Math 154B Elementary Algebra-2 nd Half Spring 2015
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1 Mth 154B Elementry Alger- nd Hlf Spring 015 Study Guide for Exm 4, Chpter 9 Exm 4 is scheduled for Thursdy, April rd. You my use " x 5" note crd (oth sides) nd scientific clcultor. You re expected to know (or hve written on your note crd) ny formuls you my need. Think out ny rules nd procedures you needed to know for homework. For exmple: the Pythgoren Theorem, etc... For Exm 4 you will need to e le to: 1. Simplify squre root expressions. For every of the sme fctors, 1 comes out. 9.1 * positive roots: * negtive roots: * imginry roots:. Rtionl nd irrtionl numers. 9.1 * Perfect squre numers re rtionl: 1, 4, 9, 16,... * All other numers re irrtionl:,, 5, 6, 7,.... Simplify squre root expressions. 9. * Fctor numers down to primes nd circle groups of two of the sme fctors. For every of the sme fctors, 1 comes out. Leftovers (numers without prtners) sty in. Multiply ll numers tht come out nd multiply ll numers tht sty in. * For vriles, divide ech exponent y. The result ecomes the exponent on the vrile outside. Otining reminder from the division mens one of the vriles stys inside. Ex: x x 4. Add or sutrct squre root expressions. Simplify squre roots efore comining like rdicls. 9. * All vriles (inside nd out) nd roots hve to e exctly the sme to dd or sutrct. * Just dd or sutrct coefficients nd keep vriles nd roots exctly the sme. Ex: 5. Multiply two squre roots y using the distriutive property or the FOIL method. If possile, simplify ny squre roots tht pper in the product. 9. * Product rule: * Distriutive property: ( c) c * FOIL: * Rememer: x x nd ( x) x ( )( c d ) c d c d 6. Simplify quotient involving squre roots. 9.4 * Quotient rule: 7. Rtionlize the denomintor. Rtionlizing mens to get rid of the root in the denomintor. You cn simplify, then rtionlize, or rtionlize, nd then simplify. * For 1 term in the denomintor, multiply top nd ottom to get rid of the root. Ex: * For terms in the denomintor, multiply top nd ottom y the denomintor s conjugte. For Conjugtes: x x y x x x y st nd st nd st nd (1 )(1 ) (1 ) ( ) Ex: x y x y x y 8. A squre root is completely simplified when 4 - No perfect squres or vriles with exponents greter thn 1 under the root. Ex: x, x x, x x x, x x,... - No frctions under the root. Ex: - No roots in the denomintor. Ex: 9. Solving rdicl equtions y 9.6 * For one rdicl: get the rdicl lone on one side of the equl sign, squre oth sides to the power of the index, nd solve the remining eqution. Ex: x ( x) ( ) x * For two rdicls: get ech rdicl to ech side of the equl sign, squre oth sides, nd solve the remining eqution. Ex: Solve for x : x x ( x) ( ) x Pendulum Formul: 10. Solve ppliction prolems tht involve squre roots. 9.7 * These prolems involve the Pythgoren Theorem nd other formuls involving roots. OR Distnce Formul: Solve for x : (leg) x (other leg) (hypotenuse) x 1 1 Digonl of solid: d l w h
2 Mth 154B Chpter 9 Exm 4 Review Nme 1. Stte whether the root is rtionl or irrtionl Simplify.. Simplify Simplify. 8x 5. Simplify x y z 6. Simplify. 7. Multiply. ( 4) 7x 7x 8. Multiply. 9. Multiply. ( 4 ) ( 9 ) 5 7 4
3 10. Simplify. 11. Simplify Simplify. 1. Multiply. y 8 y y 6( 8) 14. Multiply. 15. Multiply. ( 5 ) ( m n)( m n)
4 16. Divide nd simplify. 17. Divide nd rtionlize the denomintor x y x y Rtionlize the denomintor. xy 7xy 19. Rtionlize the denomintor Rtionlize the denomintor. 1. Solve for m. 5 8 m
5 . Solve for y. y y 6. Solve for k. k 1 k 4. Solve for x. x Solve for m. m m 1 6. Find the missing length y using the Pythgoren Theorem, c. x 6 10
6 7. Find the digonl of rectngle with length is 15 inches nd width 8 inches y using the Pythgoren Theorem, c. 8. A 14-foot ldder is plced feet wy from wll. How fr up the wll will the ldder the rech? 9. A squre hs n re of 784 squre meters. Determine the length of ech side. s A s s 0. Find the velocity of tennis ll dropped from height, h, of ft s it pproches the ground. The formul for the velocity, v, in feet per second is v gh, where g. 1. Find the distnce etween the points (-, -) nd (6, -4) using the distnce formul
7 . Find the rdius of the cone whose re is 60 cue feet using the volume formul, V r h, where. 14 nd h 4.. The length of digonl, d, for rectngulr solid is d l w h, where l is the length, w is the width, nd h is the height. Find the length of the digonl for rectngulr solid if the length is inches, the width is 4 inches, nd the height is 5 inches. 4. The period or time, T, it tkes (in seconds) for pendulum to swing ck nd forth is L T, where. 14, L is the length of the pendulum in feet, nd g is ccelertion due g to grvity ( feet per second squred). Find the period of pendulum if it s length is15 feet. 5. Give n exmple tht shows:.
8 Answers: 1.. rtionl. irrtionl. not rel numer x x 5. 4x y z xz x y y m 9n y 5xy 17. x 7x m 1, No solution. y. k 1, k 8 4. x 5 5. m 1, m 6. x 4 7. The digonl is 17 inches 8. The ldder will rech out 1.7ft up the wll 9. s 8 0. The velocity is out 11.ft/sec 1. The distnce is out The rdius is out.19ft. The digonl is out 7.1in 4. The period is out 4.sec 5. Consider the following:
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