Algebra 2: Q1 & Q2 Review
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1 Name: Class: Date: ID: A Algebra 2: Q1 & Q2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. Short Answer To which sets of numbers does the number belong? Find the opposite and the reciprocal of the number π 1
2 Name: ID: A Evaluate the expression for the given value of the variable(s). 4. 4b b 2 + 2b 3 ; b = 2 Simplify by combining like terms. 5. 3( 4y + 3) + 7y Solve the equation. 6. 3y + 20 = 3 + 2y r r = r x = 5 9. x x + 81 = 25 Solve for x. State any restrictions on the variables. 10. ax + bx + 9 = 7 Solve the inequality. Graph the solution set (3b 5) < b Solve the compound inequality. Graph the solution set x 5 < 17 or 5x + 6 > 31 Solve the inequality. Graph the solution x + 10 < A furniture maker uses the specification w for the width w in inches of a desk drawer. Write the specification as an inequality. 15. When Spheres-R-Us ships bags of golf balls, the number of balls in each bag must be within 6 balls of 300. Write an absolute value inequality and a compound inequality for an acceptable number of golf balls b in each bag. 16. Suppose f( x) = 4x 2 and g ( x) = 2x + 1. f( 5) Find the value of g ( 3). 17. Graph the equation 3x y = Find the point-slope form of the equation of the line passing through the points ( 6, 4) and (2, 5). 2
3 Name: ID: A Find an equation for the line: 19. through ( 4, 6) and parallel to y = 3x through ( 7, 4) and vertical. Graph the absolute value equation. 21. y = 2x What is the vertex of the function y = 3x + 2 4? 23. Write the equation for the translation of y = x. 24. Write the equation that is the translation of y = x left 1 unit and up 2 units. Graph the inequality x 2y < 3 3
4 Name: ID: A Write an inequality for the graph Graph the function y = 2 x + 5. Solve the system by graphing. 28. Ï Ôy = x 9 Ì Ô3x y = 11 Ó Solve the system by the method of substitution. 29. Ï x + y + 3z = 4 Ô Ì x y 2z = 5 Ô Ó 2x z = 3 Use the elimination method to solve the system. 30. Ï Ô5x + 3y = 6 Ì Ô3x 2y = 4 Ó Solve the system of inequalities by graphing. 31. Ï Ôx 2 Ì Ôy > 3 Ó 4
5 Name: ID: A Ï Ôy < x + 6 Ì Ô2x + y < 6 Ó Ï Ôy 4 Ì Ôy > 2x + 4 Ó 34. A factory can produce two products, x and y, with a profit approximated by P = 12x + 23y 900. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y What production levels yield maximum profit? 35. Use vertex form to write the equation of the parabola. 36. Write y = 2x x + 14 in vertex form. Factor the expression x x x Solve by factoring. 4x x 32 = 0 Solve the equation by finding square roots x 2 = Find 5 4i. 5
6 Name: ID: A Simplify the expression. 43. (2 5i) (3 + 4i) 44. (2 + 5i)( 1 + 5i) Use the Quadratic Formula to solve the equation x 2 x + 3 = 0 Sketch the asymptotes and graph the function. 46. y = 2 x Simplify the rational expression. State any restrictions on the variable. 47. q q + 24 q 2 5q 24 Multiply or divide. State any restrictions on the variables a 5 7b 4 2b 2 2a z 2 z + 1 z 2 + 3z + 2 z 2 + 3z x 2 x x + 6 x 2 + 5x + 4 x 2 2x 8 Add or subtract. Simplify if possible a a 2 64 b 2 2b 8 6 b 2 + b 2 b 1 6
