Math Exam

• Mixed numbers


  A number that has both an integer and a fraction part
• Adding mixed numbers


  1. Convert to improper fractions

  2. Find a common denominator

  3. Add numerators

  4. Convert back to mixed numbers
• Subtracting mixed numbers


  1. Convert to improper fractions

  2. Find a common denominator

  3. Subtract numerators

  4. Convert back to mixed numbers
• Using a number line for addition and subtraction

  1. Addition: Start at first mixed number, move right by value of second

  2. Subtraction: Start at first mixed number, move left by value of second
• Multiplying mixed numbers


  1. Convert to improper fractions

  2. Multiply numerators

  3. Multiply denominators

  4. Simplify
• Dividing mixed numbers


  1. Convert to improper fractions

  2. Multiply by reciprocal of second fraction

  3. Simplify
• Multiplying a Mixed Fraction by itself

  Follow the same steps as for multiplication
• Learning God
• Evaluate Integer Expressions involving Order of Operations

  PEMBAS/BOOMAS Parentheses/Brackets Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
• Solve Step-by-Step Evaluate powers first then follow the order of operations


  1. Example 2+3x4

  2. Evaluate exponent 3² = 9

  3. Multiply 9x4 = 36

  4. Add 2+36 = 38
• Learning Goals


  • Using a Number Line to Represent Rational Numbers
  • Plot rational numbers on a number line according to their value
  • Representing a Rational Number as Decimals
  • Convert Fraction to Decimal Divide the numerator by the denominator
  • Representing a Rational Number Using a Number Line
  • Locate Value Identify the exact position on the number line corresponding to the decimal or fraction
• Learning Goals


  • Evaluate a Rational Number Expression
  • Follow the order of operations, treating rational numbers as fractions or decimals
  • Adding Rational Numbers to Fractions and Integers
  • Convert Integers and decimals to fractions if necessary find a common denominator, then add
  • Using the Order of Operations to Evaluate a Rational Number Expression
  • Apply PEMDAS/BOOMAS to expressions Involving rational numbers
• Learning Goals


  • Evaluating an Expression with Negative Decimal Bases
  • Raise the negative decimal to the given power
  • Evaluating an Expression with Negative Fraction Bases
  • Raise the negative fraction to the given power
  • Solving a Problem Involving Powers of Rational Numbers
  • Apply the rules of exponents to rational numbers, whether they are fractions or decimals
• Learning Goals


  • Representing Algebraic Terms Geometrically
  • Visual Representation: Use geometric shapes (squares cubes) to visually represent algebraic terms
  • Area and Volume Models Relate the area of a square x and the volume of a cube x
  • Their algebraic counterparts
  • Connecting Squares and Square Roots
  • Square The Square of a number is that number multiplied by itself
  • Square Root The square root of a number is a value that, when multiplied by itself gives the original number
• Learning Goal


  • Develop and Apply Exponent Principles to Multiply and Divide Powers
  • Multiplication: When multiplying powers with the same base add the exponents
  • Division: When dividing powers with the same base, subtract the exponents
• Learning Goal


  • Simplify Expressions Involving Power of a Power
  • Exponentiation: When raising a power to another power, multiply the exponents
• Learning Goal


  • Add and Subtract Like Terms
  • Like Terms Terms that have the same variable raised to the same power
  • Addition/Subtraction: Combine the coefficients of like terms
• Learning Goal


  • Apply the Distributive Property to Polynomials
  • Distributive Property: Multiply each term in the polynomial by the monomial
• Learning Goal


  • Solve an Equation and Find the Value or Values of the Variable
  • Identify the Equation: Write down the equation
  • Isolate the Variable Use Inverse operations to isolate the variable on one side of the equation
  • Solve for the Variable Simplify the equation to find the value of the variable
  • Check the Solution: Substitute the solution back into the original equation to verify it
• Learning Goals


  • Solve Equations by Collecting Like Terms
  • Combine Like Terms Combine terms with the same variable on each side of the equation
  • Simplify the Equation: Use Inverse operations to isolate the variable
  • Solve Equations with Brackets
  • Distribute Apply the distributive property to remove brackets
  • Combine Like Terms: Simplify the equation
  • Solve for the Variable isolate the variable and solve
  • Solve Equations to Model a Geometric Relationship
  • Set Up the Equation Based on the geometric relationship set up the equation
  • Solve for the Variable Use appropriate algebraic methods to solve the equation
• Learning Goals


  • Simply Equations involving One Fraction
  • Multiply by the Denominator: Multiply both sides of the equation by the denominator to eliminate the fraction
  • Solve for the Variable Simplify and solve the resulting equation
  • Eliminate More Than One Fraction
  • Find the Lowest Common Denominator (LCD) Determine the LCD of all fractions involved
  • Multiply All Terms Multiply all terms on both sides of the equation by the LCD to clear the fractions
  • Solve for the Variable Simplify and solve the resulting equation
• Learning Goals


  • Rearrange a Formula in Terms of a Variable
  • Identify the Variable Determine which variable you need to isolate
  • Rearrange the Formula Use inverse operations to isolate the desired variable
  • Isolate the Term that Contains the Variable
  • Move Other Terms: Use Inverse operations to move other terms to the opposite side
  • Simplify Ensure the variable term is isolated on one side of the equation
• Direct Variation


  Relationship Between Two Variables Where One is a Constant Multiple of the Other
• Partial Variation


  Relationship Between Two Variables Where the Dependent Variable is the Sum of a Constant Number and a Constant Multiple of the Independent Variable
• Slope


  Measure of the Steepness of a Line
• Slope as a Rate of Change


  Change In One Variable Relative to the Change in Another (eg, km/h Expressed with Units)
• First Differences


  Differences Between Consecutive y-Values with Evenly Spaced x-Values, on a Given Table of Values
• The Equation of a Line In Slope-Intercept Form

  y=mx+b, where m is the slope and b is the y-intercept of the line
• Graph a Line using Intercepts

  Plot the x-intercept and y-intercept and draw a line through them
• Parallel and Perpendicular Lines

  Parallel lines have the same slope, perpendicular lines have slopes that are negative reciprocals
• Write the Equation of a Line Given the Slope and a Point

  Substitute the slope and point into the equation y=mx+b to solve for b