<p> Version A</p><p>Unit 5: Radical Functions & Rational Exponents</p><p>Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.</p><p>____ 1. Find all the real square roots of 0.0004.</p><p> a. 0.00632 and –0.00632 c. 0.0002 and –0.0002</p><p> b. 0.06325 and –0.06325 d. 0.02 and –0.02</p><p>Find the real-number root.</p><p>____ 2. </p><p> a. –1.6 c. –1.28</p><p> b. 1.6 d. no real number root</p><p>____ 3.</p><p> a. b. c. d.</p><p>Simplify the radical expression. Use absolute value symbols if needed.</p><p>____ 4.</p><p> a. b. c. d.</p><p>Multiply and simplify if possible.</p><p>____ 5.</p><p> a. b. c. d. not possible Version A</p><p>____ 6. Multiply and simplify . Assume that all variables are positive.</p><p> a. c.</p><p> b. d. none of these</p><p>____ 7.</p><p> a. b. c. d.</p><p>Rationalize the denominator of the expression. Assume that all variables are positive.</p><p>____ 8.</p><p> a. c.</p><p> b. d.</p><p>Add if possible.</p><p>____ 9.</p><p> a. c.</p><p> b. d. not possible to simplify</p><p>Subtract if possible.</p><p>____ 10.</p><p> a. c.</p><p> b. d. not possible to simplify Version A</p><p>____ 11. A garden has width and length . What is the perimeter of the garden in simplest radical form?</p><p> a. units c. 91 units</p><p> b. units d. units</p><p>Simplify.</p><p>____ 12.</p><p> a. b. c. 20 d. 1</p><p>____ 13. a. 512 b. 4,096 c. 16 d.</p><p>Multiply.</p><p>____ 14.</p><p> a. c.</p><p> b. d.</p><p>____ 15. Write the exponential expression in radical form.</p><p> a. b. c. d.</p><p>____ 16. Write in simplest form.</p><p> a. c.</p><p> b. d. none of these Version A</p><p>Solve the equation.</p><p>____ 17.</p><p> a. 14 b. –8 c. 4 d. –6</p><p>____ 18.</p><p> a. 11 b. 15; –1 c. –3 d. 1; –1</p><p>____ 19. Let and . Find .</p><p> a. 23 b. –53 c. –9 d. 3</p><p>____ 20. Find the inverse of .</p><p> a. c.</p><p> b. d. Version A</p><p>Graph the function.</p><p>____ 21.</p><p> a. y c. y</p><p>4 4</p><p>2 2</p><p>–4 –2 2 4 x –4 –2 2 4 x –2 –2</p><p>–4 –4</p><p> b. y d. y</p><p>4 4</p><p>2 2</p><p>–4 –2 2 4 x –4 –2 2 4 x –2 –2</p><p>–4 –4 Version A</p><p>____ 22.</p><p> a. y c. y</p><p>4 4</p><p>2 2</p><p>–4 –2 2 4 x –4 –2 2 4 x –2 –2</p><p>–4 –4</p><p> b. y d. y</p><p>4 4</p><p>2 2</p><p>–4 –2 2 4 x –4 –2 2 4 x –2 –2</p><p>–4 –4 Version A</p><p>Short Answer</p><p>23. The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius.</p><p> a. Find the temperature when the velocity of sound in air is 318 meters per second. Round the answer to the nearest degree.</p><p> b. Find the velocity of sound in meters per second when the temperature is 20°C. Round the answer to the nearest meter per second.</p><p>24. Let and .</p><p> a. Find f(g(x)).</p><p> b. Find g(f(x)).</p><p>25. The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius.</p><p> a. Graph the equation on your calculator. Make a sketch of the graph.</p><p> b. Find the temperature when the velocity is 329 meters per second. Round the answer to the nearest degree. Version A</p><p>Unit 5: Radical Functions & Rational Exponents Answer Section</p><p>MULTIPLE CHOICE</p><p>1. ANS: D DIF: L1 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 1 KEY: square root,real roots MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 2. ANS: D DIF: L1 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 2 KEY: real roots MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 3. ANS: D DIF: L2 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 2 KEY: real roots MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 4. ANS: A DIF: L2 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 3 KEY: simplifying a radical expression MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 5. ANS: A DIF: L1 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions STO: MD 1.1.3 TOP: 7-2 Example 1 KEY: multiplying radical expressions,simplifying a radical expression MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.16, TV.LV21/22.52, TV.LVALG.53 6. ANS: A DIF: L1 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions STO: MD 1.1.3 TOP: 7-2 Example 3 KEY: multiplying radical expressions,simplifying a radical expression MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.16, TV.LV21/22.52, TV.LVALG.53 7. ANS: B DIF: L2 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions STO: MD 1.1.3 TOP: 7-2 Example 4 KEY: simplifying a radical expression,divide radical expressions,rationalize the denominator MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, Version A</p><p>TV.LV21/22.12, TV.LV21/22.16, TV.LV21/22.52, TV.LVALG.53 8. ANS: C DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 6 KEY: binomial radical