Name These exercises cover topics from Algebra I and Algebra II. Complete each question the best you can.

Transcription

1 Name These eercises cover topics from Algebra I and Algebra II. Complete each question the best you can. Multiple Choice: Place through the letter of the correct answer. You may only use your calculator when indicated by an asterisk* " $ For questions -, use the given set # %$,,, Determine how many natural numbers there are in the set. A. B. E. None of the numbers. Determine how many integers there are in the set. A. B. E. None of the numbers. Determine how many rational numbers there are in the set. A. B. E. None of the numbers & $ ' ($. Determine how many irrational numbers there are in the set. A. B. E. None of the numbers 5. Which of the following is a true statement. A Both a and b are true. B. 6 = 8 E. Both a and c are true. 6 ( ) 5 6. Which of the following is a true statement. A. < Both a and c are true. B. E. Both b and c are true. 6 6

2 7. Use inequality notation to describe b is at least 5. A. b > 5 b 5 B. b 5 b < 5 8. Use inequality notation to describe is nonnegative. A. > 0 0 B. < Use inequality notation to describe y is at most 0. A. y 0 y >0 B. y <0 y 0 0.*Use a calculator to find the largest of the following numbers 7 5 B. E..*Use a calculator to find the smallest of the following numbers 0 9 B. E.. While traveling you enter the interstate near the mile marker, then eit near the 0 mile marker. Determine the number of miles traveled on the interstate. A. 6 0 B

3 !. Simplify: # $. " % & B Simplify: 6. A. ± B. none of these i 5. Simplify 6 y 6 if it is a real number. A. 8 y 8 y 7 B. y 6 y 9 6. Simplify 8 6 y 0 if it is a real number. A. i 8 y 0 y 5 B. 9 8 y 0 8 y 0 7. Simplify 0. A. 0 B Simplify 8 A. 6 B. 6 6

4 9. Simplify 8 A. B. 0. Simplify: A. 0 B.. Rationalize the denominator: A B Rational the numerator: B

5 . Simplify: B.. Simplify: y + 7 y 6 7 y A. 6 y y B. y 9 y 8y 7 y 5. Simplify: 75 8 A. B. 6. Simplify: A B ( 6 + 7)+ ( + +) ( + ) Simplify: A B. 8 + ( 5 + ) ( +) Simplify: A B. 5 ( 5) 0 + 5

6 9. Simplify: ( ) ( + + ) A B Simplify: A. B ( ) ( + ). Epand: ( y) A. + 6 y +y + 8y + y + y 8y B. 6 y +y 8y y + y 8y. Represent the area of the region as a polynomial in standard form: A B Factor: A. 5 B. 5 5 ( 5) ( 5). Factor: 8 ( 7 + ) ( 9 ) A. ( 9 ) B. 9 + ( 9 + )

7 5. Factor: ( 7) ( 7) A. + 7 ( 8 7) B. 7 ( 7) 6. Factor: A. 5 + B ( 5) ( 5 ) ( + 5) ( +0) ( 5 + ) ( 0) 7. Factor: A. + y B. + y z + yz 6w yw ( z + w) ( z + yz) ( 6w + yw) ( z w) ( y) ( z w) 8. Given is a factor of, factor completely. A. B ( ) ( ) ( ) ( ) ( + ) ( +) ( + ) ( ) ( +) ( ) 9. Factor completely over the Real Numbers. A. B. ( + ) + 9 ( + ) + ( ) ( + ) ( +6) ( + ) Factor completely over the Comple Numbers. A. B. ( + ) ( + i) ( i) ( ) ( + ) ( + i) ( + i) ( + ) ( + i) ( i) ( ) ( + ) ( + i) ( i)

8 . Factor: A. 5 B. 5 9( 5) + ( 5) ( 9 +) ( 5) 0 70 ( 6 5) ( 5) ( 5). Factor: A. 8 B. 8 + ( ) + ( ) ( 6 ) ( ) ( +) ( ). Factor: A. B. 8 + ( +) ( + +) ( +) ( +). Factor: 9 a+ + 5 a, assuming that a is a positive integer A. a B. 9 a+ + 5 a 9 a ( + 5) a ( +5) 5. Factor: over the integers A. B. ( ) ( 5) ( ) ( + ) ( 5) ( ) ( + 5) ( ) ( ) ( 6 5) 6. Determine the quadrant in which the point, y must be located if and. A. I IV B. II III > 0 y < 0

