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Name_________________________________ Algebra Application Term 3 Review Date_______________ Period__________ Define a variable and write an expression for the phrase. 1. the quotient of 5 times a number and 6 2. for m = –4, n = 2, and p = 1.5 Evaluate 3. Evaluate u + xy, for u = 4, x = 10, and y = 5. Solve the proportion. 4. 5. School guidelines require that there must be at least 2 chaperones for every 25 students going on a school trip. How many chaperones must there be for 90 students? 6. 30% of what number is 21? 7. What percent of 50 is 38? 8. 30% of 70 is what number? Simplify the expression. 9. 10. (1 – c)(–1) Solve the equation. 11. 3(y + 3) = 27 12. 2 5 x = 28 13. Solve the equation. If there is no solution, write no solution. 14. Solve the inequality. Then graph your solution. 15. –6q < –12 16. 17. 5x – 6 = 3x + 6 for x = –2. 18. Evaluate Find the slope of the line that passes through the pair of points. 19. (2, 7), (9, 3) 20. Find the slope of the line. y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x –2 –3 –4 –5 Graph the equation. 21. y = –2 22. y 1 y= x–4 4 y x x Find the x- and y-intercept of the line and graph the equation. 23. –10x – 5y = 50 x – intercept = _____________ y-intercept = _____________ y x Write an equation of a line with the given slope and y-intercept. 24. m = 4, b = –6 Find the slope and y-intercept of the line. 25. 18x + 9y = 108 26. y= Write the equation of the line in Slope-Intercept Form. 27. y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 1 2 3 4 5 x 3 2 x+2 28. Write y = 1 8 x + 10 in standard form using integers. 29. A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. Write an equation in point-slope form for the line through the given point with the given slope. 30. (4, –6); m = Write an equation for the line that is parallel to the given line and that passes through the given point. 31. y = –5x + 3; (–6, 3) Write the equation of a line that is perpendicular to the given line and that passes through the given point. 32. –2x – 12y = –2; (1, 2) Academic Algebra Midterm Review Answer Section SHORT ANSWER 1. ANS: 31 8 DIF: L1 REF: 4-1 Ratio and Proportion OBJ: 4-1.2 Solving Proportions STO: PA 2.5.A, PA 2.5.C TOP: 4-1 Example 4 KEY: proportion MSC: NAEP N4b, NAEP N4c, NAEP M1l, NAEP M2b, NAEP A2f, CAT5.LV19.46, CAT5.LV19.51, IT.LV15.PS, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.13, TV.LV19.17, TV.LVALG.53, TV.LVALG.54 2. ANS: 4 DIF: L1 REF: 6-1 Rate of Change and Slope OBJ: 6-1.2 Finding Slope STO: PA 2.8.R, PA 2.8.S TOP: 6-1 Example 3 KEY: finding slope using a graph,slope,graphing MSC: NAEP M1l, NAEP A2a, NAEP A2b, CAT5.LV19.46, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.11, TV.LV19.14, TV.LV19.15, TV.LVALG.53 3. ANS: 70 DIF: L1 REF: 4-3 Proportions and Percent Equations OBJ: 4-3.1 Applying Proportions to Percent Problems STO: PA 2.2.B TOP: 4-3 Example 3 KEY: proportion,percent,finding the whole MSC: NAEP N2a, NAEP N3g, NAEP N4d, CAT5.LV19.48, CAT5.LV19.50, IT.LV15.PS, IT.LV15.DP, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.11, TV.LV19.17, TV.LV19.52, TV.LVALG.54 