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Mr. Sokoloski *************** Algebra B Chapter 11 PRACTICE Test Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the radical expression. ____ ____ ____ ____ ____ ____ ____ ____ 1. a. b. c. d. a. 12 b. 12 2 c. 6 d. 2. 3. a. c. b. d. 4. factor 1: 1 factpr 2: 11 common factor: 2 a. b. c. d. a. b. c. d. a. b. c. d. a. 4 5 b. c. d. 5. 6. 7. 8. A student visiting the Sears Tower Skydeck is 1353 feet above the ground. Find the distance the student can see to the horizon. Use the formula to approximate the distance d in miles to the horizon when h is the height of the viewer’s eyes above the ground in feet. Round to the nearest mile. a. 45 miles b. 601 miles c. 36 miles d. 1010 miles Simplify the radical expression by rationalizing the denominator. ____ 9. a. b. c. d. Simplify the expression. ____ 10. a. b. c. d. a. b. c. d. ____ 11. ____ 12. (6 – a. b. 11 )(6 + 11 ) c. –85 d. 25 ____ 13. a. b. c. d. a. c. b. d. ____ 14. ____ 15. Find an exact solution for . Then find the approximate solution to the nearest tenth. a. c. –2; –2 b. d. Solve the equation. Check your solution. ____ 16. a. 6 b. 144 c. 2 3 d. 12 a. 126 b. 6 c. 17 d. 116 a. –3 b. 5 c. –5 d. ____ 17. ____ 18. 1 5 Match the function with its graph. ____ 19. y a. –10 –8 –6 –4 y c. 10 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 –6 –6 –8 –8 –10 –10 y b. 2 4 6 8 10 x 10 12 14 16 18 x 2 4 6 8 10 x y d. 10 12 8 10 6 8 4 6 2 4 2 –10 –8 –6 –4 –2 –2 2 4 6 8 10 x –4 –2 –2 –6 –4 –8 –6 –10 –8 2 4 6 8 ____ 20. y a. –10 –8 –6 –4 y c. 10 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 –6 –6 –8 –8 –10 –10 y b. –10 –8 –6 –4 y d. 10 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 –6 –6 –8 –8 –10 –10 2 4 6 8 10 x 2 4 6 8 10 x 2 4 6 8 10 x ____ 21. y a. –10 –8 –6 –4 10 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –4 –6 –4 –2 –2 –4 –6 –6 –8 –8 –10 –10 y –6 –10 –8 –4 b. –10 –8 y c. y d. 10 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 –6 –6 –8 –8 –10 –10 ____ 22. Find the value of sin 66°. Round to the nearest ten-thousandth. a. 0.4067 b. 2.246 c. 0.9135 Find the value of x to the nearest tenth. d. –0.0266 ____ 23. x 57 ° 6 a. 2.9 b. 3.3 c. 9.2 d. 5 ____ 24. x 35 ° 9 a. 12.9 b. 6.3 c. 11 d. –10 ____ 25. Suppose you live 4.4 miles from a hill. From your home you see a plane directly above the hill. Your angle of elevation to the plane is 30°. What is the plane’s altitude? a. –28.2 miles b. 3.8 miles c. 2.2 miles d. 2.5 miles ____ 26. A ranger spots a forest fire while on a 45-meter observation tower. The angle of depression from the tower to the fire is 12°. To the nearest meter, how far is the fire from the base of the tower? a. 212 meters b. 10 meters c. 216 meters d. 71 meters ____ 27. a. Find the value of each variable to the nearest tenth. b. Find the perimeter of the triangle to the nearest tenth. a 21 c 55° a. a = 30, c = 36.6, perimeter = 87.6 b. a = 36.6, c = 30, perimeter = 87.6 c. a = 36.6, c = 17.2, perimeter = 74.8 d. a = 17.2, c = 36.6, perimeter = 74.8 ____ 28. Use to find the value of cos A. B 25 7 A C a. 24 25 b. 24 7 25 c. 7 24 d. 24 7 Mr. Sokoloski *************** Answer Section Algebra B Chapter 11 PRACTICE Test MULTIPLE CHOICE 1. ANS: OBJ: NAT: TOP: KEY: 2. ANS: OBJ: NAT: TOP: KEY: 3. ANS: OBJ: NAT: TOP: KEY: 4. ANS: OBJ: NAT: TOP: KEY: 5. ANS: OBJ: NAT: TOP: KEY: 6. ANS: OBJ: NAT: TOP: KEY: 7. ANS: OBJ: NAT: TOP: KEY: 8. ANS: OBJ: NAT: TOP: KEY: 9. ANS: OBJ: NAT: C PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.1 Simplifying Radical Expressions Involving Products NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 1 radical expressions | Multiplication Property of Square Roots | square root A PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.1 Simplifying Radical Expressions Involving Products NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 1 radical expressions | Multiplication Property of Square Roots | square root C PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.1 Simplifying Radical Expressions Involving Products NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 2 radical expressions | Multiplication Property of Square Roots | square root B PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.1 Simplifying Radical Expressions Involving Products NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 3 multiplying two radicals | Multiplication Property of Square Roots | radical expressions D PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.2 Simplifying Radical Expressions Involving Quotients NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 5 Division Property of Square Roots | radical expressions | fractions within a radical B PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.2 Simplifying Radical Expressions Involving Quotients NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 5 Division Property of Square Roots | radical expressions | fractions within a radical A PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.2 Simplifying Radical Expressions Involving Quotients NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 6 simplying radicals by dividing | square root | radical expressions | fractions within a radical A PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.1 Simplifying Radical Expressions Involving Products NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 11-1 Example 4 Multiplication Property of Square Roots | radical expressions | word problem | problem solving A PTS: 1 DIF: L2 REF: 11-1 Simplifying Radicals 11-1.2 Simplifying Radical Expressions Involving Quotients NAEP 2005 N3a | NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.1 | ADP J.1.6 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. TOP: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: KEY: ANS: OBJ: KEY: ANS: OBJ: KEY: ANS: OBJ: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: 11-1 Example 7 radical expressions | rationalize | radicand in the denominator A PTS: 1 DIF: L2 11-2 Operations With Radical Expressions 11-2.1 Simplifying Sums and Differences NAEP 2005 A3b | ADP I.4.1 | ADP J.1.1 TOP: 11-2 Example 1 like radicals | combining like radicals C PTS: 1 DIF: L2 11-2 Operations With Radical Expressions 11-2.1 Simplifying Sums and Differences NAEP 2005 A3b | ADP I.4.1 | ADP J.1.1 TOP: 11-2 Example 2 like radicals | combining like radicals | radical expressions D PTS: 1 DIF: L2 11-2 Operations With Radical Expressions 11-2.2 Simplifying Products and Quotients NAEP 2005 A3b | ADP I.4.1 | ADP J.1.1 TOP: 11-2 Example 4 FOIL | radical expressions | Multiplication Property of Square Roots B PTS: 1 DIF: L2 11-2 Operations With Radical Expressions 11-2.2 Simplifying Products and Quotients NAEP 2005 A3b | ADP I.4.1 | ADP J.1.1 TOP: 11-2 Example 3 Multiplication Property of Square Roots | Distributive Property | radical expressions D PTS: 1 DIF: L3 11-2 Operations With Radical Expressions 11-2.2 Simplifying Products and