ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 1.2-1 What is the inverse of f ( x) 2 x 9 ? (A) f 1 ( x) x 9 2 (B) f 1 ( x) 1 2x 9 (C) f 1 ( x) x9 2 (D) f 1 ( x) 2 x9 1 1.2-2 If f ( x) 4 x 8 , what is f ( x) ? 3 (A) f ( x) 3 ( x 8) 4 (B) f ( x) 3 x 8 4 (C) f ( x) 4 x6 3 (D) f ( x) 4 ( x 8) 3 1.4-1 Which statement must be true if f and g are inverses of one another? (A) ( f g )( x) ( g f )( x) x (B) ( f g )( x) f ( x) g ( x) ( g f )( x) g ( x) f ( x) x (C) ( f g )( x) f ( g ( x)) ( g f )( x) g ( f ( x)) x (D) ( f g )( x) 2014–2015 Clark County School District 1 x ( g f )( x) Page 1 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 3.4-1 Simplify (3- 4i) + (5- 6i) . (A) (B) (C) (D) 8+10i -9 - 38i 8-10i 6 -10i 3.4-2 Simplify (1- 3i) - (-3+ 7i) . (A) (B) (C) (D) 4 -10i 4 + 4i 18 +16i -2 + 4i 3.6-1 (3.3) Solve the quadratic equation by taking the square root. 4 x 2 5 1 6 2 (A) x (B) x (C) x i 6 2 (D) x 6 4 6 4 2014–2015 Clark County School District Page 2 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 3.7-1 (3.1, 3.5) A student has learned that test scores in math are determined by this quadratic function: s(t ) (t 6)2 99 In the function, s is the score and t is the number of hours that a student spends on homework each week. a) How many hours must a student spend on homework to achieve maximum score? b) What is the maximum score? c) Based on the function, what will be the score if a student does no homework? 2 3.7-2 (3.3) Show that (3 i) is a root of x 6 x 10 0 . 2 3.7-3 (3.3, 3.6) Solve x 25 0 over the set of complex numbers. (A) 25i (B) 5 (C) 5i (D) 25 3.7-4 (3.2, 3.5) Function A and Function B are continuous quadratic functions. Function A Function B f ( x) x 2 x 6 Which function has a greater positive x-intercept? (A) Function A (B) Function B 2014–2015 Clark County School District Page 3 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 3.7-5 (3.1, 3.5) What is the equation of the parabola shown? (A) y 4 x 2 (B) y 2 x 2 (C) 1 y x2 2 (D) 1 y x2 4 2 3.7-6 (3.3) Factor 9 x 121 . (A) (3x 11)(3x 11) (B) (3x 11)(3x 11) (C) (3x 11i)(3x 11i) (D) (3x 11i)(3x 11i) 2 3.7-7 Solve the equation 6 x 24 x 126 by factoring. (A) x 7 or x 3 (B) x 7 or x 3 (C) x 7 (D) x3 2014–2015 Clark County School District Page 4 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 3.7-8 What is the solution set of y 2 2 y 3 y 14 ? (A) y7 (B) y 2 or y 7 (C) 7 y 2 (D) 2 y 7 3.7-9 Which of the following is a factor of (a 1)2 b2 ? (A) a b 1 (B) a b (C) a 1 (D) a b 1 3.8-1 (3.3, 3.7) Which of the following quadratic equation has no real roots? (A) 2 x2 7 x 9 0 (B) 2 x2 7 x (C) 2 x2 7 x 9 0 (D) 2 x2 7 x 9 0 2 3.8-2 (3.2) Find the vertex of y = x + 2x - 3 and state if it is a maximum or a minimum. (A) (-1, -4); maximum (B) (-1, -4); minimum (C) (-4, -1); maximum (D) (-4, -1); minimum 2014–2015 Clark County School District Page 5 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 3.8-3 (3.1) Consider the function f ( x) x2 2 x 48. a) Determine the roots of the function. Show your work. b) The vertex of g x is the point (3, 30). Write the function rule for g in vertex form. c) Explain how f x transformed to become g x . 2 3.8-4 For what values of c will 3x 2 x c 0 have exactly one distinct real root? (A) 3 2 (B) 1 3 (C) 1 3 (D) 2 3 3.9-1 Solve the equation by using the quadratic formula. 2 x2 5x 3 0 (A) x = 1 or x = -6 (B) x= 1 or x = -3 2 (C) x 1 or x 1 3 2 3.9-2 (3.8) Given the general form of a quadratic equation x bx c 0 , determine the effect of each condition on the solutions. a) b) c) d) b0 c0 c0 What is needed for the solutions to have imaginary parts? 2014–2015 Clark County School District Page 6 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 3.13-1(3.5) Use the graph provided to choose the best description of what the graph represents. Height (ft) Time (s) (A) A ball I dropped from a height of 42 feet and lands on the ground after 3 seconds. (B) A ball is dropped from a height of 42 feet and lands on the ground after 1.5 seconds. (C) A ball is shot up in the air and reaches a height of 42 feet after 1 second. (D) A ball is shot up in the air, reaches a height of 42 feet, and lands on the ground after 1.5 seconds. 