4. ANS: 76% DIF: L1 REF: 4-3 Proportions and Percent Equations OBJ: 4-3.1 Applying Proportions to Percent Problems STO: PA 2.2.B TOP: 4-3 Example 1 KEY: proportion,percent,finding the percent MSC: NAEP N2a, NAEP N3g, NAEP N4d, CAT5.LV19.48, CAT5.LV19.50, IT.LV15.PS, IT.LV15.DP, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.11, TV.LV19.17, TV.LV19.52, TV.LVALG.54 5. ANS: y = –5x – 27 DIF: L1 REF: 6-5 Parallel and Perpendicular Lines OBJ: 6-5.1 Parallel Lines STO: PA 2.8.E, PA 2.8.R, PA 2.8.S, PA 2.8.T TOP: 6-5 Example 2 KEY: parallel lines,linear equation MSC: NAEP G3g, NAEP A2e, CAT5.LV19.52, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.14, TV.LV19.16, TV.LV19.18, TV.LVALG.54, TV.LVALG.56 6. ANS: 7 39 DIF: L1 REF: 4-6 Probability of Compound Events OBJ: 4-6.2 Finding the Probability of Dependent Events STO: PA 2.5.B, PA 2.5.D, PA 2.7.E TOP: 4-6 Example 4 KEY: theoretical probability,compound events,dependent events,word problem,problem solving MSC: NAEP D4a, NAEP D4b, NAEP D4h, CAT5.LV19.46, CAT5.LV19.53, IT.LV15.PS, IT.LV15.DP, IT.LV15.FR, S9.TSK1.PRA, S9.TSK1.DSP, S10.TSK1.PRA, S10.TSK1.DSP, TV.LV19.11, TV.LV19.15, TV.LVALG.53 7. ANS: –x + 8y = 80 DIF: L1 REF: 6-3 Standard Form OBJ: 6-3.2 Writing Equations in Standard Form STO: PA 2.8.K, PA 2.8.L, PA 2.8.R, PA 2.8.S TOP: 6-3 Example 4 KEY: standard form of a linear equation,transforming equations MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.15, TV.LV19.16, TV.LVALG.54, TV.LVALG.55 8. ANS: or –10 –8 –6 –4 –2 0 2 4 6 8 10 DIF: L2 REF: 3-6 Absolute Value Equations and Inequalities OBJ: 3-6.2 Solving Absolute Value Inequalities STO: PA 2.8.D TOP: 3-6 Example 3 KEY: solving absolute value inequalities,graphing,solving a compound inequality containing OR MSC: NAEP N1g, NAEP A4a, NAEP A4c, CAT5.LV19.50, CAT5.LV19.55, IT.LV15.CP, IT.LV15.I, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.10, TV.LV19.14, TV.LV19.52, TV.LVALG.54 9. ANS: q>2 –8 –6 –4 –2 0 2 4 6 8 DIF: L1 REF: 3-3 Solving Inequalities Using Multiplication and Division OBJ: 3-3.2 Using Division to Solve Inequalities STO: PA 2.5.D, PA 2.8.D TOP: 3-3 Example 3 KEY: Division Property of Inequality,graphing,solving inequalities MSC: NAEP A4a, NAEP A4c, CAT5.LV19.50, IT.LV15.CP, IT.LV15.PS, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.16, TV.LV19.52, TV.LVALG.54 10. ANS: –8 –6 –4 –2 0 2 4 6 8 DIF: L1 REF: 3-5 Compound Inequalities OBJ: 3-5.1 Solving Compound Inequalities Containing And STO: PA 2.4.E, PA 2.5.B, PA 2.8.D TOP: 3-5 Example 2 KEY: solving a compound inequality containing AND,compound inequality MSC: NAEP A3a, NAEP A4c, IT.LV15.CP, IT.LV15.DI, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.17, TV.LV19.52, TV.LVALG.54 11. ANS: y + 5 = –3(x – 1); y = –3x – 2 DIF: L1 REF: 6-4 Point-Slope Form and Writing Linear Equations OBJ: 6-4.1 Using Point-Slope Form STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.R TOP: 6-4 Example 3 KEY: point-slope form,slope-intercept form,transforming equations,multi-part