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Lecture Comments (4)

3 answers

Last reply by: Professor Selhorst-Jones
Sun Apr 6, 2014 3:15 PM

Post by Tommy Lunceford on April 5, 2014

In the example about the word problems, how could I get more information on how to set up these types of equations? I understand where he got the numbers from but I would like to know if there is more info about how to set them up.

Math: Common Issues

  • This lesson covers a variety of issues that students often have with the SAT Math section and math in general. After you watch this lesson, make sure to watch both parts of the Math Concept Petting Zoo to get a sense for the concepts on the test.
  • If you need more help with a specific topic, check out the SAT Math-specific section or browse the rest of Educator.com's math lessons.
  • Word problems tend to give a lot of students trouble not because the math is hard, but because they have difficulty translating from English to math. If you can focus on carefully transforming the words into math, such problems often become much easier. Here's a general outline of what to do when working on a word problem:
    1. Set up any variables you need to solve the problem. Write down what each variable means. I'm serious about this: having a written reference helps so much when you're working on word problems.
    2. Using the information in the word problem and the variables you just created, set up your equations. Make sure your equations represent what the word problem says. If you're not certain, try plugging in a hypothetical number to make sure you set up your equation properly.
    3. Once the equation(s) are all set up and correct, solve them for whatever the world problem asked for. Yay!
  • Draw pictures that represent what you're working on. You can't do it for all problems, but when a problem talks about geometry, shapes, or something that is physically happening, you want a picture to look at.
  • Often you'll have problems where they take something and break it into pieces or remove a chunk. In such a situation, you can normally figure out the pieces, even if you can't figure out the shape you're solving for. In that case, remember: "The sum of the parts equals the whole, and the whole equals the sum of the parts."
  • Remember the order of operations!
  • When doing algebra, you need to make sure you always do the same thing on both sides of the equation. Lots of mistakes happen because people accidentally operate on only one side of the equation. Don't let that happen to you!
  • Make sure you remember your rules for fractions:
    • Fractions can only add when they have a common denominator:
      x

      d
      + y

      d
      = x+y

      d
    • To change denominators, you must multiply the top and bottom by the same thing:
      a

      b
      = a·k

      b ·k
    • Multiplying fractions doesn't require anything special-numerators multiply together while denominators multiply together:
      a

      b
      · x

      y
      = ax

      by
      ,
    • If you see a fraction over a fraction, it helps to break out the division symbol and remember what you learned in grade school: "To divide by a fraction, multiply by the fraction's reciprocal [flip top and bottom]."
      a

      b

      x

      y
      = a

      b
      ÷ x

      y
      = a

      b
      · y

      x
      = ay

      bx
  • When substituting, remember you to have to replace the whole expression. In general, when substituting, wrap parentheses around the expression before plugging it in. It will never hurt, and it will often save you from a mistake.
  • If you are solving multiple equations at the same time (simultaneous equations), there are a few methods. You can substitute between equations, add the equations together to eliminate a variable, and/or use a graphing calculator to find where the graphs intersect. For more information, watch the lesson and check out the example for each method.
  • Know all the rules for how exponents behave:
    • xa ·xb = x(a+b),
    • (xa)b = x(a·b),
    • x0 = 1,
    • x[a/b] = b√{xa},
    • ( [x/y] )−a = ( [y/x] )a = [(ya)/(xa)].
  • There are lots of ways to talk about averages. Here are the three you might see on the SAT:
    • Mean: What we normally think of as "average". This is the sum of all the numbers divided by how many there are.
    • Median: This is the value in the "middle" of the set. If you arrange the set in order, the median is the middle value. (The set must be in order to find the median!)
    • Mode: This is the value that shows up the most in the set. The most common value is the mode.
  • To change from percent to a decimal number you can use, just divide it by 100: move the decimal two places to the left.
  • Probability can be determined by taking the number of outcomes you're looking for and dividing by the total possible number of outcomes.
  • There are always a couple of funny symbol questions on the SAT and lots of students find them confusing. Have no fear! Just treat like them like you would a function. The SAT establishes a pattern, and you just need to evaluate according to that pattern.

Math: Common Issues

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Legal Disclaimer 0:07
  • Introduction 0:15
  • Word Problems 1:17
    • Make Variables
    • Make Equations
    • Example
  • Draw Pictures 7:42
    • Not Necessary, But a Visual Representation of a Problem Can Help a Lot
    • If the Problem is Not Drawn to Scale, It Can Help to Draw it to Scale
  • Area in Pieces 11:08
    • Example
    • The Idea is Expressed By…
  • Order of Operations 14:24
    • Parentheses and Brackets
    • Exponents and Roots
    • Multiplication and Division
    • Addition and Subtraction
  • Algebra 15:58
    • One of the Most Fundamental Ideas in Algebra
    • Example
    • Do the Same Thing to Both Sides
  • Fractions 18:21
    • The Basics: Addition
    • How to Change the Denominator of a Fraction
    • The Basics: Multiplication
    • Fractions Over Fractions
    • Cross Multiplication
    • Never Use Cross-Multiplication Again
  • Substitution 26:45
    • You Have to Replace with the Whole Expression
  • Solving Multiple Equations 28:05
    • Three Ways to Solve Simultaneous Equations
    • Substitution
    • Adding Equations/ Elimination
    • Graphing
  • Exponents 35:41
  • Average 36:46
    • Mean
    • Median
    • Mode
    • Example
  • Percent 39:16
    • Percent Means Per Hundred
  • Probability 40:23
    • Assume All Possible Outcomes Are Equally Likely
    • Formula for the Probability of Something Happening
  • Funny Symbol Questions 41:43
    • Example