Algebra 2 End of Year Practice Exam Specification Sheet

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1 Algebra End of Year Practice Exam Specification Sheet Free Response (Vocabular, Knowledge, Concepts, Explanations). Properties of real numbers. Procedure (write procedure or process). Concept development/linkage 4. Theorem/factual knowledge (of theorems and rules). Theorem/factual knowledge (of theorems and rules) 6. Reading translation ( math to English, English to math) Multiple choice. Solve linear equation. Solve linear inequalit. Solve compound inequalit 4. Solve absolute value equation. Solve absolute value inequalit 6. Solve radical equation 7. Solve quadratic equation using various methods 8. Solve higher degree equation 9. Solve sstem of linear equations. Solve sstem including non-linear equations (ma include writing equations). Solve sstem of equations ( variables). Find domain and range of relation. Evaluate a function 4. Inverse of a function/relation. Composition of functions 6. Properties of logarithms/exponents 7. Solve logarithmic equation 8. Solve exponential equation 9. Graph circle 0. Graph parabola. Graph - ellipse/hperbola. Graph sstem of inequalities. Graph logarithm equation 4. Graph exponential equation. Graph higher order polnomial function 6. Graph piecewise function 7. Graph rational function (identif asmptotes -vertical, horizontal or oblique) 8. End behavior of a graph 9. Write equation of a line 0. Write equation of a conic. Solve literal equation. Find extrema of a polnomial function (maximum or minimum). Sequence (arithmetic/geometric nth term) 4. Simplif rational algebraic expression. Irrational number operations 6. Complex number operations 7. Matrix operations 8. Matrix application 9. Linear programming application Algebra II Practice Final Exam Go On

2 Free Response Algebra II Practice Final Exam. Write the Distributive Propert of Real Numbers in general form and illustrate its use with an algebraic expression.. Write the procedure for solving polnomial equations using the Zero Product Propert.. Write the Quadratic Formula and describe how it is derived. 4. Write the Rational Root Theorem. Explain how the theorem can be used to solve higher order polnomial equations.. Write the Fundamental Theorem of Algebra. Explain how the number of solutions of a polnomial function is related to the degree of the polnomial. 6. Write in word form the following mathematical statement. { ( x, ) x } + ; x, R

3 . Which equation is equivalent to x = x = x = 4 x = 6 7 x = x +?. Which inequalit is equivalent to 4. Solve for values of x which make the following equation true. x + = 9 x =, 4 x = 8 x =,4 no solution n+ 6< 7n+ 4? n < 4 n < 4 n > 4 n > 4. Which inequalit is equivalent to x + <. 4 x x 4 or x 4 < < x x < 4 or x >. Solve the inequalit < x + < 7. 8< x < 6 4< x < 7< x < 4 4 < x < 8 6. Solve the equation x =. 0 0, 0 0 no solution Algebra II Practice Final Exam Go On

4 7. Which is the solution set for the quadratic equation x + x+ = 0? +, + 9 9, +, + 9 9, 8. Find all the zeros of the polnomial function { 49,, } { 7, 7, } { 7,, } f( x) = x + x 49x 49.. If the diagonal of a rectangle with perimeter 9 inches is 4 inches, find the length of the shortest side of the rectangle. A] 8 inches inches 6 inches 0 inches. Which ordered triple is a solution of the following linear sstem? A] (, 0, ) (, 0, ) (, 0, ) (, 0, ) x+ z = 4 x + z = x+ z = { 49,, } 9. Solve the sstem of linear equations for the value of x. 0 4 x 4 = x+ =. What is the domain of g(x) in the function gx ( ) = x+? {( x) x ; x R } {( x) x ; x R } {( x) x ; x R } {( x) x ; x R } no solution Algebra II Practice Final Exam Go On

5 . Evaluate f () for the function f( x) = 9x x +. f () = 8 f () = f () = 70 f () = Expand using the properties of logarithms: x log a z log + log x + log loga z a a a + log x log a + log x + log loga z a log + log x + log log z a z a a a a a 4. Which of the following is the inverse of the relation = x? =± x+ 7. Solve for x in the equation log (x + ) =. =± x + =± x + =± x 8. Let f ( x) = 9 x and gx ( ) = x. Find the composite function f ( gx ( )). f ( gx ( )) = + x f ( gx ( )) = f ( gx ( )) = x x+ = x x 9x Solve the exponential equation 9 9 9x =. f ( gx ( )) = x + 6x 7 9 Algebra II Practice Final Exam Go On

