ALGEBRA II BY HEART

TABLE OF CONTENTS


PART I
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 operations.
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 factoring.
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.

PART II
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 Problem #9.
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.

PART III
SESSION 35: (PAGE 201) Circles.
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.
SESSION 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 composition.
SESSION 44: (PAGE 271) Inverse functions.
SESSION 45: Go over Session 44 homework. End Part III.

PART IV
SESSION 46: (PAGE 278) Exponential functions, e.
SESSION 47: (PAGE 283) Logarithms.
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 unknowns.
SESSION 51: (PAGE 315) Solving systems of linear equations in three equations in three unknowns.
SESSION 52: (PAGE 322A) Systems of linear inequalities and their graphs.
SESSION 53: Go over Session 52 homework. End Part IV.
SELECTED ANSWERS (PAGE 323)
BASIC KNOWLEDGE QUESTIONS (PAGE 343)

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