question MSC: NAEP A1h, NAEP A1i, NAEP A2a, NAEP A2b, NAEP A3a, CAT5.LV19.53, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.15, TV.LV19.16, TV.LV19.17, TV.LVALG.54, TV.LVALG.55 12. ANS: 6 DIF: L1 REF: 2-3 Solving Multi-Step Equations OBJ: 2-3.2 Using the Distributive Property to Solve Equations STO: PA 2.5.A, PA 2.5.C, PA 2.8.D, PA 2.8.N TOP: 2-3 Example 4 KEY: Addition and Subtraction Properties of Equality, Multiplication and Division Properties of Equality, solving equations, multi-step equation, Distributive Property MSC: NAEP A3b, NAEP A3c, NAEP A4a, NAEP A4c, CAT5.LV19.50, IT.LV15.CP, IT.LV15.PS, IT.LV15.AM, S9.TSK1.PRA, S9.TSK1.GM, S10.TSK1.PRA, S10.TSK1.GM, TV.LV19.16, TV.LV19.17, TV.LV19.47, TV.LV19.48, TV.LV19.52, TV.LVALG.54 13. ANS: 70 DIF: L1 REF: 2-1 Solving One-Step Equations OBJ: 2-1.2 Solving Equations Using Multiplication and Division STO: PA 2.5.D, PA 2.8.D, PA 2.8.N TOP: 2-1 Example 5 KEY: Multiplication and Division Properties of Equality, equivalent equations, inverse operations, one-step equation, solving equations, fractions MSC: NAEP N5e, NAEP A4a, NAEP A4c, CAT5.LV19.50, IT.LV15.CP, IT.LV15.PS, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54 14. ANS: 6 DIF: L1 REF: 2-4 Equations With Variables on Both Sides OBJ: 2-4.1 Solving Equations With Variables on Both Sides STO: PA 2.5.C, PA 2.5.D, PA 2.8.D, PA 2.8.N TOP: 2-4 Example 1 KEY: Addition and Subtraction Properties of Equality, Multiplication and Division Properties of Equality, solving equations, multi-step equation, equations with variables on both sides MSC: NAEP A2e, NAEP A4a, NAEP A4c, CAT5.LV19.50, IT.LV15.CP, IT.LV15.PS, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.52, TV.LVALG.54 15. ANS: 2; 12 DIF: L2 REF: 6-2 Slope-Intercept Form OBJ: 6-2.1 Writing Linear Equations STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.T TOP: 6-2 Example 1 KEY: slope,linear equation,y-intercept MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.11, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.54, TV.LVALG.55 16. ANS: 3 ;2 2 DIF: L1 REF: 6-2 Slope-Intercept Form OBJ: 6-2.1 Writing Linear Equations STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.T TOP: 6-2 Example 1 KEY: linear equation,y-intercept,slope MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.11, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.54, TV.LVALG.55 17. ANS: –30 DIF: L1 REF: 1-6 Multiplying and Dividing Real Numbers OBJ: 1-6.2 Dividing Real Numbers STO: PA 2.1.A, PA 2.2.A, PA 2.5.D, PA 2.8.I TOP: 1-6 Example 6 KEY: algebraic expression, real numbers MSC: NAEP N3a, CAT5.LV19.47, IT.LV15.PS, IT.LV15.I, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.49, TV.LVALG.53 18. ANS: h = –7, h = 21 DIF: L2 REF: 3-6 Absolute Value Equations and Inequalities OBJ: 3-6.1 Solving Absolute Value Equations STO: PA 2.8.D TOP: 3-6 Example 2 KEY: absolute value,Division Property of Equality MSC: NAEP N1g, NAEP A4a, NAEP A4c, CAT5.LV19.50, CAT5.LV19.55, IT.LV15.CP, IT.LV15.I, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.10, TV.LV19.14, TV.LV19.52, TV.LVALG.54 