Exam Review 2 nd Semester Algebra I

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

Expected Information that could be on the final exam Order of operations Solving equations Writing the equation of a line

Chapter 5 – Connecting Algebra and Geometry Ratio and Proportion Scale Measurements Similarity Perimeter and Area Probability Geometric Probability

Chapter 6 – Working with Radicals The Pythagorean Theorem Rational and Irrational Numbers Calculating with Radicals Multiplying Monomials and Binomials Special Products

Chapter 7 – Solving Systems of Equations Solving systems of equations Substitution method Elimination method Graphing method Solving systems of inequalities

Chapter 8 – Quadratic Functions and Equations Graphing quadratic functions y -intercept x -intercepts vertex symmetry Solving quadratic equations The quadratic formula

Chapter 9 – Exponential Functions Graphing simple exponential functions Applications of exponential functions Simplifying expressions with exponents Positive exponents Negative exponents Scientific Notation

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

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

Unit 12 – Probability and Trigonometry Counting principle Permutations and combinations Probability Special right triangles Simple trigonometry Applications of trigonometry

Order of Operations

Solving Equations

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

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?

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?

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?

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

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.

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?

Geometric Probability Find the area of the shaded region.

Geometric Probability Find the area of the shaded region.

Pythagorean Theorem Find the missing leg length. 4 8

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

Rational or Irrational?

Simplify the radical

Add/Subtract

Multiply

Find the product. (2x + 1)(2x + 3)

Find the product.

Find the product.

Expand. (x + 2) 2

Solving systems of equations Substitution method

Solving systems of equations Elimination method

Solving systems of equations Graphing method

Solving systems of inequalities

Graphing quadratic functions State the vertex, the x - and y -intercepts. Show all work to find the vertex and the x - and y -intercepts.

Solving quadratic equations

The quadratic formula

Graphing simple exponential functions Determine whether the following is exponential growth or decay. Graph.

Graphing simple exponential functions Determine whether the following is exponential growth or decay. Graph.

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 Alyisha’s 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?

Simplifying expressions with exponents

Scientific Notation Write in scientific notation.

The Discriminant Determine the number of x -intercepts for each of the following.

Factoring Factor completely, if possible.

Solving quadratic equations

Simplifying polynomial expressions – (+ and - )

Simplifying polynomial expressions (  and  )

Graphing simple rational functions Graph

Graphing simple rational functions Graph

Solving rational equations

Simplifying rational expressions (  and  ) Simplify

Simplifying rational expressions (  and  ) Simplify

Simplifying rational expressions (  and  ) Simplify

Simplifying rational expressions (+ and - )