9 7. Determine the quadrant in which the point, y must be located if and. A. I IV B. II III 8. Determine the quadrant in which the point, y must be located if. A. II I and III B. II and III II and IV 9. Determine the slope of the line that passes through the points, and. A. 5 B Describe the behavior of the line that passes through 5,6 and. A. Leans left Vertical B. Leans right Horizontal < 0 y > 0 y < 0 (, ) (,6 ) 5. Determine whether the lines, L and L are parallel, perpendicular, or neither given L passes through,8 and & passes through and (,7) L ( 9,0) ( 0,) A. Parallel Neither B. Perpendicular Reduce: B

10 Multiply and simplify: B Divide and simplify: A. 585 B ( + 7) Add and simplify: ( + ) ( ) + + ( + ) ( ) + B. + ( + ) + + y 56. Simplify:. y y y y B. y y y

11 57. Simplify: A. + + B Simplify: A B Which of the following does not represent a function. A. + y = 8 + y = 6 B. y = y = 6 #% 60. Given f ( ) = + < $, find &% 6 7 A. 9 5 B Find the domain of the function: A. (, ) (,), B. (,) (,) (, ) (, ) f ( ) = f ( ) + %, $ # & ' ( # % $, & ( '

12 6. Find the range of the function{ (,), (,), (,9) } A.,9 B.,,,,9 { } {,,9} { } {,,} 6. Given f and, find. A. 5 0 B. = g( ) =+ ( f + g) ( ) + = g( ) = ( fg) ( ) 6. Given f and, find. A + B. = g( ) = + ( f! g) ( ) 65. Given f and, find. + B Given f and g, find B. 67. Given f and, find f! g. A. 9 B. + = = = + g( ) = ( f / g) ( ) ( )

13 68. Which is the inverse of f ( ) =. A. B. + ( + ) Determine which sets of functions are not inverses of each other. A. f ( ) = 5 5 & g( ) = All of these are inverses of each other B. f ( ) = & g( ) = are inverses of each other c. f ( ) = & g ( ) = Which sequence of transformations of f ( ) = yields f ( ) = + 9. A. Reflection about -ais Horizontal shift 9 right Vertical shift down Reflection about -ais Horizontal shift 9 left Vertical shift down B. Reflection about y-ais Horizontal shift 9 left Vertical shift down E. Reflection about y-ais Horizontal shift 9 right Vertical shift up Reflection about -ais Horizontal shift 9 left Vertical shift up 7. Which of the following is a sketch of the graph of the equation f ( ) = + A. B.

14 7. Find a polynomial function with the given zeros:,,,. A. f B. f 7. Write in radical form: B. 5 = ( + ) ( + ) ( ) f ( ) = ( + ) ( ) ( ) = ( ) ( ) ( + ) = ( ) ( ) ( ) f Write in eponential form: 5 A. 5 B. 5 5 " 75. Simplify $ # 6 y 5 6 % ' & 0 5 y 5 ( y) 0 B. y 5 5 y *Use your calculator to evaluate A B ( ) to the nearest hundredth. 77. Epress in eponential form log 7 9 = A. 7 = 9 9 = 7 B. 7 = 9 9 = 7

15 78. Epress in logarithmic form 5 5 = A. log 5 = 5 5 log 5 = B. log = 5 log = Epress in epanded form 5 log 0log 8 8 B. log 8 +0log 8 log log Epress as a single logarithm form log5 log5 y, if possible z A. log 5 not possible y y B. log 5 z log 5 yz log Convert θ = 0 degrees to radians. A. π π B. π 00 π log 5 z 8. Convert θ = π radians to degrees. 5 A B Convert θ = rotation, counterclockwise to degrees. A. 0 0 B. 0 0

16 8. Convert θ = 5 rotation, clockwise to degrees. A B Convert θ = 5 to rotation measure. A. 5 rotation, counterclockwise 8 5 rotation, clockwise 8 B. 5 rotation, counterclockwise 5 rotation, clockwise 86. A right triangle has an acute angle such that cscθ = 7. Find tanθ. A B Determine the Quadrant in which θ lies if sinθ < 0 and cosθ > 0 : A. I IV B. II III 88. Find r for the triangle shown A 6 B Find the reference angle for θ = 05 A B Find the reference angle for θ = 7π A. π π B. π π 6

17 9. Divide A B Find all real roots for = 0 A.,,,,6 B.,, 6,, 9. Given f, find h A. h B. + h 9. Find a mathematical model for the statement: y varies jointly with the square of and the square root of z A. = k z y = k z B. k y = z y ( ) ( + ) f ( + h) f ( ) = y = k z 95. Find a mathematical model for the statement: y is inversely proportional to 7 A. y 7 = y = k 7 B. 7y = k y = k 7