19. ANS: y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x –2 –3 –4 –5 DIF: L1 REF: 6-3 Standard Form OBJ: 6-3.1 Graphing Equations Using Intercepts STO: PA 2.8.K, PA 2.8.L, PA 2.8.R, PA 2.8.S TOP: 6-3 Example 3 KEY: graphing,horizontal and vertical lines MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.15, TV.LV19.16, TV.LVALG.54, TV.LVALG.55 20. ANS: 1 DIF: L1 REF: 5-2 Relations and Functions OBJ: 5-2.2 Evaluating Functions STO: PA 2.8.A, PA 2.8.O, PA 2.8.Q TOP: 5-2 Example 4 KEY: function MSC: NAEP A1g, CAT5.LV19.53, CAT5.LV19.54, IT.LV15.DI, IT.LV15.PS, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.14, TV.LV19.16, TV.LVALG.56 21. ANS: DIF: L1 REF: 6-4 Point-Slope Form and Writing Linear Equations OBJ: 6-4.1 Using Point-Slope Form STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.R TOP: 6-4 Example 2 KEY: slope-intercept form,linear equation MSC: NAEP A1h, NAEP A1i, NAEP A2a, NAEP A2b, NAEP A3a, CAT5.LV19.53, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.15, TV.LV19.16, TV.LV19.17, TV.LVALG.54, TV.LVALG.55 22. ANS: DIF: L1 REF: 1-1 Using Variables OBJ: 1-1.1 Modeling Relationships With Variables STO: PA 2.5.B, PA 2.8.D TOP: 1-1 Example 2 KEY: algebraic expression, modeling relationships MSC: NAEP A3a, NAEP A3c, NAEP A4a, CAT5.LV19.54, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.18, TV.LVALG.53 23. ANS: y = 6x – 4 DIF: L1 REF: 6-5 Parallel and Perpendicular Lines OBJ: 6-5.2 Perpendicular Lines STO: PA 2.8.E, PA 2.8.R, PA 2.8.S, PA 2.8.T TOP: 6-5 Example 3 KEY: perpendicular lines,linear equation MSC: NAEP G3g, NAEP A2e, CAT5.LV19.52, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.14, TV.LV19.16, TV.LV19.18, TV.LVALG.54, TV.LVALG.56 24. ANS: DIF: L1 REF: 4-6 Probability of Compound Events OBJ: 4-6.1 Finding the Probability of Independent Events STO: PA 2.5.B, PA 2.5.D, PA 2.7.E TOP: 4-6 Example 1 KEY: theoretical probability,independent events,compound events MSC: NAEP D4a, NAEP D4b, NAEP D4h, CAT5.LV19.46, CAT5.LV19.53, IT.LV15.PS, IT.LV15.DP, IT.LV15.FR, S9.TSK1.PRA, S9.TSK1.DSP, S10.TSK1.PRA, S10.TSK1.DSP, TV.LV19.11, TV.LV19.15, TV.LVALG.53 25. ANS: 867 DIF: L1 REF: 1-2 Exponents and Order of Operations OBJ: 1-2.1 Simplifying and Evaluating Expressions and Formulas STO: PA 2.1.A, PA 2.2.A, PA 2.5.C TOP: 1-2 Example 1 KEY: order of operations, exponential expression, power MSC: NAEP A3b, CAT5.LV19.49, CAT5.LV19.50, IT.LV15.PS, IT.LV15.I, S9.TSK1.NS, S9.TSK1.PRA, S9.TSK1.GM, S10.TSK1.NS, S10.TSK1.PRA, S10.TSK1.GM, TV.LV19.51, TV.LV19.52, TV.LVALG.53 26. ANS: –1 + c DIF: L1 REF: 1-7 The Distributive Property OBJ: 1-7.2 Simplifying Algebraic Expressions STO: PA 2.1.A, PA 2.2.A, PA 2.5.B TOP: 1-7 Example 4 KEY: Distributive Property, real numbers MSC: NAEP A3b, CAT5.LV19.51, CAT5.LV19.54, IT.LV15.CP, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.11, TV.LV19.16, TV.LVALG.53, TV.LV19.52 27. ANS: 1 y= x1 2 DIF: L1 REF: 6-2 Slope-Intercept Form OBJ: 6-2.1 Writing Linear Equations STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.T TOP: 6-2 Example 3 KEY: graphing,slope,y-intercept,slope-intercept form,finding slope using a graph MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.11, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.54, TV.LVALG.55 28. ANS: 21 DIF: L1 REF: 4-3 Proportions and Percent Equations OBJ: 4-3.1 Applying Proportions to Percent Problems STO: PA 2.2.B TOP: 4-3 Example 2 KEY: proportion,percent,finding the part MSC: NAEP N2a, NAEP N3g, NAEP N4d, CAT5.LV19.48, CAT5.LV19.50, IT.LV15.PS, IT.LV15.DP, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.11, TV.LV19.17, TV.LV19.52, TV.LVALG.54 29. ANS: 4 7 DIF: L1 REF: 6-1 Rate of Change and Slope OBJ: 6-1.2 Finding Slope STO: PA 2.8.R, PA 2.8.S TOP: 6-1 Example 4 KEY: finding slope using points,slope MSC: NAEP M1l, NAEP A2a, NAEP A2b, CAT5.LV19.46, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.11, TV.LV19.14, TV.LV19.15, TV.LVALG.53 30. ANS: y = 4x – 6 DIF: L1 REF: 6-2 Slope-Intercept Form OBJ: 6-2.1 Writing Linear Equations STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.T TOP: 6-2 Example 2 KEY: linear equation,slope,y-intercept MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.11, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.54, TV.LVALG.55 31. ANS: 8 chaperones DIF: L2 REF: 4-1 Ratio and Proportion OBJ: 4-1.2 Solving Proportions STO: PA 2.5.A, PA 2.5.C KEY: ratio,proportion,word problem,problem solving MSC: NAEP N4b, NAEP N4c, NAEP M1l, NAEP M2b, NAEP A2f, CAT5.LV19.46, CAT5.LV19.51, IT.LV15.PS, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.10, TV.LV19.13, TV.LV19.17, TV.LVALG.53, TV.LVALG.54 32. ANS: 54 DIF: L1 REF: 1-2 Exponents and Order of Operations OBJ: 1-2.1 Simplifying and Evaluating Expressions and Formulas STO: PA 2.1.A, PA 2.2.A, PA 2.5.C TOP: 1-2 Example 2 KEY: order of operations MSC: NAEP A3b, CAT5.LV19.49, CAT5.LV19.50, IT.LV15.PS, IT.LV15.I, S9.TSK1.NS, S9.TSK1.PRA, S9.TSK1.GM, S10.TSK1.NS, S10.TSK1.PRA, S10.TSK1.GM, TV.LV19.51, TV.LV19.52, TV.LVALG.53 33. ANS: y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x –2 –3 –4 –5 DIF: L1 REF: 6-2 Slope-Intercept Form OBJ: 6-2.2 Graphing Linear Equations STO: PA 2.8.E, PA 2.8.K, PA 2.8.L, PA 2.8.T TOP: 6-2 Example 4 KEY: linear equation,graphing equations,slope,y-intercept MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.11, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.54, TV.LVALG.55 34. ANS: y 4 2 –4 –2 2 4 x –2 –4 DIF: L2 REF: 5-3 Function Rules¸ Tables¸ and Graphs OBJ: 5-3.1 Modeling Functions STO: PA 2.8.A, PA 2.8.O, PA 2.8.Q TOP: 5-3 Example 3 KEY: graphing,function,quadratic function MSC: NAEP A1e, NAEP A2a, CAT5.LV19.53, CAT5.LV19.54, IT.LV15.DI, S9.TSK1.DSP, S10.TSK1.DSP, TV.LV19.16, TV.LV19.18, TV.LVALG.55, TV.LVALG.56 35. ANS: x-intercept is –5; y-intercept is –10. DIF: L1 REF: 6-3 Standard Form OBJ: 6-3.1 Graphing Equations Using Intercepts STO: PA 2.8.K, PA 2.8.L, PA 2.8.R, PA 2.8.S TOP: 6-3 Example 1 KEY: x-intercept,y-intercept,standard form of a linear equation MSC: NAEP A1h, CAT5.LV19.54, IT.LV15.CP, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.15, TV.LV19.16, TV.LVALG.54, TV.LVALG.55