3.14-1 (3.4, 3.7) The height of Carl, the human cannonball, is given by h(t ) 16t 2 56t 40 where h is in feet and t is in seconds after the launch. a) What was his height at the launch? b) What is his maximum height? c) How long before he lands in the safety net, 8 feet above the ground? 3.14-2 (3.5, 3.13) Several values of the quadratic function f ( x) are given in the table. 2014–2015 Clark County School District Page 7 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 x f ( x) 4 96 2 24 0 0 4 96 9 486 The function g ( x) is given by g ( x) ( x 2)2 3 . Which function has the greater maximum for which value of x ? (A) f ( x); for x 0 (B) f ( x); for x 6 (C) g ( x); for x 2 (D) g ( x); for x 3 3.14-3 (3.8) Which statement best describes these two functions? f x x2 x 4 g x 3x 2 3x 7 (A) The maximum of f ( x) is less than the minimum of g ( x) . (B) The minimum of f ( x) is less than the maximum of g ( x) . (C) The maximum of f ( x) is greater than the minimum of g ( x) . (D) The minimum of f ( x) is greater than the maximum of g ( x) . 3.14-4 (3.1, 3.13) The amount of fuel F (in billions of gallons) used by trucks from 1990 through 2009 can be approximated by the function F f (t ) 20.5 0.035t 2 where t 0 represents 1990. a) Describe the transformation of the common function f (t ) t 2 . Then sketch the graph over the interval 0 t 19. f (19) f (0) b) Find and interpret . 19 0 2014–2015 Clark County School District Page 8 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 c) Rewrite the function so that t 0 represents 2000. Explain how you got your answer. d) Use the model from part (c) to predict the amount of fuel used by trucks in 2015. Does your answer seem reasonable? Explain. 4.2-1 What is the 4th term of the expanded binomial (2 x 1) 6 ? (A) 240x3 (B) 60x3 (C) 240 x3 (D) 160 x3 4.2-2 Suppose xy 9 and ( x y)2 21 . What is x2 y 2 ? (A) 3 (B) 12 (C) 36 (D) 81 4.3-1 The table lists all the real roots of a 5th degree polynomial p ( x) and the multiplicity of each root. x Multiplicity 3 1 1 1 1 2 2 1 Which general factorization correctly represents p ( x) ? (A) a( x 3)( x 1)2 ( x 2) 2014–2015 Clark County School District Page 9 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 (B) a( x 3)( x 1)3 ( x 2) (C) a( x 3)( x 1)( x 1)2 ( x 2) (D) a( x 3)( x 1)3 ( x 2) 4.3-2 A 4th degree polynomial with real coefficients is found to have exactly two distinct real roots. What must be true about the other two roots? (A) One root is real and the other is imaginary. (B) Both roots must be real. (C) Both roots are imaginary roots that are complex conjugates. (D) All the roots have been found. 4.4-1 Divide ( x 4 2 x3 7) ( x2 1) using long division. (A) x2 2 x 1 6 x 1 (B) x2 2 x 1 2x 6 x2 1 (C) x2 2 x 1 2x 6 x2 1 (D) x2 2 x 1 2x 6 x2 1 2 4.4-2 The volume V ( x) and height ( h ) of the prism is given. Find a polynomial expression for the area of the base ( B ) in terms of x . (Hint: V Bh ) h x2 2014–2015 Page 10 of 22 V ( x) 2 x 5 x 4 3 Clark County School District 2 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 (A) 2 x2 x 2 (B) 2 x2 4 x 4 (C) x6 (D) x2 5x 3 4.4-3 Write an expression that represents the width of a rectangle with length x 5 and area x3 12 x 2 47 x 60 . (A) x3 7 x 2 12 x (B) x 2 7 x 12 x 2 17 x 38 x50 5 ALGEBRA II(C) Honors 2013–2014 SEMESTER EXAMS x 2 17 x 132 720 (D) x 5 PRACTICE MATERIALS SEMESTER 1 (4.3)graph Use of the pgraph answer questions p ( x) to 28.4.6-1 Use the answer questions. ( x) toof a) True or False: The leading term of p ( x) , when written in standard form, is a) True orpositive. False: The leading term of p ( x) , when written in standard form, is positive. b) 2014–2015 True or False: From the graph, p(-3) Page The multiplicity of the factor Revised even. Explain = 0 . 11 ( x + 3) is of 22 July 2014 your answer. Clark County School District 29. If f ( x ) = 2 x 4 + 7 x 3 + 3 x 2 - 8 x - 4 , find the possible rational roots of f ( x) . ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 b) True or False: From the graph, p(3) 0 . The multiplicity of the factor ( x 3) is even. Explain your answer. 4.6-2 (4.3) Which graph represents f ( x) x5 6 x3 9 x ? 2014–2015 Clark County School District Page 12 of 22 Revised July 2014 ALGEBRA II Honors 2013–2014 SEMESTER EXAMS PRACTICE MATERIALS ALGEBRA II SEMESTER 1 SEMESTER EXAMS 2014–2015 PRACTICE MATERIALS 40.SEMESTER Which graph1represents f ( x) = x 5 - 6 x 3 + 9 x ? (A) (B) (C) (D) 2013–2014 2014–2015 Clark County School District Clark County School District Page 13 of 29 Page 13 of 22 Revised November 2013 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 4.7-1 (4.6) Use the information in the table. Interval Value of f(x) (, 2) Negative (2,1) Positive (1, 4) Negative (4, ) Positive a) What are the three real zeros of the polynomial function f ? b) What can be said about the behavior of the graph of f at x 0 ? c) What is the least possible degree of f ? Explain. Can the degree of f ever be even? Explain. 4.8-1 According to the Fundamental Theorem of Algebra, how many roots does the following equation have? 6 x 2 4 11x (A) 2 (B) 4 (C) II6Honors ALGEBRA 2013–2014 EXAMS (D) SEMESTER 11 PRACTICE MATERIALS SEMESTER 4.9-1( 4.3, 4.6)1Consider the graph of p ( x) below. Which general factorization correctly represents p ( x) . 26. Consider the graph of p ( x) below. Which general factorization correctly represents p ( x) . Which general factorization correctly represents p ( x) ? Which general factorization correctly represents p ( x) ? 2014–2015 (A) a( x + 3)( x - 2)( x - 4) Page 14 of 22 (B) a( x + 3)( x + 2)( x + 4) (C) a( x - 3)( x + 2)( x - 4) (D) a ( x - 3)( x - 2)( x - 4) Clark County School District Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 Which general factorization correctly represents p ( x) ? x x3)( x x2)( (A)(A) a( xa+(3)( - 2)( - x4) 4) x x3)( x2)( (B) (B) a( xa+(3)( + x2)( + x4) 4) x x3)( x2)( (C) (C) a( xa-(3)( + x2)( - x4) 4) x x3)( x2)( (D)(D) a( xa-(3)( - x2)( - x4) 4) ) is shown below. 4.9-2 (4.3, 4.6)of Thep (graph of p ( xbelow. 27. The graph x) is shown p( x) ? Which general factorization Which general factorization correctlycorrectly representsrepresents p( x) ? x x3)( x x2)( (A)(A) -4(x4( - 3)( - 2)( - x4) 4) x x3)( x2)( (B) (B) 6( x 6( - 3)( + x2)( + x4) 4) (C) (C) 1 1 ( x 3)( x 2)( x 4) ( x + 3)( x - 2)( x - 4) 4 4 x x3)( x2)( (D)(D) 4( x 4( + 3)( + x2)( + x4) 4) 2013–2014 4.9-3 9 of 29 Revised 2013 f ( x)November 4 , find (4.3) If f ( x) 2 x 4 7 x3 3x 2 8x Page the possible rational roots of . Clark County School District (A) x 1, 4 (B) x 1, 4 (C) 1 x , 1, 2 2 (D) 1 x , 1, 2, 4 2 2014–2015 Clark County School District Page 15 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 4.9-4 (4.3) Given polynomial q( x) , q(4) 6 . Which statement is correct? (A) x 4 is not a root (B) x 4 is a root (C) ( x 4) is a factor (D) ( x 4) is not a factor 4.9-5 (4.3) p( x) 3x5 13x 4 19 x3 17 x2 16 x 4 a) Show that p(2) is a root. b) Factor p ( x) completely c) If f ( x) p( x 3) , what are the real roots of f ( x) ? 4.9-6 (4.3) Given the polynomial p( x) x 4 3x3 12 x 16 : a) Show that p(2i) is a root. b) What other root must also be a root of p ( x) ? Explain. c) Factor p ( x) completely. 4.9-7 Write a cubic function that passes through the following points: (-2, 0) (3, 0) (1, 0) and (1, 2). (A) y x3 7 x 6 (B) y x3 7 x 6 (C) y (D) 1 7 y x3 x 1 6 6 1 3 7 x x 1 6 6 4.9-8 How many possible rational zeros exist for the polynomial function y 3x6 9 x 2 4 x 12 ? (A) 9 (B) 12 2014–2015 Clark County School District Page 16 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 (C) 18 (D) 24 4.9-9 This polynomial function has at least one rational root. p( x) x 4 kx 2 9 a) What are all the possible integer values of k ? Show your work or explain how you know. b) What are all the possible real roots of the function? Show your work or explain how you know. 4.11-1 (4.3, 4.9) Consider p( x) 2 x4 x3 11x2 5x 5 . a) Show that x 5 and x 5 are zeros of p ( x) . b) Completely factor p ( x) where all the coefficients are rational numbers. c) h( x) is p ( x) translated 4 units right and 2 units up. What is the equation of h( x ) ? 