Algebra I
Concept - Syllabus
The Beverly Institute, Inc.

  1. Graph integers on a number line.
  2. Find the midpoint of the segment connecting two coordinates on a number line.
  3. Find the opposite of any real number.
  4. Find the absolute value of any real number.
  5. Add real integers
  6. Use the properties of real numbers when adding integers
  7. Rewrite subtraction as adding the opposite
  8. Subtract integers
  9. Multiply integers
  10. Identify and use the properties of multiplication when multiplying integers.
  11. Divide integers
  12. Demonstrate the division by 0 is undefined.
  13. Define exponent, base, and exponential form.
  14. Evaluate problems using the properties of exponents  
  15. Demonstrate the zero exponent rule and use it to evaluate exponential problems.
  16. Define Prime and Composite Numbers
  17. To factor any number into its prime factor.
  18. Greatest Common Factor and Least Common Multiple
  19. Identify the different number systems used in Algebra I.
  20. Classify numbers.
  21. Convert between decimal and fractional form.
  22. Add rational numbers.
  23. Subtract rational numbers.
  24. Multiply rational numbers.
  25. Divide rational numbers.
  26. Evaluate a numerical expression using the order of operations.
  27. Evaluate algebraic expression that contain grouping symbols.
  28. Insert grouping symbols in an algebraic expression to produce a specified answer.
  29. Identify the perfect square and their square, cube, and fourth root of numbers.
  30. Evaluate expressions with absolute value symbols, fraction bars, and radical signs using the order of
    operations.
  31. Identify sets using set notation.
  32. Identify the union and intersection of sets.
  33. Diagram one or more sets using a Venn Diagram.
  34. Identify and differentiate variables and constants in an algebraic expression.
  35. Translate basic English phrases into algebraic expressions.
  36. Translate varied English phrases into algebraic expressions.
  37. Convert between positive and negative exponents in an algebraic expression.
  38. Evaluate a problem by applying the laws of exponents to negative exponents.
  39. Evaluate an algebraic expression given values for the variables.
  40. Identify terms add like terms in an algebraic expression.
  41. Simplify an algebraic expression by combining like terms.
  42. Simplify algebraic expressions by removing grouping symbols.
  43. Apply formulas, given values for the variables.
  44. Determine if an equation is true of false.
  45. To recognize the properties of equality.
  46. Translate word sentences into algebraic equations.
  47. Reviewing the basic operations with algebraic numbers
     Order of Operations
     Addition Polynomials
     Subtraction of polynomials
             Removal of Parentheses
             Grouping Terms in Parentheses
             Collecting Coefficients
  • Using special cases of multiplication of multiply polynomials
     Multiplication of monomials to monomials
     Multiplication of monomials to polynomials
     Squaring a binomial produces a Perfect square Trinomial
     The product of a sum and difference produces a difference of Squares
     Foil     
  • Division of polynomials
     Division by Monomials                
     Division of polynomials
     Synthetic division
     Divide by inspection
  • Solving linear equations and inequalities (Positive and Negative)
  • Solving equations involving absolute values
  • Solving word problems
  • Identifying a common monomial factor
  • Factoring a perfect square trinomial and the difference of two squares.
  • Completing the Square
The Quadractic Trinomial
Trinomials of the General Form ax^2+bx=c
Polynomials Whose terms may be Grouped to show a common polynomial factor
Making a Perfect Square Trinomials in Order to factor A Difference of Squares
Summary of all Cases of Factoring
This is an 8th -9th Grade Class