Class: Date: Chapters 1 and 2 Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2r 9 6 Solve the inequality. Graph the solution set. a. r 1 1 2 c. r 1 1 2 b. r 7 1 2 d. r 7 1 2 2. 26 + 6b 2(3b + 4) a. all real numbers c. b 1 1 2 b. b 1 1 2 d. no solutions Solve the compound inequality. Graph the solution set. 3. 5x + 10 10 and 7x 7 14 a. x 4 or x 1 c. x 4 or x 3 b. x 0 and x 1 d. x 0 and x 3 9
4. 4x 5 < 17 or 5x + 6 > 31 a. x < 3 or x > 5 c. x < 3 or x > 7 2 5 b. x < 5 1 2 or x > 72 5 d. x < 5 1 2 or x > 5 Solve the inequality. Graph the solution. 5. 2x 3 19 a. x 22 or x 16 c. x 11 or x 8 b. x 8 or x 8 d. x 11 or x 8 6. 2x 10 26 a. 18 > x > 8 c. 36 < x < 16 b. 18 < x < 8 d. x 8 or x 8 7. A furniture maker uses the specification 21.88 w 22.12 for the width w in inches of a desk drawer. Write the specification as an inequality. a. w 0.24 22.12 c. w 22 0.24 b. w 0.12 22 d. w 22 0.12 2
8. Write the ordered pairs for the relation. Find the domain and range. a. {( 2, 5), ( 1, 2), (0, 1), (1, 2), (2, 5)}; domain: { 2, 1, 0, 1, 2}; range: {1, 2, 5} b. {(5, 2), (2, 1), (1, 0), (2, 1), (5, 2)}; domain: { 2, 1, 0, 1, 2}; range: {1, 2, 5} c. {( 2, 5), ( 1, 2), (0, 1), (1, 2), (2, 5)}; domain: {1, 2, 5}; range: { 2, 1, 0, 1, 2} d. {(5, 2), (2, 1), (1, 0), (2, 1), (5, 2)}; domain: {1, 2, 5}; range: { 2, 1, 0, 1, 2} 3
9. Graph the equation 6x 6y 30 by finding the intercepts. a. c. b. d. Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. 10. x y 6 24 18 72 54 216 162 648 a. yes; k = 4; y =4x c. yes; k = 6; y =6x b. yes; k = 3; y =3x d. no 4
11. 6y = 5x Determine whether y varies directly with x. If so, find the constant of variation k. a. yes; 5 6 b. yes; 6 5 c. yes; 5 d. no Graph the absolute value equation. 12. y 2x 3 a. c. b. d. 13. Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function. y 2 x and y 2 x 3 a. The second function is the graph of y 2 x moved to the right 3 units. b. The second function is the graph of y 2 x moved up 3 units. c. The second function is the graph of y 2 x moved to the left 3 units. d. The second function is the graph of y 2 x moved down 3 units. 5
14. The equation y x 5 describes a function that is translated from a parent function. a. Write the equation of the parent function. b. Find the number of units and the direction of translation. c. Sketch the graphs of the two functions. a. y x ; 5 units right; c. y x ; 5 units left; b. y x ; 5 units right; d. y x ; 5 units left; 6
Graph the inequality. 15. 3x + y 5 a. c. b. d. 7
Graph the absolute value inequality. 16. x 1 y 5 a. c. b. d. 17. What is the vertex of the function y 3x 2 4? 2 a. ( 3, 4) b. (2 3, 4) c. (2 3, 4) d. ( 2 3, 4) Find an equation for the line: 18. through (2, 6) and perpendicular to y = a. y = 5 4 x 7 2 b. y = 4 5 x 38 5 5 4 x + 1. c. y = 4 5 x 22 5 19. through ( 4, 6) and parallel to y = 3x + 4. a. y = 3x 6 b. y = 3x 18 c. y = 1 3 x 22 3 d. y = d. y = 5 4 x 17 2 1 3 x 14 3 8
Write in standard form an equation of the line passing through the given point with the given slope. 20. slope = 8; ( 2, 2) a. 8x + y = 18 b. 8x + y = 18 c. 8x y = 18 d. 8x + y = 18 Short Answer Evaluate the expression for the given value of the variable(s). 21. 4(3h 6) 1 h ; h 2 Simplify by combining like terms. 22. 3( 4y 3) 7y Solve the equation. 23. 5y 9 (y 1) 24. 3 3x 4 7 5 Solve the equation or formula for the indicated variable. 25. S 5r 2 t, for t Solve for x. State any restrictions on the variables. 26. ax bx 9 7 Solve the equation. Check for extraneous solutions. 27. 4 4 3x 4x 6 28. Suppose f x 4x 2 and g x 2x 1. f 5 Find the value of g 3. 9
Find the slope of the line through the pair of points. 29. 30. Find the point-slope form of the equation of the line passing through the points ( 6, 4) and (2, 5). Find the slope of the line. 31. y 1 2 x 4 32. x = a Find an equation for the line: 33. through ( 7, 4) and vertical. Find the value of y for a given value of x, if y varies directly with x. 34. If y = 166 when x = 83, what is y when x = 23? 10
35. Write an equation for the horizontal translation of y x. 11
