Integers –

• Definitions:
  • Integers are… Whole numbers and their opposites (ex. 5, -5)
• Addition & Subtraction
  • 64 + (-1.23)
  • (-7.8) – 5.73
• Multiplication & Division
  • 65 x (-2.5)
  • -4.71 1
• BEDMAS (brackets, exponents, division, multiplication, addition, subtraction). Ex;
  • -9.5 + 2.4 -6.8
  • [3.7 – (2.1)] x 9.5

Numbers –

• Definitions;
  • Rational and irrational numbers (rational = terminates or repeats, irrational = non-terminating, and non-repeating)
• How to identify Rational numbers out of a group of numbers. (ex. = 7 = 7.0 = 7/1, 14/2, etc.)
• Word problems;
  • On Saturday, the temperature at the Blood Reserve near Stand Off, AB decreased by 1.2 °C/h for 3.5 h. It then decreased by 0.9 °C/h for 1.5 h.
    • What was the total decrease in temperature?
    • What was the mean rate of decrease in temperature?
  • A hot air balloon climbed at 0.8 m/s for 10 s. It then descended at 0.6 m/s for 6 s.
    • What was the overall change in altitude?
    • What was the average rate of change in altitude?
  • Problem Solving with Rational Numbers in Fraction Form;
    • What is 4 as an improper fraction?
    • What is as a mixed number?
  • Square Roots of Rational Numbers
    • Definition of a perfect square?
      • A number is a perfect square if it can be expressed as the product of two equal rational factors. (ex. 0.5 x 0.5 = 0.25, therefore 0.25 is a perfect square.)
    • Evaluating expressions;
      • Estimating square roots –
        • Underestimating and overestimating

Exponents –

• Definitions;
  • Power: An expression made up of a base and an exponent.
  • Base: The number you multiply by itself in a power.
  • Exponent: The number of times you multiply the base in a power.
• Product Law
  • When we multiply exponent with the same base, we add the exponents.
• Quotient Law
  • When dividing exponents with the same base, we subtract the exponents.
• Power of a Power Law
  • When an exponent is raised to another exponent, we multiply the exponents.
• Zero Law
  • X⁰ = 1

Polynomials –

• Simplifying and collecting like terms
  • 2x² – 2x + 1 – x² + 4x – 3 = x² + 2x – 2
• Adding & subtracting polynomials
  • (X² – 5 + 2x) + (-3x – 2x² + 1) = -x² – x – 4
• Multiplying & dividing monomials
  • (2y) (2y) = 4y²
• Multiplying & dividing polynomials by monomials
  • (x) (-2x + 3) = -2x² + 3x
• Models (e.g. algebra tiles)
• Surface area
  • Length x Width x Height
  • 2y x 2y x 2y = 8y² (perfect square)