__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)**

Math
Trilogy Page

Algebra
II Logic
for Understanding Mathematics Calculus
I

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