6 9. Graph the circle x + = Graph the parabola = ( x ). Algebra II Practice Final Exam 4 Go On

7 . Graph the ellipse with vertices (0, 6) and (0, 6) and co-vertices of (, 0) and (, 0).. Determine the solution to the sstem of inequalities: x+ x+ 7 Algebra II Practice Final Exam Go On

8 . Which sketch most closel represents the logarithmic function = log x? 4. Which sketch most closel represents the exponential function = ( x )? Algebra II Practice Final Exam 6 Go On

9 . Graph f x ( ) x = x. 6. Which sketch from a graphing calculator most closel represents the piecewise function below? x, x 0 f( x) =, 0< x x, x> Algebra II Practice Final Exam 7 Go On

10 7. Find the vertical asmptotes of ( x 6)( x+ ) hx ( ) =. x ( ) x=, x= x= 6, x= x=, x= 6 no vertical asmptotes 0. Write the standard form of the equation of the circle with radius and center at (, ). x + = ( x ) + ( + ) = ( + ) + ( ) = x ( ) ( ) x + + = 8. What is the behavior of the value of as x increases to infinit in the equation = x? approaches 0 approaches approaches negative infinit approaches positive infinit 9. Write an equation of the line that passes through the points ( 4, ) and (, ).. Solve for b in the formula A = hb ( ) + b. b = A h b A b = b h ( A h) b = b A b = b h = x+. Find the maximum value of the quadratic equation = x + 8x. = x+ max = = x = x max = max = max = 7 Algebra II Practice Final Exam 8 Go On

11 . What is the 4 th term of a geometric sequence if the first term is, and the common ratio is 4? Which expression is equivalent to the rational expression ( x ) ( ) ( x ) + + x + 7x+ x 6 ( x x 7 ) ( x+ 4)( x 4)( x+) ( x 9) ( x+ )( x 4 4 ) ( x 9) ( x+ 4)( x+ ) ( )?. Which of the following irrational numbers is 4 the same as? Write the expression ( + i)( 4i) as a complex number in standard form. i + i i 4 i ( x 9 x ) ( x+ 4)( x 4)( x+) 7. Calculate the determinant of the matrix Algebra II Practice Final Exam 9 Go On

12 8. A school fundraiser sells different sizes of gift baskets with a varing assortment of meat and cheese. A basic basket contains cheeses and 4 meats. A big basket contains cheeses and 7 meats. Cheese costs the school $4, and meat costs $8. Algebra II Practice Final Exam 9. An electronics firm makes two kinds of radios an FM set and an AM-FM set. The firm has the equipment to manufacture an number of FM sets, up to and including 600 per month, or AM-FM sets, up to per month. Which of the following shows the use of matrices to find the total cost for each size of basket? basic big 7 8 = 76 It takes 0 man hours to produce an FM set and 40 man hours to make an AM-FM set. The firm has up to 400 man hours per month available for radio production each month. The profit gained on each FM set is $6 and each AM-FM set is $4. basic 4 big = 7 The grid ma help graph the feasible region using linear programming procedures. basic big 4 4 = 40 basic big 7 4 = 68 Find the number of FM sets the firm should manufacture to earn a maximum profit each month. A] 0 FM sets 0 FM sets 0 FM sets 0 FM sets Algebra II Practice Final Exam Go On

13 Algebra End of Year Practice Exam Answer Ke -6 Free Response C C B 4 A C 6 A 7 A 8 B 9 B B B A C 4 B D 6 A 7 D 8 C 9 D 0 B B A D 4 A B 6 A 7 A 8 D 9 D 0 B B D D 4 B B 6 D 7 B 8 A 9 C Algebra II Practice Final Exam Go On

Algebra 2 End of Year Practice Exam Specification Sheet

Algebra 2 End of Year Practice Exam Specification Sheet Algebra End of Year Practice Exam Specification Sheet Free Response (Vocabular, Knowledge, Concepts, Explanations). Properties of real numbers. Procedure (write procedure or process). Concept development/linkage