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  Algebra Midterm Study Guide 2017
  *Remember - this is not everything you need to know. You will have to refer back to old packets, study
  guides, and do practice questions in order to be successful on the midterm exam. :)
  Calculator Keys
  Negative
  Fraction
  Converting Fractions to Decimals/Decimals to Fractions
  Absolute Value
  Exponent
  Graphing
  Table
  Graphing Picture
  Test Taking Strategies
  Multiple Choice Strategies
  Free Response Strategies
  Eliminate Choices
  Guess and Check
  Multiple Methods of Solution
  Process of Elimination
  Highlight keywords
  Break the question into chunks that you understand.
  Show all work!
  1
  If the question asks you to
  explain...
  Is it rational?
  “Yes, because it’s an integer”
  Is it irrational?
  “Yes, because it’s a non-terminating,
  non-repeating decimal”
  Is the point a solution?
  “Yes, because it lies on the line”
  “Yes, because it lies in the shaded region”
  OR
  “No, because it does not
  lie on the line”
  “No, because it does not
  region”
  What does the slope(rate of change) mean?
  “Rate of _______ per ________”
  What does the y-intercept mean?
  “Initial amount, cost, fee…”
  Is the point a solution? (system of
  inequalities)
  “Yes, because it lies in the double shaded
  region”
  OR
  “No, because it does not
  lie in the double
  Is it a function?
  “Yes, because each input has only one
  output”
  OR
  “No, because an input has 2 different outputs”
  2
  Unit 1 - Polynomials
  Multiplying Polynomials/Distributive Property
  (Box Method)
  1. Identify terms that have the same base and same
  exponent.
  3. Keep the base and the exponent.
  4. Standard form - greatest exponent first and then
  1. Multiply coefficients.
  2. Keep the base.
  4. Combine like terms (see box to the left).
  Example of Substitution
  Example of using the “Box Method”
  3
  Unit 2 - Equations
  Example of Solving an Equation
  Example of Solving a Literal Equation
  Given the formula , solve for t.atd =
  2
  1
  2
  4
  Unit 3 - Inequalities
  *When solving inequalities, we use the same steps as solving equations.*
  **Remember to reverse the inequality symbol when we divide by a negative number!!**
  x
  < 4
  x
  > 4
  x ≤ 4
  x ≥ 4
  x
  is less than 4”
  Open circle
  x
  is greater than 4”
  Open circle
  x
  is less than or equal to 4”
  Closed circle
  x
  is greater than or equal to 4”
  Closed Circle
  Interval Notation
  Meaning
  Compound Inequality
  Graph
  (-2, 3)
  -2 is not included
  3 is not included
  {-1, 0, 1, 2}
  -2 < x
  < 3
  (-2, 3]
  -2 is not included
  3 is included
  {-1, 0, 1, 2, 3}
  -2 < x
  3
  [-2, 3)
  -2 is included
  3 is not included
  {-2, -1, 0, 1, 2}
  -2 x
  < 3
  [-2, 3]
  -2 is included
  3 is included
  {-2, -1, 0, 1, 2, 3}
  -2 x
  3
  “at most”
  “no more than”
  “at least”
  “no less than”
  5
  Unit 4 - Graphing
  Graphing Linear Equations
  Standard form of a line:
  y
  = m
  x
  + b
  m
  represents the slope/rate of change of the line.
  b
  represents the y
  -intercept of the line.
  x
  and y
  represent a point, (x
  , y
  ), on the line.
  Key Feature
  Algebraic Solution
  Graphic Solution
  x-intercept
  Cover the y
  and solve for x
  .
  Point where the function intersects with the x
  -axis.
  y-intercept
  Cover the x
  and solve for y
  .
  Point where the function intersects with the y
  -axis.
  Solution
  Substitute (x
  , y
  If true, then it is a solution.
  If false, then it is not a solution.
  In order for a point to be a solution it must be on the
  table and line.
  Rate of Change
  x x
  2 1
  y y
  2 1
  “Rise over Run”
  Graphing Inequalities
  Notes
  Example
  < is a dashed line and shade down.
  > is a dashed line and shade up.
  is a solid line and shade down.
  is a solid line and shade up.
  *Remember - you must have...
  A Table
  Arrows
  Labels
  ...to earn full credit on your midterm exam!
  6
  Unit 5 - Systems of Linear Equations & Inequalities
  Linear System
  Inequality System
  Graph each line separately!
  Remember - you must have tables, arrows,
  and labels for everything in order to get full
  Graph each inequality separately!
  < is a dashed line and shade down.
  > is a dashed line and shade up.
  is a solid line and shade down.
  is a solid line and shade up.
  Any point in this area (not on the lines) is true
  for BOTH inequalities.
  Remember - you must have tables, arrows, and
  labels for everything to get full credit on your
  midterm!
  Solving Systems of Equations Algebraically
  Elimination Method
  Substitution Method
  Step 1: Switch your coefficients and make one
  negative (multiply top on bottom, and bottom on
  top).
  Step 2: Distribute to each term.
  Step 3: Combine like terms and solve for y
  .
  Step 4: Substitute y
  into one equation and solve
  for x
  .
  *Make sure equations are in “y
  ” = format.
  Step 1: Set equations equal to each other.
  Step 2: Solve for x
  .
  Step 3: Substitute x
  into one equation and solve
  for y
  .
  Your solution should be written as a point (x
  , y
  )
  7
  Your solution should be written as a point (x
  , y
  )
  unless it is a real world situation.
  unless it is a real world situation.
  Unit 6 - Functions
  Key Feature
  Meaning
  Example
  Domain
  “Input” of a function (x
  -values).
  Domain: All Real Numbers
  Range: (x)f ≥ 2
  Range
  “Output” of a function (y
  -values).
  *Each input can only have 1 output.*