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Comprehensive Review: Algebra Concepts and Problem-Solving Techniques

This review covers key concepts in Algebra with examples and solutions. Topics include function transformations, combinatorics in room design, permutations for student council positions, and appetizers selection methods. Probability calculations are demonstrated with real-life scenarios involving dice rolls and candy likelihoods. Additionally, polynomial function construction based on population data and trigonometric function equations with specific properties are addressed. Designed to reinforce understanding and application of algebraic principles through varied exercises.

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Comprehensive Review: Algebra Concepts and Problem-Solving Techniques

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  1. Semester 2 Final Review Algebra 3

  2. Ex: Given f(x) Answer: 1

  3. Ex: Describe the transformation of g(x) = from f(x) = x2 Answer: right 1, down 7

  4. Ex: A woman is redecorating her bedroom. She can choose from 6 paint colors, 4 beds, and 6 dressers. How many ways can she choose to design her room? Answer: 108

  5. Ex: Fourteen high school students are running for student council positions of president, vice president, and secretary. How many ways can these 14 students fill the 3 positions? Answer: 2184

  6. Ex: A menu at a restaurant offers 10 different appetizers. How many ways can a group order 5 appetizers? Answer: 252

  7. Ex: Below is the results of a person rolling a number cube 100 times. What is the experimental probability that a person rolls a 1 or a 6? Answer: 24%

  8. Ex: What is the probability that a point chosen at random is inside the shaded area? Answer: 56%

  9. Ex: A person counted the number of candy he had of each flavor. The results are shown below. If he picks a piece at random, what is the probability that the candy is orange? Answer: 21%

  10. Ex: A company is testing a new method of manufacturing a part for their machines. They tested parts using the old and new methods. What is the probability that a part chosen at random from this group is new and passed the test? Answer: 8.8%

  11. Ex: Find all the zeros for the equation: = 0 Answer: x = 0, 6, -3

  12. Ex: Find all the zeros for the equation: = 0 Answer: x = 2,

  13. Ex: The table below shows the population of a city from 1970 to 2000. Write a polynomial function for the data. (start with 1970 as year zero and use the best answer given.) Answer:

  14. Ex: Write the equation of a trigonometric function with a phase shift of left 90o and an amplitude of 5 from the parent function y = cosx Answer: y = 4cos(x – 90o)

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