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Introduction..............................................................................................xiii

1: Algebra...................................................................................................1

1.1: Variables and Equations...................................................................2Variables, Consecutive Integers, d=rt, HarmonicMean, Moles Digging Holes.

1.2: Linear Equations.............................................................................10Slope, Intercepts, Slope-Intercept Form, Point-Slope Form, Standard Form, Parallel/Perpendicu-lar Lines, Horizontal and Vertical Lines.

1.3: Systems of Equations.....................................................................16Substitution, Elimination, Common WordProblems, Cheating the System.

1.4: Ratios, Proportions, and Percents..................................................23Ratios, Proportions, Percents, and Percent ofChange.

Review 1.1 to 1.4......................................................................................301.5: Distribution.......................................................................................31

The Distributive Property, Difference of Squaresand Perfect Squares, Sum of the Reciprocals.

1.6: Quadratics.......................................................................................35Perfect Squares, Difference of Squares, FactoringBy Grouping, Solving Quadratics by Factoring,The Quadratic Formula, Word Problems, Sum andProduct of the Roots.

1.7: Exponents and Radicals.................................................................44Multiplying, Dividing, Raising a Power to aPower, Fractional Exponents, Square Roots.

1.8: Statistics..........................................................................................49Mean, Median, Mode and Range.

1.9: Sequences and Series.....................................................................52Arithmetic Sequences and Series,Geometric Sequences and Series.

1.10: More Substitution.........................................................................58Nested Square Roots, Continued Fractions.

Chapter Review........................................................................................60

2: Counting..............................................................................................63

2.1: Basics................................................................................................64Simple Counting Techniques.

2.2: Venn Diagrams.................................................................................67Two and Three-Set Venn Diagrams.

2.3: Bowling Pins and Handshakes......................................................70Triangular Number Patterns.

2.4: Counting Outcomes.........................................................................73The Fundamental Counting Principle.

2.5: Casework..........................................................................................75Keeping Organized.

Review 2.1 to 2.5......................................................................................772.6: Factorials and Permutations...........................................................78

Factorials, Permutations, Permutations withRestrictions.

2.7: Combinations...................................................................................84Combinations, Paths on a Grid, Beyond Case-work, Complementary Counting.

Review 2.1 to 2.7......................................................................................912.8: Sticks and Stones...........................................................................93

With and Without Restrictions.2.9: Pascals Triangle...............................................................................97

Combinations and Pascals Triangle.Chapter Review........................................................................................100

3: Probability........................................................................................103

3.1: Probability Basics..........................................................................104Compound Events, Dependent and Independent,Replacement, Cards.

3.2: Compound Events and Counting...............................................111Combining Counting Techniques and CompoundProbability.

3.3: Casework and Probability.............................................................1143.4: Probability and Combinations....................................................1163.5: Complementary Counting and Probability................................118Review 3.1 to 3.5......................................................................................1203.6: Geometric Probability....................................................................1213.7: Expected Value..............................................................................124

Finding the average outcome.Chapter Review........................................................................................126

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4: Number Theory.........................................................................129

4.1: Primes and Divisibility..................................................................130Sieve of Eratosthenes, Primes, Divisibility Rules.

4.2: Factors............................................................................................137The Fundamental Theorem of Arithmetic, FactorCounting.

4.3: Factor Tricks..................................................................................143Product of the Factors, Sum of the Factors, GCFand LCM, Factorials.

Review 2.1 to 2.5......................................................................................1544.4: Different Bases.............................................................................155

Notation, Basic Arithmetic.4.5: The Units Digit.............................................................................159

Addition, Multiplication, Perfect Squares,Exponents.

4.6: Fractions and Decimals................................................................163Repeating/Terminating, Conversions.

4.7: Modular Arithmetic......................................................................167Chapter Review........................................................................................172

5: Geometry......................................................................................175

5.1: Geometry Basics...........................................................................176Lines, Angles, Triangles, Polygons, Trapezoids,Parallelograms, Kites.

5.2: Circles.............................................................................................185Chords, Secants, Tangents, Arcs, InscribedAngles, Properties, Circumference and ArcLength.

5.3: Pythagorean Theorem..................................................................193Triples, Special Right Triangles, DistanceFormula, Algebra and the Pythagorean Theorem.

5.4: Area.................................................................................................204Formulas, Herons Formula, Altitudes, WorkingBackwards.

5.5: Three-Dimensional Geometry......................................................208Polyhedra, Faces, Vertices, and Edges, Volume.

5.6: Similarity.........................................................................................215Right Triangles, Circles, Parallel Lines, Area andVolume Relationships.

Chapter Review........................................................................................226

6: Solutions...........................................................................................229

AlgebraKey..........................................................................................230Solutions................................................................................232

CountingKey..........................................................................................260Solutions................................................................................261

ProbabilityKey..........................................................................................288Solutions................................................................................289

Number TheoryKey..........................................................................................308Solutions................................................................................310

GeometryKey..........................................................................................334Solutions................................................................................336

7: Appendix.............................................................................................363Useful Lists and Formulas.

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