a b a b ab b b b Math 154B Elementary Algebra Spring 2012

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1 Math 154B Elementar Algera Spring 01 Stud Guide for Eam 4 Eam 4 is scheduled for Thursda, Ma rd. You ma use a " 5" note card (oth sides) and a scientific calculator. You are epected to know (or have written on our note card) an formulas ou ma need. Think aout an rules and procedures ou needed to know for homework. For eample: the Pthagorean Theorem, etc... For Eam 4 ou will need to e ale to: 1. Simplif square root epressions. For ever of the same factors, 1 comes out. 9.1 * positive roots: * negative roots: * imaginar roots:. Rational and irrational numers. 9.1 * Perfect square numers are rational: 1, 4, 9, 16, 5, * All other numers are irrational:,, 5, 6, 7. Simplif square root epressions. 9. * Factor numers down to primes and circle groups of two of the same factors. For ever of the same factors, 1 comes out. Leftovers (numers without partners) sta in. Multipl all numers that come out and multipl all numers that sta in. * For variales, divide each eponent. The result ecomes the eponent on the variale outside. Otaining a remainder from the division means one of the variales stas inside. E: 4. Add or sutract square root epressions. You might need to simplif square roots efore the can e comined. 9. * All variales (inside and out) and roots have to e eactl the same to add or sutract. * Just add or sutract coefficients and keep variales and roots eactl the same. E: a a a 5. Multipl two square roots using the distriutive propert or the FOIL method. If possile, simplif an square roots that appear in the product. 9. * Product rule: a a * Distriutive propert: a ( c) a ac * FOIL: ( a )( c d ) ac ad c d * Rememer: and ( ) 6. Simplif a quotient involving square roots. 9.4 a a * Quotient rule: 7. Rationalize the denominator. Rationalizing means to get rid of the root in the denominator. You can simplif, then rationalize, or rationalize, and then simplif. * For 1 term in the denominator, multipl top and ottom whatever is needed to get rid of the root. E: a a a

2 * For terms in the denominator, multipl top and ottom the denominator s st nd st nd st nd conjugate. Rememer: (1 )(1 ) (1 ) ( ) E: 8. A square root is completel simplified when - No perfect squares or variales with eponents greater than 1 under the root. 4 E:,,,,... - No fractions under the root. a a a E: - No roots in the denominator. 1 1 E: 9. Solving radical equations 9.6 * For one radical: get the radical alone on one side of the equal sign, square oth sides to the power of the inde, and solve the remaining equation. E: Solve for : a a ( ) ( a) a * For two radicals: get each radical to each side of the equal sign, square oth sides, and solve the remaining equation. E: Solve for : a a ( ) ( a) a 10. Solve application prolems that involve square roots. 9.7 * These prolems involve the Pthagorean Theorem and other formulas involving roots. OR (leg) (other leg) (h potenuse) Diagonal of solid d l w h Practice Prolems The answer to all the prolems listed elow, even and odd, are in the ack of the ook. For those of ou who have the Chapter Test Prep Video cd that came with the ook, ou can use it to see someone solving each of the prolems in the Chapter Tests. If ou don't have it, it is availale at the math la. Chapter 9 Practice Test Page 590 #6, 7, 8, 10, 1, 16, 19, 0, 4, 5 Also tr: Page 588 #11, 18, 6, 8,, 7, 47, 50, 55, 6, 66, 71

3 Chapter 9 Eam Review 1. State whether the root is rational or irrational. Math 154B Name a Simplif. 15. Simplif Simplif Simplif z 6. Simplif. 7. Multipl. ( a 4) Multipl. 9. Multipl. ( 4a ) ( 9a ) 5 7 a 4a

4 10. Simplif. 11. Simplif a 5 a 8 a 1. Simplif. 1. Multipl. 8a a a 6 ( 8) 14. Multipl. 15. Multipl. ( 5 ) ( m n)( m n)

5 16. Divide and simplif. 17. Divide and rationalize the denominator. 5 15a 5a Rationalize the denominator. 19. Rationalize the denominator. 7 a Rationalize the denominator. 1. Solve for m. 8 5 m

6 . Solve for.. Solve for k. 6 k 1 k 4. Solve for. 5. Solve for m m m 1 6. Find the missing length using the Pthagorean Theorem, a c. 6 10

7 7. Find the diagonal of a rectangle with length is 15 inches and width 8 inches using the Pthagorean Theorem, a c. 8. A 14-foot ladder is placed feet awa from a wall. How far up the wall will the ladder the reach? 9. A square has an area of 784 square meters. Determine the length of each side. s A s s 0. Find the velocit of a tennis all dropped from a height, h, of ft as it approaches the ground. The formula for the velocit, v, in feet per second is v gh, where g. 1. Find the distance etween the points (-, -) and (6, -4) using the distance formula

8 . Find the radius of the cone whose area is 60 cue feet using the volume formula, V r h, where.14 and h 4.. The length of a diagonal, d, for a rectangular solid is d l w h, where l is the length, w is the width, and h is the height. Find the length of the diagonal for a rectangular solid if the length is inches, the width is 4 inches, and the height is 5 inches. L 4. The period or time, T, it takes (in seconds) for a pendulum to swing ack and forth is T, g where. 14, L is the length of the pendulum in feet, and g is acceleration due to gravit ( feet per second squared). Find the period of a pendulum if it s length is15 feet. 5. Give an eample that shows: a a.