Algebra II Non-Calculator Spring Semester Exam Review
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1 Algebra II Non-Calculator Spring Semester Eam Review Name: Date: Block: Simplify the epression. Leave only positive eponents.. ( a ). ( p s ). mn 9cd cd. mn. ( w )( w ) Write the answer in scientific notation. 8. (. 0 )(. 0 ) 9. (.0 0 ) Describe the end behavior of the graph of the polynomial function. 0. P = + +. ( ) 7 P ( ) = + 9. P( ) = + +. P ( ) = 7 + AlgSpring EXAMREVIEW08-09.doc
2 Use synthetic substitution to evaluate the polynomial function for the given value of.. P ( ) = ; =. P ( ) = + ; = Find the sum or difference.. ( + + ) ( + ) 7. ( + + ) ( + ) Find the product of the polynomials. 8. ( m+ n) 9. m( m ) Factor the polynomial completely a a a a a Find the real-number solutions of the equation.. + = = 0 AlgSpring EXAMREVIEW08-09.doc
3 . Rewrite the epression in radical notation. b.) 7. Rewrite the epression in rational eponent notation. b.) ( ) 8. Simplify the epression. 9 b.) 9. Simplify the epression. b.) 0. Use the properties of rational eponents to simplify: b.). Use the properties of rational eponents to simplify: b.) ( ) c.) 7 7 d.). Solve the equation + = + 0. Solve the equation 8 = 7 AlgSpring EXAMREVIEW08-09.doc
4 . Solve the equation =. Solve the equation 9+ =. Solve the equation + = 7. Solve = 8. Solve ( ) = 7 9. What is the value of? 0. What is the value of?. What is the value of 0 8? AlgSpring EXAMREVIEW08-09.doc
5 Rewrite the epression in eponential form:. log =. log =. log = 0 Evaluate the epression:. log. log 7 7. log 8. log 9. log 0. log Use the properties of logarithms to epand:.. log log yz log y. Use the properties of logarithms to condense:. log + log. log + log. log + logy+ logz 7. log( + 9) = log(+ ) 8. log ( ) = 9. log+ log( ) = 0. log (+ ) = log ( 9). log ( ) =. log ( + ) + log=. Which equation represents inverse variation? y= b.) y= + c.) AlgSpring EXAMREVIEW08-09.doc y = d.) y=
6 . If y varies directly with and y= 0 when =, what is the value of y when=? b.) c.) d.). Which function has the domain of all real numbers ecept -? y= b.) y= c.) y= d.) y = +. What are the asymptotes of the function y= + + = 0, y= 0 b.) =, y= c.) = 0, =, y= d.) =, =, y= 7. Which epression is the product of ab ac abc bc? 8a b b.) 8abc c.) 8a bc d.) ac 8b 8. What is the simplified form of 7 y y y y? 9. Perform the indicated operation and simplify: What are the asymptotes of the graph y=? Perform the indicated operation and simplify: 7. State the domain and range of the function y= +. domain: all real numbers ecept, range: all real numbers ecept b.) domain: all real numbers ecept, range: all real numbers ecept - c.) domain: all real numbers ecept -, range: all real numbers ecept d.) domain: all real numbers ecept -, range: all real numbers ecept - AlgSpring EXAMREVIEW08-09.doc
7 7. Perform the indicated operation and simplify: = 7. = = 77. = = You may use a calculator on this part! Use the change-of-base formula to evaluate (Round to three decimal places.): 79. log 80. log9 8. log 8. The value of a television has been decreasing by 8% each year since it was new. After years, the value is $0. Find the original cost of the television. Hint: Eponential Decay can be modeled by the equation: y a r = ( ) t. AlgSpring EXAMREVIEW08-09.doc
8 8. You deposit $00 in an account that pays % annual interest. Find the balance after 7 years if the interest is compounded monthly. Hint: Compound Interest can be modeled by the equation: A P nt r = + n. 8. In 00, the average price of a concert ticket for Super Grouper was $7. Ticket prices increased an average of % each year. How much did a ticket cost after years? Hint: Eponential growth can be modeled by the equation: y= a( + r) t. 8. Harry invested $000 at % interest compounded quarterly. How much will the investment be worth after years. Hint: Compound Interest can be modeled by the equation: A P nt r = + n. 8. A men s basketball has a surface area of about 000 square inches. Find the radius of the basketball. (Hint: Use the formula S = πr for the surface area of a sphere.) 87. Find the value of. 88. What is the domain of the function y =? 89. Solve the equation ( ) = 90. Solve the equation + + = AlgSpring EXAMREVIEW08-09.doc
9 Spring Eam Review Answers 8. a. 7p s. n m. d. w (.8 0 ) 9. (. 0 ) ( )( + ) m + mn+ n. ( + ) 9. m 0m + m. a a+ a ( )( ) 0. a + a ( )( ). =, ±. =±, ± ) a) ( ) b) 7) a) b) 8) a) b) 9) a) 8 b) 0) a) b) ) a) b) c) 7 8 d) ) = ) = 8 ) = ) = ) = 7 7) = 8) = 8 9) 0) - ). =. = 0. =. =. = 7. = 8. = 9. = 0 0. =. log log. log + log y. log+ logy+ log z. log. log. logyz 7. = 8. = 9. = 0 AlgSpring EXAMREVIEW08-09.doc
10 0. = 7. =. =. A. B. D. D 7. C 8. y 9. + ( ) 70. =, y= ( )( + ) 7. D ( )( + ) 7. =± 7. = 8 7. = 77. =, = = $8. 8. $ $ $ R 88. = = 8 = AlgSpring EXAMREVIEW08-09.doc
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