Exam Review

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Exam Review

• 2nd Semester
• Algebra I

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Topics Covered

• Essential Questions from First Semester
• Chapter 6 Working with Radicals
• Chapter 7 Solving Systems of Equations
• Chapter 8 Quadratic Functions and Equations
• Chapter 9 Exponential Functions
• Chapter 10 Polynomial Functions and Equations
• Chapter 11 Rational Functions and Equations
• Unit 12 Probability and Trigonometry

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Expected Information that could be on the final
exam

• Order of operations
• Solving equations
• Writing the equation of a line

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Chapter 5 Connecting Algebra and Geometry

• Ratio and Proportion
• Scale Measurements
• Similarity
• Perimeter and Area
• Probability
• Geometric Probability

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Chapter 6 Working with Radicals

• The Pythagorean Theorem
• Rational and Irrational Numbers
• Calculating with Radicals
• Multiplying Monomials and Binomials
• Special Products

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Chapter 7 Solving Systems of Equations

• Solving systems of equations
• Substitution method
• Elimination method
• Graphing method
• Solving systems of inequalities

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Chapter 8 Quadratic Functions and Equations

• Graphing quadratic functions
• y-intercept
• x-intercepts
• vertex
• symmetry
• Solving quadratic equations
• The quadratic formula

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Chapter 9 Exponential Functions

• Graphing simple exponential functions
• Applications of exponential functions
• Simplifying expressions with exponents
• Positive exponents
• Negative exponents
• Scientific Notation

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Chapter 10 Polynomial Functions and Equations

• The Discriminant
• Factoring
• Solving quadratic equations
• Simplifying polynomial expressions
• Involving multiplication and/or division
• Involving addition and/or subtraction

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Chapter 11 Rational Functions and Equations

• Graphing simple rational functions
• Solving rational equations
• Simplifying rational expressions
• Involving multiplication and/or division
• Involving addition and/or subtraction

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Unit 12 Probability and Trigonometry

• Counting principle
• Permutations and combinations
• Probability
• Special right triangles
• Simple trigonometry
• Applications of trigonometry

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Order of Operations
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Solving Equations
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Writing the Equation of a Line

• Find an equation of a line passing through the
  points (-1, 3) and (-2, -5).

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Ratio and Proportion
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Ratio and Proportion

• 800 children a day ride on the roller coaster,
  but another 200 are turned away because they're
  not tall enough. What proportion of the total
  number of children are turned away?

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Ratio and Proportion

• At Washington High School, two out of every three
  students usually buys a yearbook. How many
  yearbooks should the school plan for if there are
  1460 students at the school?

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Ratio and Proportion

• Methane is a compound consisting of a 1 4
  ratio of carbon and hydrogen atoms. If a sample
  of methane contains 1565 atoms, how many carbon
  and hydrogen atoms are present?

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Similarity

• A tree 48 feet high casts a shadow 36 feet long.
  If a flag pole casts a shadow 12 feet long, the
  height of the flag pole is

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Perimeter and Area

• The perimeters of ?ABC is 2 ft. The perimeter of
  ?DEF is 15 in. These two figures are similar.
• Find the ratio of the corresponding side
  lengths.
• Find the ratio of the areas.

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Probability

• A six sided die was rolled 60 times. 1 came up
  12 times, 2 came up 9 times, 3 came up 15 times,
  4 came up 8 times, 5 came up 10 times. What is
  the theoretical and the experimental probability
  of getting an even roll?

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Geometric Probability

• Find the area of the shaded region.

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Geometric Probability

• Find the area of the shaded region.

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Pythagorean Theorem

• Find the missing leg length.

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4
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Pythagorean Theorem

• Is a triangle with side lengths 4, 5, 6 a right
  triangle? Justify your answer.

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Rational or Irrational?
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Rational or Irrational?
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Rational or Irrational?
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Rational or Irrational?
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Rational or Irrational?
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Simplify the radical
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Simplify the radical
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Simplify the radical
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Add/Subtract
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Add/Subtract
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Multiply
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Multiply
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Find the product.

• (2x 1)(2x 3)

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Find the product.

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Find the product.

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Expand.

• (x 2)2

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Solving systems of equationsSubstitution method
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Solving systems of equationsElimination method

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Solving systems of equationsGraphing method

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Solving systems of inequalities

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Graphing quadratic functions

• State the vertex, the x- and y-intercepts.
  Show all work to find the vertex and the x-
  and y-intercepts.

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Solving quadratic equations

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Solving quadratic equations

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Solving quadratic equations

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The quadratic formula

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The quadratic formula

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Graphing simple exponential functions

• Determine whether the following is exponential
  growth or decay. Graph.

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Graphing simple exponential functions

• Determine whether the following is exponential
  growth or decay. Graph.

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Applications of exponential functions

• Alyisha is saving for her college tuition. She
  has 2000 in a savings account that pays 6
  annual interest.
• Write an equation giving the amount of money in
  Alyishas account at any time in the future
  assuming she makes no deposits or withdrawals.
• How much money will Alyisha have in her account 4
  years from now?

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Simplifying expressions with exponents

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Simplifying expressions with exponents

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Scientific Notation

• Write in scientific notation.

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The Discriminant

• Determine the number of x-intercepts for each of
  the following.

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Factoring

• Factor completely, if possible.

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Solving quadratic equations

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Solving quadratic equations

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Solving quadratic equations

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Simplifying polynomial expressions ( and - )
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Simplifying polynomial expressions (? and ?)

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Simplifying polynomial expressions (? and ?)

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Simplifying polynomial expressions (? and ?)

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Graphing simple rational functions

• Graph

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Graphing simple rational functions

• Graph

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Solving rational equations

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Solving rational equations

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Simplifying rational expressions (? and ?)

• Simplify

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Simplifying rational expressions (? and ?)

• Simplify

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Simplifying rational expressions (? and ?)

• Simplify

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Simplifying rational expressions ( and - )

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Simplifying rational expressions ( and - )

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