Algebra II Practice Semester Exam Specification Sheet

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1 Algebra II Practice Semester Exam Specification Sheet 1. Properties of real numbers. Procedure (write procedure or process) 3. Concept development/linkage. Theorem/factual knowledge (of theorems and rules) 5. Theorem/factual knowledge (of theorems and rules) 6. Reading translation ( math to English English to math) 1. Evaluate algebraic expressions. Simplif algebraic expressions 3. Rewrite formulas and equations. Solve inequalit (one variable) 5. Solve absolute value equalit/inequalit 6. Identif functions and their graphs 7. Slope rate of change application 8. Rewrite literal equations and formulas 9. Find domain/range of a function. Write linear equation 11. Graph/evaluate piecewise functions 1. Linear equation 13. Graph linear equation/inequalit 1. Linear inequalit 15. Use functions to solve real-life problems 16. Solve sstem of linear equations (various methods) 17. Graph sstem of equations/inequalities 18. Solve sstem of linear equations (various methods) 19. Solve sstem of linear equations (3 variables) 0. Linear programming application 1. Matrix operations. Matrix operations 3. Matrix application. Determinants 5. Solve sstem of linear equations using inverse matrix 6. Solve quadratic equations b factoring 7. Forms of quadratic equations (vertex intercept standard) 8. Solve quadratic equations b finding square roots 9. Solve quadratic equations b completing the square 30. Solve quadratic equations using quadratic formula 31. Simplif complex numbers 3. Discriminant (determine tpes of roots of quadratic equation) 33. Graph quadratic functions 3. Graph quadratic inequalities 35. Graph polnomial functions 36. Evaluate polnomial functions using direct or snthetic substitution 37. Solve quadratic equations with complex solutions 38. Polnomial operations 39. Factor polnomials 0. Solve polnomials 1. Rational zeros of polnomial functions. Appl Theorems (remainder factor or rational zero) 3. Analze graphs of polnomial functions / identif end behavior. Graph higher order polnomial functions Algebra II Practice Semester Exam 1 Go On

2 Free Response Algebra II Practice Semester Exam 1. Write the Associative Propert for Addition of Real Numbers in general form. Illustrate its use with a numeric expression.. Write the procedure for solving a sstem of linear equations using the substitution method. 3. Use snthetic division to divide 3 x x 5x 1 b x. Explain how the results can be used to write the polnomial expression in factored form.. Write the discriminant of the general quadratic equation ax bx c + + = 0. Explain how it is used to determine the number of real solutions of the equation 5x 3x+ 1=0. 5. Write the Factor Theorem. Explain how it can be used to find zeroes of a polnomial function. 6. The solution set of real numbers greater than and less than or equal to can be written using mathematical notation. Write this solution set as it would be written in set notation.

3 1. Evaluate c = b ac for a = 3 b=1 and. Which of the following expresses all of the solutions for the compound inequalit below? 1 and 9 1 z 9 3( z 8) 3 and 5 + 3z z 1 and z 9 no solution. Which is a simplified form of the expression 1( x 1) (6x 18)? 3 8x 6x + 6 8x 16x 5. Rewrite the absolute value inequalit as a compound inequalit for 6 7 x + <. 13 < x < 1 x < 13 or x > 1 x > 13 or x < 1 no solution 3. Which is a solution for in the equation 3x + = 5x 6+? = x+ 6 = x 6 6. Which of the following is a function? x = + {(6 5) (6 ) ( 1)} {( 1 6) (3 6) ( 5 6)} = 8x 6 = 8x+ 6 3x + 6 5= 1 Algebra II Practice Semester Exam 1 Go On

4 7. You are hiking in the mountains. When ou begin the hike at 1:00 p.m. the temperature is 8 o F. When ou return at :00 p.m. the temperature is 57 o F. What is the average rate of change in the temperature? 7 o F per hour 9 o F per hour 9 o F per hour. Write the standard form of the equation of the line that passes through the point ( 1 ) and is parallel to the line 5x+ = 1. 5x+ = 9 5x+ = 1 x 5 = 8 x 5 = 1 7 o F per hour 8. Rewrite the formula below for surface area of a right circular clinder to solve for the height h. A= π rh+ π r π r A h = π r A h = π r π r 11. Evaluate f ( 3) for the piecewise function x x 0 f( x) =. x 3 x x> 0 f ( 3) = 18 f ( 3) = 3 f ( 3) = 0 f ( 3) = 18 h = A π r π r A h = r π r 1. What is the value of n if 9 n + = 5? What is the range of the following relation? { 1 5} { 1 5} { 3 0} {( 0)(1 3)(5 ) }? all real numbers Algebra II Practice Semester Exam Go On

