M101: Advanced Problems in Pre-Algebra Part 1

Math
Hardware/Software/Books Required?

PC/Mac with high speed internet and internal/external Microphone https://www.amazon.com/Prealgebra-Richard-Rusczyk/dp/1934124214

Course Description

This course is for advanced students who have completed an elementary school (grades 1-5) math curriculum and are eager for a more challenging mathematical experience. Students can try the Prealgebra 1 "Are You Ready?" diagnostic test to see if they are prepared to take this course. Prealgebra 1 covers the fundamentals of arithmetic, including fractions, exponents, and decimals. We also introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorization, basic equations and inequalities, and ratios.

Pretest download link:  https://data.artofproblemsolving.com/course-docs/diagnostics/prealgebra1-pretest.pdf

Topic 1	Arithmetic Rules Rigorous rules for addition and multiplication Longer, more complicated sums Gauss's clever summation technique Reciprocals Rigorous definition of division to set the stage for fractions
Topic 2	Exponents and Exponent Laws Squares and higher powers Products and quotients of powers Power of a power
Topic 3	Non-positive Exponents Zero as an exponent Negative exponents Extension of exponent laws to non-positive exponents
Topic 4	Multiples and Divisibility Principles of multiples Divisibility tests for 2, 3, 4, 5, 6, 8, 9
Topic 5	Primes and Prime Factorization Primes and composites Prime factorization Problem-solving with prime factorizations Infinitude of primes
Topic 6	Least Common Multiple (LCM) and Greatest Common Divisor (GCD) Common multiples and common divisors Definition of LCM and GCD Application of prime factorizations to LCM and GCD
Topic 7	Fractions Formal definition of fractions Fraction multiplication and division Fraction simplification Fraction comparison Fraction addition and subtraction Word problems with fractions
Topic 8	Linear Equations Expressions and Equations Expression simplification One- and two-step linear equations Basic word problems
Topic 9	Advanced Linear Equations and Word Problems Complicated linear equations More complex word problems Linear equations with no solution or with infinitely many solutions
Topic 10	Inequalities Principles of inequalities Inequalities on the number line Linear inequalities Word problems with inequalities
Topic 11	Decimal Arithmetic Definition of decimals Decimal addition, subtraction, multiplication, and division Decimal comparison
Topic 12	Decimals and Fractions Decimal approximation Conversion between decimals and fractions Rational numbers and their decimal representation
Topic 13	Ratio and Proportion Definition of ratio and proportion Proportional thinking Part-to-part and part-to-whole problem-solving Word problems with ratios and proportions
Topic 14	Conversion, Speed, and Other Rates Units and conversion factors Relationship between speed, distance, and time Joint work, relative speed, and average speed