expressions,conjugates,multiplying binomial radical expressions,simplifying a radical expression MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 9. ANS: C DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 1 KEY: binomial radical expressions,adding radical expressions,like radicals MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 10. ANS: C DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 1 KEY: binomial radical expressions,adding radical expressions,like radicals MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 11. ANS: B DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 2 KEY: adding radical expressions,problem solving MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 12. ANS: C DIF: L1 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 1 KEY: rational exponent MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 13. ANS: C DIF: L1 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 4 KEY: rational exponent MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 14. ANS: B DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 4 KEY: binomial radical expressions,simplifying a radical expression,multiplying binomial radical expressions MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 15. ANS: A DIF: L1 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 2 KEY: rational exponent,radical form MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 16. ANS: A DIF: L1 REF: 7-4 Rational Exponents Version A</p><p>OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 5 KEY: rational exponent MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 17. ANS: D DIF: L1 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STO: MD 1.1.1 TOP: 7-5 Example 1 KEY: radical equation, MSC: NAEP A4a, CAT5.LV21/22.50, CAT5.LV21/22.55, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.13, TV.LV21/22.52, TV.LVALG.53 18. ANS: B DIF: L1 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STO: MD 1.1.1 TOP: 7-5 Example 2 KEY: radical equation,rational exponent MSC: NAEP A4a, CAT5.LV21/22.50, CAT5.LV21/22.55, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.13, TV.LV21/22.52, TV.LVALG.53 19. ANS: B DIF: L1 REF: 7-6 Function Operations OBJ: 7-6.2 Composition of Functions STO: MD 1.1.3 TOP: 7-6 Example 3 KEY: composition of functions,operations with functions MSC: NAEP A1g, NAEP A3b, CAT5.LV21/22.49, CAT5.LV21/22.50, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.51, TV.LV21/22.52, TV.LVALG.56 20. ANS: A DIF: L1 REF: 7-7 Inverse Relations and Functions OBJ: 7-7.1 The Inverse of a Function STO: MD 1.1.2 TOP: 7-7 Example 2 KEY: inverse relations and functions, MSC: NAEP A2c, CAT5.LV21/22.50, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.14, TV.LV21/22.52, TV.LVALG.56 21. ANS: A DIF: L1 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions STO: MD 2.1.3 TOP: 7-8 Example 1 KEY: domain,graphing,range,radical function,translation MSC: NAEP A2a, CAT5.LV21/22.53, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.DSP, S9.TSK3.GM, S10.TSK3.DSP, S10.TSK3.GM, TV.LV21/22.14, TV.LV21/22.15, TV.LVALG.56 22. ANS: C DIF: L1 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions STO: MD 2.1.3 TOP: 7-8 Example 2 KEY: domain,graphing,range,radical function,translation MSC: NAEP A2a, CAT5.LV21/22.53, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.DSP, S9.TSK3.GM, S10.TSK3.DSP, S10.TSK3.GM, TV.LV21/22.14, TV.LV21/22.15, TV.LVALG.56</p><p>SHORT ANSWER</p><p>23. ANS: a. –20°C b. 342 meters per second</p><p>DIF: L2 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STO: MD 1.1.1 TOP: 7-5 Example 1 KEY: radical equation,problem solving,multi-part question,word problem MSC: NAEP A4a, CAT5.LV21/22.50, CAT5.LV21/22.55, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.13, TV.LV21/22.52, TV.LVALG.53 24. ANS: Version A</p><p> a. </p><p> b. </p><p>DIF: L2 REF: 7-6 Function Operations OBJ: 7-6.2 Composition of Functions STO: MD 1.1.3 TOP: 7-6 Example 3 KEY: composition of functions,multi-part question,operations with functions MSC: NAEP A1g, NAEP A3b, CAT5.LV21/22.49, CAT5.LV21/22.50, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.51, TV.LV21/22.52, TV.LVALG.56 25. ANS: v</p><p>400</p><p>300</p><p> a. 200</p><p>100</p><p>–80 –40 40 80 t</p><p> b. –2°C</p><p>DIF: L2 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions STO: MD 2.1.3 TOP: 7-8 Example 5 KEY: domain,graphing,range,radical function,multi-part question,problem solving,word problem MSC: NAEP A2a, CAT5.LV21/22.53, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.DSP, S9.TSK3.GM, S10.TSK3.DSP, S10.TSK3.GM, TV.LV21/22.14, TV.LV21/22.15, TV.LVALG.56</p>