5 13. Graph the linear equation 9x 7 = The inequalit 3x + 5 can be represented b which of the following? 3 7 x 3 7 x 3x 7 x In 000 the average price of a home in West Count was $ B 007 the average price of a home was $ Which of the following is a linear model for the price of a home P in West Count in terms of the ear t? Let t = 0 correspond to 000. P= t P= t P= t P= t 16. Solve the following linear sstem. 5x = 8 5 = x+ 3 (0 ) ( 8) infinitel man solutions no solution Algebra II Practice Semester Exam 3 Go On

6 17. Graph the following sstem of inequalities. x+ 1 x Find the x-coordinate of the solution to the linear sstem. 5 3x = 1 x + = 5 no solution 19. What is the x-coordinate of the solution to the following sstem of equations? x + z = 5 x + 3z = 1 x 3+ z = Algebra II Practice Semester Exam Go On

7 0. Using linear programming procedures the equation C = x+ 7 is to be maximized subject to the following constraints: x 0 0 x+ 3x+ 8 5x The grid ma be used to graph the feasible region. 1. Which is the sum of A + B given that A = B = 3 7? What is the maximum value for the objective function? Given A = and find the product AB not possible 1 B = Algebra II Practice Semester Exam 5 Go On

8 3. A school fundraiser sells different sizes of gift baskets with a varing assortment of books and pencils. A basic basket contains 3 books and pencils. A big basket contains 7 books and 8 pencils. Books cost $5 and pencils cost $. Which of the following shows the use of matrices to find the total cost for each size of basket? basic 3 6 big 7 8 = 5 5 basic big 7 8 = 51 basic big 8 = The inverse of the coefficient matrix is given. Use the inverse to solve the linear sstem. 3x+ + z = x 3z = 0 x+ + 6z = = A Which of the following is the z-coordinate for the solution to the sstem? basic big 8 = 36. Calculate the determinant of the matrix Solve the equation factoring. x = ± 9 x = 9 x = 9 no solution x 18x+ 81 = 0 b Algebra II Practice Semester Exam 6 Go On

9 7. Rewrite the equation form. x x = in vertex 30. Which of the following shows the solution for x + 7x+ 1= 0 using the quadratic formula? = + ( x ) 1 = + + ( x ) 7 = + ( x ) 13 = + + ( x ) Which are solutions for (6x + ) = 77? Write the expression i 3+ 9i number in standard form i i + i 5 as a complex 9. Which are solutions for x + 6x 0= 0 when solved b completing the square? i 3. Use the discriminant to determine the number and tpe of solutions of the equation 9x 30x + 5= 0. 1 real solution 1 imaginar solution no real solutions imaginar solutions 1 real solution no imaginar solution real solutions Algebra II Practice Semester Exam 7 Go On

10 33. Which graph from a graphing calculator represents the function = ( x + 8x+ 15)? 3. Which of the following graphs from a graphing calculator represents the graph of x x? Algebra II Practice Semester Exam 8 Go On

11 35. Which graph represents the factored function f( x) = x( x 3)( x+ )? 36. Evaluate f ( 1) for the function 3 f( x) = 3x x + 7x. f ( 1) = 16 f ( 1) = 6 f ( 1) = f ( 1) = Solve the quadratic equation 5 + i 3 5 i i 73 5 i i 3 5 i i 73 5 i x 5x + =. 38. Multipl the following polnomials. ( x+ )( x + x+ ) x + x x + 5x + 8x x + 3x + 8x + 16 x + 5x Algebra II Practice Semester Exam 9 Go On

12 39. Factor the polnomial x completel. ( x 1)( x+ 1)( x + 9) x ( x 8) 9 ( x 3)( x+ 3)( x + 1) ( x 3)( x + 3) 8x 9 0. Which of the following represents the solution set of the polnomial equation below? 3 x 8x x+ = 0. According to the rational zero theorem which of the following would be tested as a possible rational zero for the function below? f x x ax x 3 ( ) = State the end behavior of the graph of 3 f ( x) = x + 7x+ as x. f( x) + { 0 1 } f( x) 1 f( x) f( x) 0 1. Which lists the set of all rational zeros of the polnomial function below? { 3 } { 38 } { 18 } { 3 8 } f x x x x 3 ( ) = Algebra II Practice Semester Exam Go On

13 . Which best represents the sketch of the 3 polnomial function = x x 5 x? Algebra II Practice Semester Exam 11 Go On

14 Algebra II Practice Semester Exam Answer Ke 1-6 Free Response 1 D C 3 B D 5 A 6 C 7 B 8 D 9 C B 11 B 1 C 13 A 1 A 15 B 16 D 17 B 18 B 19 B 0 D 1 A B 3 B C 5 A 6 C 7 A 8 C 9 D 30 A 31 B 3 C 33 D 3 A 35 D 36 B 37 C 38 C 39 C 0 A 1 A D 3 A B Algebra II Practice Semester Exam 13 Go On

APPLIED ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY

APPLIED ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Constructed Response # Objective Sllabus Objective NV State Standard 1 Graph a polnomial function. 1.1.7.1 Analze graphs of polnomial functions