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Algebra II – Review Questions for 1st Semester Final Exam Chapter 1 Review Questions 1) Evaluate 6d 3e for d = –5 and e = 3. a. 39 b. –2 c. 9 d. –21 2) Evaluate 15 + c for c = 17. a. 2 c. 32 b. –2 d. –32 Simplify the expression. 3) a. c. b. d. 4) 5g + 18g a. g + 23 c. 23g b. –13g d. 5) 3r 7r 9r a. 13r c. 5r b. 19r d. –19r Determine which value is a solution of the equation. 6) a. 15 b. c. 18 d. 28 7) a. 16 b. 17 c. 15 d. 14 8) a. 135 b. 126 c. 134 d. 130 9) 10x + 7 = 57 a. 64 b. 50 c. 2 d. 5 10) a. 20 c. –3 b. –7 d. 15 11) The literature club is printing a storybook to raise money. The print shop charges $3 for each book, and $45 to create the film. How many books can the club print if their budget is $525? a. 165 b. 170 c. 175 d. 160 12) Use an equation to model the sentence. How many raisins are left in a jar of 49 raisins after you have eaten some? a. R = 49 – N b. c. d. R = 49 + N 13) Solve for t in the equation . a. b. c. d. 14) Solve for p: a. 7 c. p= q p= 6 b. 6 d. p= q p= 7 15) Solve for A : B = (A – 11) a. b. c. d. 16) Solve for t in the equation a. b. c. d. 17) Solve for c in the equation . a. b. c. d. 18) A grocery store sells 2 boxes of cereal for $4.95. Which method can be used to find the total cost c of purchasing n boxes of cereal? a. Multiply n by the cost of one box. b. Divide n by c. c. Multiply n by c. d. Divide n by the cost of one box. 19) An oil tank contains 208.3 gallons of oil. Whenever the amount of oil drops below 50 gallons, an alarm sounds. If 182.5 gallons are pumped into a delivery truck, how many gallons must be pumped back into the tank in order to shut off the alarm? a. at least 25.4 gallons b. at least 24.2 gallons c. at least 134.1 gallons d. at least 25.8 gallons 20) On a road in the city of Hinkley, the maximum speed is 50 miles per hour and the minimum speed is 20 miles per hour. If x represents speed, which sentence best expresses this condition? a. b. c. d. 21) a. 1, 1 c. 2 8 , 5 5 b. 2 8 d. 1, 2 , 5 5 22) a. c. or b. d. or 23) Write in ascending order and graph on a number line a. b. c. d. 24) Which of the properties of real numbers is illustrated below? 3 x (4 + 2) = 3 x 4 + 3 x 2 A. commutative property C. associative property B. distributive property D. inverse property 25) Solve. 5x + 5 ≤ 2x – 4 A. x = –9 C. x 3 B. x –3 D. x 9 26) Solve the compound inequality. x + 3 ≤ 8 or x – 2 ≥ 25 A. x ≤ 5 B. x ≤ 5 or x ≥ 27 C. x ≥ 27 D. 5 ≤ x ≤ 27 Chapter 2 Review Questions 1. Which relation is a function? A. (3,6), (3,6), (4,6), (4,6) B. (4,3), (4,3), (5,3), (5,3) C. (1,9), (1,9), (1,9), (1,9) D. (2,3), (2,3), (7,3), (7,3) 2. Which relation is not a function? A. B. C. D. 3. What is the slope of the line passing through points (-1,3) and (2, -1)? 