MATH102: Advanced Problems in Pre-Algebra (Part 2)

  • Challenging Math
  • Level 2
  • Hardware/Software/Books Required?

    PC/Mac with high speed internet and internal/external Microphone
    Prealgebra Book

Course Description

This course is for students who have completed an elementary school (grades 1-5) math curriculum and is a continuation of Prealgebra 1 with more advanced topics. Students can try the Prealgebra 2 "Are You Ready?" diagnostic test to see if they are prepared to take this course. Prealgebra 2 covers the fundamentals of arithmetic, including percentages, angles, and square roots. We also introduce topics in geometric theory and statistics which include Pythagorean's Theorem, averages, and probability calculation.

Pretest download link: https://data.artofproblemsolving.com/course-docs/diagnostics/prealgebra2-pretest.pdf

Topic 1 Introduction to Percents
  • Definition of percent
  • Relationships among percents, fractions, and decimals
  • Percents of numbers
  • Basic percent word problems
Topic 2 Percent Increase and Decrease
  • More percent word problems
  • Percentage increase and decrease
Topic 3 Squares and Square Roots
  • Definition of square root
  • Equations with square roots
  • Non-integer square roots
Topic 4 Arithmetic with Square Roots
  • Products and quotients of square roots
  • Simplification of square roots
  • Sums and differences of square roots
Topic 5 Angles and Parallel Lines
  • Angle measurement
  • Parallel lines
Topic 6 Angles in Polygons
  • Angles in a triangle
  • Angles in other polygons
Topic 8 More Triangles and Circles
  • Triangle area
  • Circumference of a circle
  • Area of a circle
  • Unusual areas
Topic 9 Pythagorean Theorem
  • Pythagorean Theorem fundamentals
  • Pythagorean triples
Topic 10 Special Triangles
  • Challenging Pythagorean Theorem problems
  • 30-60-90 and 45-45-90 triangles
Topic 11 Quadrilaterals
  • Types of quadrilaterals
  • Quadrilateral area
Topic 12 Basic Statistics
  • Average (mean)
  • Averages as a balancing act
  • Median, mode, and range
Topic 13 Statistics, Graphs, and Charts
  • Limits of basic statistics
  • Types of graphs and charts
Topic 14 Counting as Arithmetic
  • Numbers in lists
  • Venn diagrams
  • Multiplication principle
  • Casework
Topic 15 Counting and Probability
  • Pairs
  • Introduction to probability
Topic 16 Problem-Solving Strategies
  • Find a pattern
  • Make a list
  • Draw a picture
  • Work backwards