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) 5. 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 5. 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 5. 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 5. 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 5. Irrational number operations 6. Complex number operations 7. Matrix operations 8. Matrix application 9. Linear programming application Go On
. 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. Go On
4. Write the Rational Root Theorem. Algebra II Practice Final Exam Explain how the theorem can be used to solve higher order polnomial equations. 5. 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 } + 5; x, R Go On
. Which equation is equivalent to x = x = x = 4 x = 6 7 5 x = x +?. Which inequalit is equivalent to 4. Solve for values of x which make the following equation true. 5x + = 9 x =, 4 5 x = 5 8 x =,4 5 no solution n+ 6< 7n+ 4? n < 4 n < 4 n > 4 n > 4 5. 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 5 = 5., 0 0 no solution Go On
7. Which is the solution set for the quadratic equation x + 5x+ = 0? 5 + 5, 5 + 9 5 9, +, 5 +, 5 9 5 5 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 5 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 = 5 { 49,, } 9. Solve the sstem of linear equations for the value of x. 0 4 x 4 = x+ = 5. 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 4 Go On
. Evaluate f () for the function f( x) = 9x x +. f () = 8 f () = 5 f () = 70 f () = 78 6. Expand using the properties of logarithms: 5x log a 5 z log 5+ log x + log 5log z a a a a 5 + log x 5log a 5+ log x + log 5log z a a a log 5+ log x + log 5log z a z a a a a 4. Which of the following is the inverse of the relation = 5x? =± 5 x+ 7. Solve for x in the equation log 5(x + ) =. =± x + 5 5 =± 5 x + =± 5x 8 5. Let f ( x) = 9 x and gx ( ) = x. Find the composite function f ( gx ( )). f ( gx ( )) = + x f ( gx ( )) = = x x+ 8. Solve the exponential equation 9 9 9x 5 =. f ( gx ( )) f ( gx ( )) = x x x+ = x + 9 7 6x 7 9 5 Go On
9. Graph the circle x 8 + =. 0. Graph the parabola = ( x ). x x x x x x x x 6 Go On
. 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+ x+ 7 x x x x x x x 7 Go On
. Which sketch most closel represents the logarithmic function = 5logx? 4. Which sketch most closel represents the x exponential function = ( )? 8 Go On
5. Graph f ( x) x x =. x Algebra II Practice Final Exam 6. Which sketch from a graphing calculator most closel represents the piecewise function below? x, x 0 f( x) =, 0< x x, x> x x x 9 Go On
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 5 and center at (, ). x + = 5 ( x ) + ( + ) = 5 ( x+ ) + ( ) = 5 ( x ) + ( + ) = 5 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 (, 5).. Solve for b in the formula A= h ( b ) + 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 5 = x max = max = max = 7 Go On
. What is the 4 th term of a geometric sequence if the first term is, and the common ratio is 4? 5 6 8 9 4. Which expression is equivalent to the rational expression ( x ) ( ) ( x ) + 5 + x + 7x+ x 6 ( x x 7 ) ( x+ 4)( x 4)( x+ ) ( x 9) ( x+ 4)( x 4) ( x 9) ( x+ 4)( x+ ) ( )? 5. Which of the following irrational numbers is 4 the same as? 5+ 0 + 4 7 0 4 6 4 7 6. Write the expression ( + i)( 4i) as a complex number in standard form. i + i i 4 5i ( x 9 x ) ( x+ 4)( x 4)( x+ ) 7. Calculate the determinant of the matrix 4 0 8. 0 40 40 44 Go On
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 5 cheeses and 7 meats. Cheese costs the school $4, and meat costs $8. Which of the following shows the use of matrices to find the total cost for each size of basket? 9. You are making hand made jewelr to sell at an art fair. It takes ou hours to make a bracelet and hours to make a necklace. You make a profit of $ for a bracelet and $0 for a necklace. If ou have no more than 0 hours available to make the jewelr and want to sell at least pieces of jewelr how man bracelets should ou make to maximize our profit? basic 4 4 44 big 5 7 = 8 76 The grid ma help graph the feasible region using linear programming procedures. basic 5 4 5 big 4 7 = 8 7 basic 5 7 8 68 big 4 = 4 40 basic 4 8 40 big 5 7 = 4 68 A] 6 bracelets bracelets 5 bracelets 0 bracelets Go On
Algebra End of Year Practice Exam Answer Ke -6 Free Response C C B 4 A 5 C 6 A 7 A 8 B 9 B C B D C 4 B 5 D 6 A 7 D 8 C 9 D 0 B B A D 4 A 5 B 6 A 7 A 8 D 9 B 0 B B D D 4 B 5 B 6 D 7 B 8 A 9 A 4 Go On