3 4 3 4 A. B. C. D. 4 3 4 3 4. Find an equation of the line perpendicular to the graph of y = 5x + 4 and passing through the point (10, -1). A. x + 5y = 5 B. x – 5y = 15 C. 5x – y = 51 D. 5x – y = – 49 5. Which equation is linear? A. f(x) = 7x3 – 20 B. y = 3x2 + 5x – 1 C. 4x – 6y = 15 D. f(x) = 2│x –4│– 10 6. What is the slope-intercept form of – 5x + 6y = 20? 5 10 5 10 6 10 6 10 A. y = x+ B. y = – x+ C. y = x– D. y = – x+ 6 3 6 3 5 3 5 3 7. What is the x-intercept of the graph of 4x – 5y = 20? 4 A. B. –4 C. 5 D. 20 5 3 8. Find an equation of the line through the point (-2, 1) with slope . 4 A. 3x + 4y = –10 B. 3x – 4y = –10 C. 3x – 4y = 10 D. – 3x – 4y = –10 9. Which equation is a direct variation equation that has (-2, 6) as a solution? 3 2 1 A. y = x + 8 B. y = x C. y = x D. y = –3x 2 5 10. Which equation describes the graph shown to the right? A. y = 2│x + 5│+ 2 B. y = –2│x – 5│+ 2 C. y = 2│x – 5│+ 2 D. y = –2│x + 5│+ 2 11. What is the vertex of f(x) = 7│x – 4│– 11 ? A. (-4,-11) B. (4, -11) C. (4, 11) D. (-4, 11) 12. The graph of y = 5│x│ will be __________ than the graph of y = │x│. A. wider B. narrower C. translated right D. translated left 13. Which graph is a reflection of the graph y = -7│x│ over the x-axis? 1 1 A. y = 7│x│ B. y = – 7│x│ C. – │x│ D. y = │x│ 7 7 14. Which ordered pair is not a solution of – 2x + 4y > 22? A. (1, 8) B. (-1, 10) C. (5, 0) D. (-8, 3) 15. Which equation describes the graph shown to the right? y A. y > 3│x – 2│– 2 B. y ≥ 3│x + 2│– 2 C. y < 3│x – 2│– 2 D. y ≤ 3│x + 2│– 2 (3,1) x (2,-2) Chapter 3 Review Questions 1. Which of the ordered pairs below is a solution of the system of equations: 4x – y = 4 x + 2y = 10 A. (0, 5) B. (1, 0) C. (2, 4) D. (6, 7) 2. How many solutions are there for the following system of equations? 2y = 6x + 2 4y = -12x + 10 A. no solutions B. 1 solution C. 2 solutions D. infinitely many solutions 3. Which expression can be substituted in for ‘y’ in the bottom equation in order to solve the system by substitution? 4x y 4 4 x 2y 10 A. 4x + 4 B. x + 5 C.2x + 5 D. 5 – 2x 4x y 4 4. Solve the system of equations by elimination. What is the value of x? 6 x 5 y 1 3 1 19 A. B. 2 C. D. 2 2 14 5. Which matrix equation can be used to represent the system of equations? x + y+ z=2 2x + y + 2z = 3 3x – y + z = 4 1 1 1 1 2 x 1 1 1 x 2 A. 2 1 2 · 3 = y B. 2 1 2 · y = 3 3 1 1 4 z 3 1 1 z 4 1 1 1 x 2 x 1 1 1 2 2 1 2 3 C. 2 1 2 · y = 3 D. y · = 3 1 1 z 4 z 3 1 1 4 1 6. A represents A. the discriminant of a matrix B. the determinant of a matrix C. a matrix D. the inverse of a matrix 1 8 7. Evaluate 5 2 A. 38 B. – 42 C. -38 D. 18 3 x 5 y 7 8. Which expression can be used to calculate x in the system at the right? 2 x 4 y 10 7 5 3 5 3 7 7 5 10 4 2 4 2 10 10 4 A. B. C. D. 3 5 7 5 3 5 3 5 2 4 10 4 2 4 2 4 9. What is the identity matrix ‘I’ for a 2 2 matrix? 1 1 1 0 0 1 0 0 A. B. C. D. 1 1 0 1 1 0 0 0 2 2 1 1 0 10. Find the product if possible. 2 1 3 2 1 0 5 8 1 B. C. D. Cannot be multiplied 0 A. 1 6 4 because dimensions 7 do not match 3 1 11. Which matrix is the inverse if A = . 