MATH101: Advanced Problems in Pre-Algebra

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.

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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