION 16: (PAGE 91)
Division of complex numbers, Jugular Problem #5, operations
involving a negative under a square root.
SESSION 17: Go
over Session 16 homework. End Part I.
SESSION 18: (PAGE 95)
Solving equations, identities, inconsistent, and conditional
equations, equivalent equations.
SESSION 19: (PAGE
101) Extraneous solutions.
SESSION 20: (PAGE
105) Solving quadratics by factoring and completing the square.
SESSION 21: (PAGE
114) Solving quadratics by the quadratic formula, discriminant.
SESSION 22: (PAGE
119) Advanced solving by factoring, Jugular Problem #6.
SESSION 23: (PAGE
121) Solving equations with a square root, Jugular Problem #7.
SESSION 24: (PAGE126)
Solving equations in quadratic form, solving with unknown raised
to a fractional exponent.
SESSION 25: (PAGE
131) Word problems Part I.
SESSION 26: (PAGE
143) Word problems Part II.
SESSION 27: (PAGE
151) Open, closed, half-open intervals.
SESSION 28: (PAGE
156) Elementary solving inequalities.
SESSION 29: (PAGE
161) Intersection and union of intervals, absolute value removal
involving inequalities, Mini-Jugular Problem #8.
SESSION 30: (PAGE
167) Solving quadratic and other rational inequalities, Jugular
SESSION 31: (PAGE
178) Cartesian coordinate system, distance, midpoints.
SESSION 32: (PAGE
185) Slope of a line.
SESSION 33: (PAGE
191) Various equation forms for lines.
SESSION 34: Go
over Session 33 homework. End Part II.
SESSION 35: (PAGE
SESSION 36: (PAGE
206) Parabolas, Jugular Problem #10.
SESSION 37: (PAGE
218) Function basics and evaluating functions.
SESSION 38: (PAGE
223) Equations defining functions, finding domains and ranges.
SESSION 39: (PAGE
231) More range finding, piece-wise defined functions.
40: (PAGE 241) Sketching graphs via reflections, translations,
stretching and compressing graphs.
SESSION 41: (PAGE
249) Graphs of rational functions, horizontal and vertical
asymptotes, symmetry, even and odd functions.
SESSION 42: (PAGE
257) Graphing weapons, ellipses, hyperbolas.
SESSION 43: (PAGE
262) Function addition, subtraction, multiplication, division and
SESSION 44: (PAGE
271) Inverse functions.
SESSION 45: Go
over Session 44 homework. End Part III.
SESSION 46: (PAGE
278) Exponential functions, e.
SESSION 47: (PAGE
SESSION 48: (PAGE
288) Log graphs, log properties, Jugular Problem #11.
SESSION 49: (PAGE
301) Synthetic division, Remainder Theorem, Factor Theorem,
Fundamental Theorem of Algebra.
SESSION 50: (PAGE
309) Solving systems of linear equations in two equations in two
SESSION 51: (PAGE
315) Solving systems of linear equations in three equations in
SESSION 52: (PAGE
322A) Systems of linear inequalities and their graphs.
SESSION 53: Go
over Session 52 homework. End Part IV.
ANSWERS (PAGE 323)
KNOWLEDGE QUESTIONS (PAGE 343)
for Understanding Mathematics Calculus