Abs.Value Equations/Inequalities, Direct Variation, and Parallel/Perpendicular Lines - QUIZ Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which equation does NOT represent a direct variation? 2. Which equation describes a line that passes through and is perpendicular to the line described by? F. H. G. J. 3. Which equation describes the line that passes through and is parallel to the line described by? 4. Tell whether the relation is a direct variation. Explain. x 10 9 1 y 20 18 F. This is a direct variation, because it can be written as, where. G. This is a direct variation, because it can be written as, where k =. H. This is not a direct variation, because it cannot be written in the form. J. This is a direct variation, because it can be written as, where k =. 5. Solve. A. x = 55 or x = 3 C. x = 13 or x = 1 B. x = 55 D. x = 13 6. Solve. F. No solution H. x = 11 6 G. x = 8 3 J. x = 1 7. Solve and graph the solutions of. Write the solutions as a compound inequality. A. x < 9 OR x > 21 4 2 0 18 16 14 12 10 B. 9 < x < 21 4 2 0 18 16 14 12 10
C. x < 15 OR x > 15 4 2 0 18 16 14 12 10 D. x > 21 4 2 0 18 16 14 12 10 8. Solve the inequality. F. The solution set is OR. G. The solution set is. H. The solution set is all real numbers. J. The solution set is. 9. The value of y varies directly with x, and when. Find y when
Abs.Value Equations/Inequalities, Direct Variation, and Parallel/Perpendicular Lines - QUIZ Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Average TOP: Chapter 4 Multiple Choice Test, Form B MSC: DOK 1 2. ANS: G PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.GPE.5 TOP: Chapter 4 Multiple Choice Test, Form B MSC: DOK 2 3. ANS: A PTS: 1 DIF: Average NAT: NT.CCSS.MTH.10.9-12.G.GPE.5 TOP: Section 4B Quiz MSC: DOK 1 4. ANS: J Write an equation in the form where k is the constant of variation. Find for each ordered pair. ; ; This is a direct variation, because is the same for each ordered pair. is the constant of variation. F G H J Check the sign of the constant of variation. You reversed the order of x and y when calculating the constant of variation. Find y/x instead of x/y. This is a direct variation, because the ratio of y to x is the same for each ordered pair. PTS: 1 DIF: Basic REF: 10cf4c26-4683-11df-9c7d-001185f0d2ea OBJ: 4-5.2 Identifying Direct Variations from Ordered Pairs STA: AL.ALCOS.MTH.09.AL1.4.1 AL.ALCOS.MTH.09.AL1.7.3 LOC: MTH.C.10.07.02.04.002 TOP: 4-5 Direct Variation KEY: direct variation function MSC: DOK 2 5. ANS: C Divide both sides by 7. What numbers are 7 units from 0? Case 1: Case 2: Rewrite the equation as two cases. x 6 = 7 x 6 = 7 The solutions are x = 13 or x = 1. A B C D Divide before you add or subtract. Divide before you add or subtract. There are two cases to solve. Absolute value means distance from zero. Solve the second case when the number inside the absolute value is negative. PTS: 1 DIF: Average REF: 0fb13106-4683-11df-9c7d-001185f0d2ea
OBJ: 1-7.1 Solving Absolute-Value Equations LOC: MTH.C.01.03.09.001 MTH.C.10.06.02.01.008 TOP: 1-7 Solving Absolute-Value Equations MSC: DOK 2 6. ANS: F First, isolate the absolute value expression. STA: AL.ALCOS.MTH.09.AL1.7.3 KEY: absolute value equation Subtract 8 from both sides. The absolute value expression is equal to a negative number, which is impossible. The equation has no solution. F G Subtract the term outside the absolute value bars. H Isolate the absolute value by subtracting the term outside absolute value bars. J An absolute value must be greater than or equal to 0. PTS: 1 DIF: Average REF: 0fb15816-4683-11df-9c7d-001185f0d2ea OBJ: 1-7.2 Special Cases of Absolute-Value Equations STA: AL.ALCOS.MTH.09.AL1.7.3 LOC: MTH.C.01.03.09.001 MTH.C.10.06.01.013 TOP: 1-7 Solving Absolute-Value Equations KEY: absolute value equation MSC: DOK 2 7. ANS: A x 6 < 15 OR x 6 > 15 x < 9 OR x > 21 Add 3 to both sides to undo the subtraction and isolate the absolute value. Think: What numbers have an absolute value less than 15 or greater than 15? Solve the two inequalities. 6 4 2 0 18 16 14 12 10 26 A B C D PTS: 1 DIF: Advanced REF: 103ddc3a-4683-11df-9c7d-001185f0d2ea OBJ: 2-7.2 Solving Absolute-Value Inequalities Involving > STA: AL.ALCOS.MTH.09.AL1.7.3 LOC: MTH.C.10.08.03.001 MTH.C.10.08.03.002 TOP: 2-7 Solving Absolute-Value Inequalities KEY: multistep inequality absolute value compound solving MSC: DOK 3 8. ANS: H
The solution set is all real numbers. Subtract 9 from both sides. Absolute-value expressions are always nonnegative. Therefore, the statement is true for all values of x. F G H J Use subtraction to isolate the absolute-value expression first. Solve the inequality and check to see if you get a statement that is true or false for all values of the variable. Absolute-value expressions are always nonnegative. PTS: 1 DIF: Average REF: 103e034a-4683-11df-9c7d-001185f0d2ea OBJ: 2-7.4 Special Cases of Absolute-Value Inequalities STA: AL.ALCOS.MTH.09.AL1.7.3 LOC: MTH.C.10.08.03.001 TOP: 2-7 Solving Absolute-Value Inequalities KEY: inequality absolute MSC: DOK 2 9. ANS: D PTS: 1 DIF: Average TOP: Section 4A Quiz MSC: DOK 1