Chapters 1 and 2 Test Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: L2 REF: 1-4 Solving Inequalities OBJ: 1-4.1 Solving and Graphing Inequalities TOP: 1-4 Example 1 KEY: inequality graphing 2. ANS: A PTS: 1 DIF: L2 REF: 1-4 Solving Inequalities OBJ: 1-4.1 Solving and Graphing Inequalities TOP: 1-4 Example 2 KEY: inequality graphing 3. ANS: D PTS: 1 DIF: L2 REF: 1-4 Solving Inequalities OBJ: 1-4.2 Compound Inequalities TOP: 1-4 Example 4 KEY: compound inequality containing AND graphing compound inequality 4. ANS: A PTS: 1 DIF: L2 REF: 1-4 Solving Inequalities OBJ: 1-4.2 Compound Inequalities TOP: 1-4 Example 5 KEY: compound inequality containing OR graphing compound inequality 5. ANS: C PTS: 1 DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities OBJ: 1-5.2 Absolute Value Inequalities TOP: 1-5 Example 4 KEY: absolute value graphing compound inequality containing OR 6. ANS: B PTS: 1 DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities OBJ: 1-5.2 Absolute Value Inequalities TOP: 1-5 Example 5 KEY: absolute value graphing compound inequality containing AND 7. ANS: D PTS: 1 DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities OBJ: 1-5.2 Absolute Value Inequalities TOP: 1-5 Example 6 KEY: absolute value compound inequality word problem problem solving 8. ANS: A PTS: 1 DIF: L2 REF: 2-1 Relations and Functions OBJ: 2-1.1 Graphing Relations TOP: 2-1 Example 2 KEY: ordered pair domain range relation 9. ANS: B PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.1 Graphing Linear Equations TOP: 2-2 Example 2 KEY: linear equation x-intercept y-intercept 10. ANS: A PTS: 1 DIF: L2 REF: 2-3 Direct Variation OBJ: 2-3.1 Writing and Interpreting a Direct Variation TOP: 2-3 Example 1 KEY: constant of variation direct variation 11. ANS: A PTS: 1 DIF: L2 REF: 2-3 Direct Variation OBJ: 2-3.1 Writing and Interpreting a Direct Variation TOP: 2-3 Example 2 KEY: constant of variation 12. ANS: D PTS: 1 DIF: L2 REF: 2-5 Absolute Value Functions and Graphs OBJ: 2-5.1 Graphing Absolute Value Functions TOP: 2-5 Example 1 KEY: absolute value 1
13. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 1 KEY: compare absolute value vertical translation 14. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 3 KEY: horizontal translation multi-part question 15. ANS: B PTS: 1 DIF: L2 REF: 2-7 Two-Variable Inequalities OBJ: 2-7.1 Graphing Linear Inequalities TOP: 2-7 Example 1 KEY: inequality graphing 16. ANS: D PTS: 1 DIF: L3 REF: 2-7 Two-Variable Inequalities OBJ: 2-7.2 Graphing Two-Variable Absolute Value Inequalities TOP: 2-7 Example 3 KEY: absolute value 17. ANS: B PTS: 1 DIF: L3 REF: 2-5 Absolute Value Functions and Graphs OBJ: 2-5.1 Graphing Absolute Value Functions TOP: 2-5 Example 1 KEY: absolute value vertex 18. ANS: C PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 7 KEY: slope perpendicular equation of a line 19. ANS: A PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 7 KEY: slope equation of a line 20. ANS: A PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 4 KEY: point-slope form standard form of linear equation SHORT ANSWER 21. ANS: 48 PTS: 1 DIF: L3 REF: 1-2 Algebraic Expressions OBJ: 1-2.1 Evaluating Algebraic Expressions TOP: 1-2 Example 1 KEY: algebraic expression order of operations 22. ANS: 19y 9 PTS: 1 DIF: L3 REF: 1-2 Algebraic Expressions OBJ: 1-2.2 Simplifying Algebraic Expressions TOP: 1-2 Example 4 KEY: like terms combine like terms algebraic expression 2
23. ANS: 2 1 2 PTS: 1 DIF: L2 REF: 1-3 Solving Equations OBJ: 1-3.1 Solving Equations TOP: 1-3 Example 2 KEY: solve an equation Distributive Property 24. ANS: x = 0 or x = 2 2 3 PTS: 1 DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities OBJ: 1-5.1 Absolute Value Equations TOP: 1-5 Example 2 KEY: absolute value 25. ANS: S t 5r 2 PTS: 1 DIF: L2 REF: 1-3 Solving Equations OBJ: 1-3.1 Solving Equations TOP: 1-3 Example 3 KEY: solve an equation transforming a formula 26. ANS: 2 x a b ; a b PTS: 1 DIF: L2 REF: 1-3 Solving Equations OBJ: 1-3.1 Solving Equations TOP: 1-3 Example 4 KEY: solve an equation restrictions on a variable 27. ANS: 5 x 8 or x 11 4 PTS: 1 DIF: L3 REF: 1-5 Absolute Value Equations and Inequalities OBJ: 1-5.1 Absolute Value Equations TOP: 1-5 Example 3 KEY: absolute value extraneous solutions 28. ANS: 2 4 7 PTS: 1 DIF: L3 REF: 2-1 Relations and Functions OBJ: 2-1.2 Identifying Functions TOP: 2-1 Example 6 KEY: function notation 3
29. ANS: 4 PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.1 Graphing Linear Equations TOP: 2-2 Example 3 KEY: slope 30. ANS: y + 4 = 1 (x + 6) 8 PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 5 KEY: point-slope form ordered pair 31. ANS: 1 2 PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 6 KEY: slope 32. ANS: undefined PTS: 1 DIF: L3 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 7 KEY: vertical line horizontal line undefined slope slope 33. ANS: x = 7 PTS: 1 DIF: L2 REF: 2-2 Linear Equations OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 7 KEY: vertical line horizontal line equation of a line 34. ANS: 46 PTS: 1 DIF: L2 REF: 2-3 Direct Variation OBJ: 2-3.1 Writing and Interpreting a Direct Variation TOP: 2-3 Example 4 KEY: direct variation 35. ANS: y x 4 PTS: 1 DIF: L2 REF: 2-6 Families of Functions OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 2 KEY: horizontal translation 4