Quotients NAEP 2005 A3b | ADP I.4.1 | ADP J.1.1 TOP: 11-2 Example 5 radical expressions | rationalize | conjugates A PTS: 1 DIF: L2 11-2 Operations With Radical Expressions 11-2.2 Simplifying Products and Quotients NAEP 2005 A3b | ADP I.4.1 | ADP J.1.1 TOP: 11-2 Example 6 radical expressions | rationalize | radical equation | Multiplication Property of Square Roots B PTS: 1 DIF: L2 REF: 11-3 Solving Radical Equations 11-3.1 Solving Radical Equations TOP: 11-3 Example 1 radical | radical equation | solving equations D PTS: 1 DIF: L2 REF: 11-3 Solving Radical Equations 11-3.1 Solving Radical Equations TOP: 11-3 Example 1 radical | radical equation | solving equations B PTS: 1 DIF: L2 REF: 11-3 Solving Radical Equations 11-3.1 Solving Radical Equations TOP: 11-3 Example 3 radical | radical equation | solving equations | equations with radical expressions on both sides B PTS: 1 DIF: L3 11-4 Graphing Square Root Functions 11-4.2 Translating Graphs of Square Root Functions NAEP 2005 M1e | ADP J.1.6 | ADP J.2.2 | ADP J.2.3 | ADP K.6 translation | square root | graphing B PTS: 1 DIF: L2 11-4 Graphing Square Root Functions 11-4.2 Translating Graphs of Square Root Functions NAEP 2005 M1e | ADP J.1.6 | ADP J.2.2 | ADP J.2.3 | ADP K.6 TOP: 21. ANS: REF: OBJ: NAT: TOP: 22. ANS: OBJ: NAT: KEY: 23. ANS: OBJ: NAT: KEY: 24. ANS: OBJ: NAT: KEY: 25. ANS: REF: OBJ: NAT: TOP: KEY: 26. ANS: REF: OBJ: NAT: TOP: KEY: 27. ANS: OBJ: NAT: KEY: 28. ANS: OBJ: NAT: KEY: 11-4 Example 3 KEY: translation | square root | graphing D PTS: 1 DIF: L2 11-4 Graphing Square Root Functions 11-4.2 Translating Graphs of Square Root Functions NAEP 2005 M1e | ADP J.1.6 | ADP J.2.2 | ADP J.2.3 | ADP K.6 11-4 Example 4 KEY: translation | square root | graphing C PTS: 1 DIF: L2 REF: 11-5 Trigonometric Ratios 11-5.1 Finding Trigonometric Ratios ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 TOP: 11-5 Example 2 sine | cosine | tangent | trigonometric ratios | calculator C PTS: 1 DIF: L2 REF: 11-5 Trigonometric Ratios 11-5.1 Finding Trigonometric Ratios ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 TOP: 11-5 Example 3 tangent | sine | cosine | trigonometric ratios | right triangle C PTS: 1 DIF: L2 REF: 11-5 Trigonometric Ratios 11-5.1 Finding Trigonometric Ratios ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 TOP: 11-5 Example 3 cosine | right triangle | sine | tangent | trigonometric ratios D PTS: 1 DIF: L2 11-6 Angles of Elevation and Depression 11-6.1 Solving Problems Using Trigonometric Ratios NAEP 2005 M1f | NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.2.3 | ADP K.11.1 | ADP K.11.2 11-6 Example 1 angle of elevation | trigonometric ratios | tangent | word problem | problem solving A PTS: 1 DIF: L2 11-6 Angles of Elevation and Depression 11-6.1 Solving Problems Using Trigonometric Ratios NAEP 2005 M1f | NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.2.3 | ADP K.11.1 | ADP K.11.2 11-6 Example 2 angle of elevation | trigonometric ratios | tangent | word problem | problem solving A PTS: 1 DIF: L3 REF: 11-5 Trigonometric Ratios 11-5.1 Finding Trigonometric Ratios ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 TOP: 11-5 Example 3 cosine | sine | tangent | trigonometric ratios | perimeter | multi-part question A PTS: 1 DIF: L2 REF: 11-5 Trigonometric Ratios 11-5.1 Finding Trigonometric Ratios ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 TOP: 11-5 Example 3 trigonometric ratios | sine | cosine | tangent | right triangle