Life of Fred: High School Advanced Algebra Expanded Edition
ISBN: 9781937032135; Hardcover
Advanced Algebra: Expanded Edition is the second book in the Life of Fred High School Mathematics Series, and is designed for students in 10th grade who have already finished the preceding Beginning Algebra, Expanded Edition. This new edition of Algebra replaces the both the earlier Life of Fred Advanced Algebra and Fred's Home Companion Advanced Algebra books; it also contains all problems completely worked out. The sold-separately Zillions of Practice Problems for Advanced Algebra book is an optional resource for students who want more practice opportunities.
Ten chapters with multiple sub-lessons (105 total) are included. Each lesson ends with a "Your Turn to Play" segment with a small number of thought-provoking questions. Answers are provided on the next page for students to go over themselves after attempting to solve the problems. Chapters conclude with three problem sets, each of which is named after a city. This full-year curriculum will provide students with a thorough knowledge of Algebra II, and should be used directly after finishing Beginning Algebra. To ensure students are adequately prepared, a placement exam is provided at the beginning.
Advanced Algebra covers: Ratios, Median averages, Proportions, Dividing by zero, Cross-multiplying, Constants of proportionality, Inverse variation, Direct variation, Joint variation, Weight varies directly as the cube of the height, Area varies directly as the square of the height, Volume varies directly as the cube of the height, Laws of exponents, Rationalizing the denominator, Pythagorean theorem, Solving radical equations, Surface area of a cone, A Brief History of mathematics, Natural numbers, Whole numbers, Integers, Irrational numbers, Real numbers, Imaginary numbers, Complex numbers, Velocity, Conversion factors, Unit analysis, Venn diagrams, Union of sets, Disjoint sets, Subsets, Intersection of sets, Significant digits in addition and multiplication, Scientific notation, Exponential equations, Logarithms, Product, quotient, birdie, and power rules for logarithms, Using a scientific calculator, Finding antilogs, Three definitions of logarithms, Change-of-base rule for logarithms, Graphing, Abscissa, Ordinate, Quadrants, Slope, Slope given two points, Slope-intercept and double-slope forms of the line, Slopes of perpendicular lines, Multiplying binomials, Factoring binomials, Factoring a difference of squares, Factoring trinomials, Adding, subtracting, multiplying and dividing polynomial fractions, Complex fractions, Linear equations, Quadratic equations, Radical equations, Systems of Equations, Inconsistent, dependent and independent equations, Graphing planes in three dimensions, Cramer's rule, Determinants, Ellipses, Circles, Reflective property of ellipses, Parabolas, Hyperbolas, Graphing inequalities, Definition of a function, Domain, Codomain, Range, Functional notation, One-to-one, Onto, Inverse functions, Ordered pairs, Long division of polynomials, Partial fractions, Proofs by math induction, Linear Programming, Arithmetic progressions, and series, Adding and multiplying matrices, Geometric sequences and progressions, Sigma notation, Fundamental principle of counting, Factorial, Permutations, Combinations, Binomial formula, Pascal's Triangle.
Life of Fred is a unique, complete (not supplemental), math program that uses a highly engaging narrative to teach math without fear and with enjoyment. Students follow the life of Fred Gauss (a math professor who grows up to the age of six), who has many humorous, unlikely, and zany adventures over the course of the curriculum.