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Algebra II Name:___________________________ Chapter XII Exam Review Date:________ Period:________ Matching Examine each of the functions below. Decide which graph best represents that equation. Write the corresponding letter in the space provided. 1. ________ 𝑓(𝑥) = √𝑥 + 1 − 2 2. ________ 𝑓(𝑥) = √𝑥 − 1 + 2 3 3. ________ 𝑓(𝑥) = √𝑥 − 1 + 2 3 4. _______ 𝑓(𝑥) = √𝑥 + 1 − 2 A. B. C. D. Multiple Choice Examine each problem. Decide which of the four possible solutions is the best and write the corresponding letter in the space provided. 5. ________ Solve the equation 3𝑥 2 − 5𝑥 + 3 = 0 ? 3 6. ________ Simplify the radical expression √250𝑥 3 𝑦 6 7. ________ Simplify the expression (3𝑥 2⁄ 5 5 𝑦) 8. ________ Let 𝑓(𝑥) = 2𝑥 + 4 and 𝑔(𝑥) = 3𝑥 2 + 𝑥 − 5. What is equivalent to 𝑓 − 𝑔? 9. ________ Let 𝑓(𝑥) = 5𝑥 − 7 and 𝑔(𝑥) = 2𝑥 2 − 2𝑥 + 3, what is 𝑓(2) + 𝑔(3) 10. ________ 𝑓 𝑔(𝑥)? Let 𝑓(𝑥) = 2𝑥 2 − 6 and 𝑔(𝑥) = 𝑥 + 3. What expression is equivalent to 11. ________ What is the inverse of the function 𝑘(𝑥) = 25𝑥 2 − 225 𝑓𝑜𝑟 𝑥 ≥ 0 12. ________ Solve for x in the equation √3𝑥 + 3 − 1 = 8? 13. ________ What is the minimum value for the parabola 𝑓(𝑥) = 2𝑥 2 + 6𝑥 + 3 14. ________ matrix? Show how to find the solution to the system of equations using an inverse 5𝑥 + 2𝑦 = −1 3𝑥 + 2𝑦 = 1 15. ________ Solve the matrix equation below. 3 −4 𝑥 10 [ ]∙[ ] = [ ] 2 −2 𝑦 6 16. ________ Simplify the expression (2 − 3𝑖) ∙ (1 + 𝑖) 17. ________ Simplify the expression (2 − 24𝑖) ÷ (5 − 2𝑖) 18. ________ A witness to an auto accident reports getting a partial license plate. The question marks indicate the characters the witness was unable to see. If the license plate uses three letters (without the letter “O”) followed by three numbers, how many possible license plates are there for the suspect? ?BD??5 19. ________ 6 Olympic athletes are competing in the broad jump. How many ways can a gold medal, silver medal, and bronze medal be awarded? 20. ________ 8 painters are displaying their work. The best 2 paintings will be exhibited at a local museum. How many ways can the 2 paintings be chosen from the 8? 21. ________ What is the expanded form for the binomial (2𝑥 − 𝑦)5 ? 22. ________ What is the coefficient of the 𝑥 3 𝑦 3 term from the binomial (𝑥 + 3𝑦)6 23. ________ A deck of cards has 8 red cards, 5 blue cards, and 2 green cards. If three cards are drawn at random without being replaced, which expression shows the probability of drawing a red card, a green card, and another red card? 24. ________ A group of students take a test. 𝑥̅ = 87 and 𝜎 = 5. What percentage of the people who took the test scored above 82? 25. ________ An awards banquet is held for 160 honors students. 64 students won awards in English. 104 students won awards in English or Mathematics. 40 students won awards in English and Mathematics. If a student at the banquet is selected at random to give a speech, what is the probability the student won an award in Mathematics?