7 Algebra 2: Q1 & Q2 Review Answer Section MULTIPLE CHOICE 1. ANS: A DIF: L2 OBJ: Using Vertex Form SHORT ANSWER 2. ANS: rational numbers, real numbers DIF: L2 OBJ: Graphing and Ordering Real Numbers 3. ANS: 1 π 4, 4 π DIF: L3 OBJ: Properties of Real Numbers 4. ANS: 21 DIF: L4 OBJ: Evaluating Algebraic Expressions 5. ANS: 19y 9 DIF: L3 OBJ: Simplifying Algebraic Expressions 6. ANS: 17 DIF: L2 OBJ: Solving Equations 7. ANS: 9 4 DIF: L3 OBJ: Solving Equations 8. ANS: x = 0 or x = DIF: L2 OBJ: Absolute Value Equations 9. ANS: 4, 14 DIF: L2 OBJ: Solving Equations by Completing the Square 1
8 10. ANS: 2 x = a + b ; a b DIF: L2 OBJ: Solving Equations 11. ANS: no solutions DIF: L2 OBJ: Solving and Graphing Inequalities 12. ANS: x < 3 or x > 5 DIF: L2 OBJ: Compound Inequalities 13. ANS: 18 < x < 8 DIF: L2 OBJ: Absolute Value Inequalities 14. ANS: w DIF: L2 OBJ: Absolute Value Inequalities 15. ANS: b 300 6; 294 b 306 DIF: L3 OBJ: Absolute Value Inequalities 16. ANS: DIF: L3 OBJ: Identifying Functions 2
9 17. ANS: DIF: L3 OBJ: Graphing Linear Equations 18. ANS: y + 4 = 1 (x + 6) 8 DIF: L2 OBJ: Writing Equations of Lines 19. ANS: y = 3x 6 DIF: L2 OBJ: Writing Equations of Lines 20. ANS: x = 7 DIF: L2 OBJ: Writing Equations of Lines 21. ANS: DIF: L2 OBJ: Graphing Absolute Value Functions 3
10 22. ANS: ( 2 3, 4) DIF: L3 OBJ: Graphing Absolute Value Functions 23. ANS: y = x + 4 DIF: L2 OBJ: Translating Graphs 24. ANS: y = x DIF: L2 OBJ: Translating Graphs 25. ANS: DIF: L2 OBJ: Graphing Linear Inequalities 26. ANS: y x 3 1 DIF: L2 OBJ: Graphing Two-Variable Absolute Value Inequalities 4
11 27. ANS: DIF: L2 OBJ: Stretches Shrinks and Reflections 28. ANS: ( 5, 4) DIF: L2 OBJ: Systems of Linear Equations 29. ANS: ( 1, 6, 1) DIF: L2 OBJ: Solving Three-Variable Systems by Substitution 30. ANS: (0, 2) DIF: L2 OBJ: Solving Systems by Elimination 5
12 31. ANS: DIF: L2 OBJ: Solving Systems of Inequalities 32. ANS: DIF: L2 OBJ: Solving Systems of Inequalities 6
13 33. ANS: DIF: L2 OBJ: Solving Systems of Inequalities 34. ANS: x = 1000 y = 0 DIF: L2 OBJ: Writing Linear Programs 35. ANS: y = 3(x + 2) DIF: L2 OBJ: Using Vertex Form 36. ANS: y = 2(x + 3) 2 4 DIF: L2 OBJ: Using Vertex Form 37. ANS: (3x + 5)(x + 7) DIF: L2 OBJ: Finding Common and Binomial Factors 38. ANS: (3x + 4)(3x 4) DIF: L2 OBJ: Factoring Special Expressions 39. ANS: 8, 1 DIF: L2 OBJ: Solving by Factoring and Finding Square Roots 40. ANS: 7, 7 DIF: L2 OBJ: Solving by Factoring and Finding Square Roots 7
14 41. ANS: 6 4i 3 DIF: L2 OBJ: Identifying Complex Numbers 42. ANS: 41 DIF: L2 OBJ: Identifying Complex Numbers 43. ANS: 1 9i DIF: L2 OBJ: Operations With Complex Numbers 44. ANS: i DIF: L2 OBJ: Operations With Complex Numbers 45. ANS: 1 8 ± i 47 8 DIF: L2 OBJ: Using the Quadratic Formula 46. ANS: DIF: L2 OBJ: Graphing Translations of Reciprocal Functions 47. ANS: q + 8 q 8 ; q 3, q 8 DIF: L2 OBJ: Simplifying Rational Expressions 8
15 48. ANS: 4a 7 b 2, a 0, b 0 DIF: L2 OBJ: Multiplying and Dividing Rational Expressions 49. ANS: z 2 + 2z z + 3, z 1, 0, 3 DIF: L2 OBJ: Multiplying and Dividing Rational Expressions 50. ANS: (x 4) 2 ; x 4, 3, 2, 1, 4 (x + 3)(x + 1) DIF: L3 OBJ: Multiplying and Dividing Rational Expressions 51. ANS: 7a 49 (a 8)(a + 8) DIF: L2 OBJ: Adding and Subtracting Rational Expressions 52. ANS: b 10 b 1 DIF: L2 OBJ: Adding and Subtracting Rational Expressions 9
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