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Math 100 Survey of College Mathematics

  • Sample of what you should know before taking Math 100:
    1. Find the equation of the line (in both point-slope form and slope-intercept form) that goes through the points, open parenthesis 2 comma negative 1 close parenthesis and open parenthesis negative 6 comma 3 close parenthesis.
      • Solution
        First, find slope of the line using the formula m equals start fraction y 2 minus y 1 over x 2 minus x 1 end fraction:
        m equals start fraction 3 minus negative 1 over negative 6 minus 2 end fraction equals start fraction 3 plus 1 over negative 8 end fraction equals start fraction 4 over negative 8 end fraction equals start fraction negative 1 over 2 end fraction
        Now use either of the given points, say open parenthesis 2 comma negative 1 close parenthesis and the slope m equals start fraction negative 1 over 2 end fractionto first find the equation of the line in point-slope form: y minus negative 1 equals start fraction negative 1 over 2 end fraction open parenthesis x minus 2 close parenthesis
        Now, solve for  to get the slope-intercept form: y plus 1 equals start fraction negative 1 over 2 end fraction times x plus 1 double right arrow y equals start fraction negative 1 over 2 end fraction times x
    2. Solve 50 times e superscript 0.2 x baseline equals 2000 and round your answer to the nearest hundredth.
    3. Graph y equals negative open parenthesis x minus 2 close parenthesis superscript 2 baseline plus 1 and find its vertex.
     
  • Sample of what you will learn in Math 100:
    1. Use one of DeMorgan’s Laws to write an equivalent statement: “Joan is not busy and she is not trying to do too much.”
      • Solution
        It is not the case that Joan is busy or trying to do too much.
    2. Convert 13976 subscript ten baseline to base 8. 
      • Solution
        13976 divided by 8 equals 1747 remainder 0
        1747 divided by 8 equals 218 remainder 3
        218 divided by 8 equals 27 remainder 2
        27 divided by 8 equals 3 remainder 3
        3 divided by 8 equals 0 remainder 3
        So, 13976 subscript ten baseline equals 33230 subscript eight baseline
    3. Shade the appropriate region in the Venn Diagram that corresponds with A complement intersect open parenthesis B intersect C complement close parenthesis complement.
    a Venn diagram showing three intersecting circles labeled A B and C