4.11-2 (4.3, 4.9) Consider p( x) x4 2.5x3 7.5x2 15x 9 . a) Show that x 6 are roots of p ( x) , then write p ( x) as the appropriate factorizations at this point. b) Factor p ( x) completely. c) Let q( x) p(4 x) . List out the roots of q( x) . d) Let f ( x) be p ( x) vertically stretched by 2, translated 2 units to the right and 4 units up. Write out the algebraic relationship between f ( x) and p ( x) . 4.11-3 (4.6) Consider the function f ( x) 3x3 9 x 2 3x 9 . a) Use the leading coefficient and degree of f ( x) to describe the end behavior. b) Write the rule for the function g ( x) f ( x) , and describe the transformation. c) Describe the end behavior of g ( x) . How does the end behavior of g ( x) relate to the transformation of f ( x) ? 2014–2015 Clark County School District Page 17 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 4.12-1 (4.6, 4.7) The town of Frostburg experienced a bit of a heat wave during January of this year. The graph below shows the curve of best fit that represents the low temperature of every day in January. A newspaper journalist is writing a story on the weather and needs to report some information. He needs a bit of guidance with interpreting the graph. 1) Write a few sentences describing the key characteristics of the graphs as it relates to the context of the problem. Be sure to include domain, range, intervals where the function increases and decreases, x and y intercepts, and any other important information 2014–2015 Clark County School District Page 18 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 The graph below shows the curve of best fit that represents the low temperature of every day in February. 2) Three different models have been proposed that could be used to determine the temperature for a particular date in February. The models are given below: Model 1: y ax 2 bx c Model 2: y a( x 3)( x 9)( x 20)2 Model 3: y a( x 3)( x 9)( x 20)2 Which model would best describe the low temperatures for February? Explain why you chose that model. The weather in July showed a related pattern to the weather in February. The curve of best fit for July is shown below: 3) Explain the relationship between the graph for February and the graph for July. Use that relationship to create an equation for the temperatures in July. 2014–2015 Clark County School District Page 19 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 5.2-1 (5.1) If f (x) = x 2 -1 and g(x) = x -1 , which expression represents f (x) g(x) for x 1 ? (A) x (B) x -1 (C) x +1 (D) 1 x +1 5.3-1 Identify the x and y intercepts of the function f ( x) 3 x 8 . (A) (8,0) and (0,-2) (B) (2,0) and (0,2) (C) (8,0) and (0,8) (D) (-2,0) and (0,8) 5.3-2 Which is the domain of the function f ( x) 5 x 4 3 ? (A) {x | x 4} (B) {x | x 3} (C) {x | x 0} (D) {x | x } 5.4-1 (5.3) Compare the graph of y 6 3 x with the graph of its parent function f ( x) 3 x . (A) Shifts 6 units down (B) Reflects across the x-axis and shifts 6 units down (C) Reflects across the x-axis and shifts 6 units up (D) Reflects across the y-axis and shifts 6 units up 2014–2015 Clark County School District Page 20 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 5.5-1 (5.1, 5.2) Which value of x makes this equation true? 4 9(x - 7) 3 = 9 (A) 1 (B) 7 (C) 8 (D) 34 5.5-2 (5.1,5.2) Solve for x : 3 4x 1 5 (A) x 31 (B) x6 (C) x 31 (D) No real solution 5.5-3 Solve for x . x 7 x 1 (A) x 5 and x 10 (B) x5 (C) x 10 (D) No real solutions 5.5-4 Solve for x . x 3 x 3 (A) x4 (B) x6 (C) x9 (D) No real solutions 2014–2015 Clark County School District Page 21 of 22 Revised July 2014 ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 5.5-5 (5.2) If 3 12 x 28 4 , what is the value of x3 ? (A) -8 (B) 3 (C) 12 (D) 27 5.6-1 Which is the inverse of f ( x) (2 x 1)3 4 ? (A) a ( x) 3 2 x 1 4 (B) b( x ) (C) a( x) (D) a( x) 3 x 4 3 x4 1 2 3 x 4 1 2 2014–2015 Clark County School District 1 2 Page 22 of 22 Revised July 2014
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