4 2 1 1 1 1 2 1 B. 3 2 3 4 1 C. 3 A. . D. 4 3 1 2 1 2 4 2 2 12. Which equation would be used to solve this system by the matrix inverse method? – 2x + y = -6 3x – 3y = 12 1 1 2 1 x 6 2 1 6 x A. 3 3 y 12 B. 3 3 12 y 1 1 1 6 2 1 x 6 x 2 1 C. D. 12 3 3 y 3 3 y 1 12 13. Solve the following system using any algebraic method: 2x y z 1 x 2y 2z 10 2x z 3 A. (0, 2, 1) B. (2, -1, 0) C. (6, 2, 2) D. (0, 2, 3) y x 14. Graph the linear system and estimate the solution: y 2x 3 A. (0, 0) B. (2, -2) C. (-1, 1) D. (-2, 2) 15. Graph the linear system then classify it as consistent and independent, consistent and dependent or inconsistent. y x3 y 2x Chapter 4 Review Questions 1. Find the equation of the axis of symmetry for the graph of y 2 x 2 x 17 , and state whether the axis of symmetry contains the minimum or maximum point of the graph. 1 1 A. x ; maximum B. x ; minimum 4 4 1 1 C. x ; minimum D. x ; maximum 4 4 2. Which function does NOT have a maximum value? A. y = -x2 – 5x – 6 B. y = -x2 – x – 6 C. y = 3x2 – 15x + 2 D. y = 49 – x2 3. What are the x-intercepts of y = -2(x – 7)(x + 2)? A. -7 and 2 B. 7 and -2 C. 14 and -4 D. 14 and -2 4. Which of the graphs below shows the graph of the equation y = -(x – 3)2 – 1? y y A. B. x x C. y D. y x x 5. How would you translate the graph of y = -x2 to produce the graph of y = -(x + 1)2? A. Translate the graph of y = -x2 up 1 unit B. Translate the graph of y = -x2 down 1 unit C. Translate the graph of y = -x2 left 1 unit D. Translate the graph of y = -x2 right 1 unit 6. Which of the following most accurately describes the translation of the graph y = (x + 3)2 – 2 to the graph of y = (x – 2)2 + 2? A. up 4 and 5 to the right B. down 2 and 2 to the right C. down 2 and 3 to the left D. up 4 and 2 to the left 7. Find the axis of symmetry of the function y = (x – 9)(x + 5) A. axis of symmetry is x = -4 B. axis of symmetry is x = -2 C. axis of symmetry is x = 4 D. axis of symmetry is x = 2 8. Find the axis of symmetry of the function y = (x + 3)(x – 11) A. axis of symmetry is x = -4 B. axis of symmetry is x = 4 C. axis of symmetry is x = 8 D. axis of symmetry is x = -8 9. Factor the expression x2 + 14x + 48 A. (x – 8)(x – 6) B. (x + 24)(x + 2) C. (x – 24)(x – 2) D. (x + 8)(x + 6) 10. What are the roots of the equation z2 + 11z – 42 = 0? A. -3, -14 B. 3, -14 C. -3, 14 D. 3, 14 11. Factor the expression 8x2 + 28x + 12. A. 2(x + 2)(4x + 3) B. 2(x + 3)(2x + 1) C. 4(x + 1)(2x + 3) D. 4(x + 3)(2x + 1) 12. What are the solutions of the equation (7x – 5)(x + 3) = 0? A. x = -7/5 or x = -3 B. x = 7/5 or x = -3 C. x = -5/7 or x = -3 D. x = 5/7 or x = -3 13. Simplify the expression 3 5 10 A. 315 B. 15 3 C. 152 D. 350 14. Simplify the expression 2 2 + 3 A. 4/13 B. 2 C. 4 – 23 D. 4 – 23 -5 15. Simplify the expression 7 5 + 2 A. 49/25 B. 7/23 B. 35 + 72 C. 35 – 72 25 23 16. Solve for x 3x2 = 12 A. 36 B. 2 C. 9 D. 6 17. Solve for x 2x2 – 39 = 33 A. 3 B. 6 C. 6 D. i6 18. Solve for x 3(x + 7)2 – 17 = 25 A. 42 14 B. 42 13 C. -7 13 D. -7 14 19. Write the expression as a complex number in standard form. (-2 + 4i) + (3 – 9i) A. -5 + 13i B. 30 + 30i C. 1 – 5i D. 1 + 5i 20. Write the expression as a complex number in standard form. (12 + 4i) – (6 – 9i) A. 72 – 36i B. 6 – 5i C. -6 + 13i D. 6 + 13i 21. Which value of c makes the expression x2 – 5x + c a perfect square trinomial? A. -5/2 B. 5/2 C. 25/4 D. 25 22. Which value of c makes the expression x2 + 7x + c a perfect square trinomial? A. -7/2 B. 7/2 C. -49/4 D. 49/4 23. Write the expression as a complex number in standard form. 4 + 4i 2 – 9i A. 4 – 4i 11 7 B. -28 + 44i 85 85 C. 2 + 4i 9 D. 44 – 28i 85 85 24. Rewrite the equation y = x2 – 4x – 3 in vertex form. A. y = (x + 2)2 – 7 B. y = (x + 2)2 + 1 C. y = (x – 2)2 – 7 D. y = (x – 2)2 + 1 25. Rewrite the equation y = x2 + 8x + 17 in vertex form. A. y = -(x + 8)2 + 1 B. y = -(x + 4)2 + 1 C. y = (x + 8)2 + 1 D. y = (x + 4)2 + 1 26. Solve by completing the square: x2 + 8x – 9 = 0 A. -9, -1 B. 9, -1 C. -9, 1 D. 9, 1 27. What is the value of the discriminant of -2x2 – 3x + 7 ? A. -47 B. 47 C. -65 D. 65 28. If the discriminant of a quadratic equation of the form ax 2 bx c 0 is 0, then the equation has: A. one real solution B. two real solutions C. one imaginary solution D. two imaginary solutions 29. Solve 3x 2 5x 16 0 3 6 3 5 6 3 5 167 5 217 A. B. C. D. 5 5 6 6 Chapter 5 Review Questions Simplify the expression. Give your answer in exponential form. 1) a. b. c. d. Simplify the expression. 2) a. c. b. d. 3) a. b. c. d. 4) Which is the graph of the function f(x) = ? a. y c. y 10 10 –10 x –10 x –10 –10 b. y d. y 10 10 –10 x –10 x –10 –10 5) Find the sum or difference. a. c. b. d. 6) Find the missing term: . a. 12 b. 3 c. 6 d. 9 7) A rectangle has a length of and a width of . Which equation below describes the perimeter, P, of the rectangle in terms of x? a. c. b. d. 8) Find the real-number solutions of the equation. a. 4, –5 c. –4, 4 b. 0, –4 d. 0, 4 9) The volume of one of the buildings in the downtown area is 826,200 cubic meters. The building is 17 times as tall as the radio tower on top of the building. The square base has a side that is 30 times 3 meters less than the height of the radio tower. How tall is the radio tower? a. 6 meters c. 16 meters b. 12 meters d. 8 meters 10) Divide. a. c. b. d. 11) a. c. b. d. 12) a. c. b. d. 13) A rectangle has an area of square meters and a width of meters. Find its length, in terms of x. a. meters c. meters b. meters d. meters 14) List the possible rational zeros of the function using the rational zeros theorem. a. c. b. d. 15) Use synthetic substitution to evaluate f ( x) 2 x3 3x 4 when x=2 a. –6 b. 8 c. 4 d. –29 16) Factor . a. b. c. d. 17) Factor 6 x3 24 x a. 6(x + 2)(x – 2) b. 6(x + 2)2 c. 6(x – 2)2 d. prime 22) Find the product of (2 x 3)( x 2 5 x 4) a. -11x2 +23x -12 b. 2x3 -13x2 + 23x -12 c. 2x3 -3x2 - 10x -12 d. 2x3 -13x2 - 7x -12