Advanced Algebra & Trigonometry Midterm Review Packet
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1 Nme Dte Advnced Alger & Trigonometry Midterm Review Pcket The Advnced Alger & Trigonometry midterm em will test your generl knowledge of the mteril we hve covered since the eginning of the school yer. SECTIONS AND SCORING Your midterm em will e roken down in to two sections. Prt (no clcultors: 0 multiple choice 0 points 6 open-ended 6 points Prt (clcultors: 0 multiple choice 0 points 6 open-ended 9 points Top score possile on the midterm 0 points PREPARATION The est wy to prepre for the midterm is to re-tke your old tests nd quizzes, focusing on ny questions you did not do correctly. In ddition, this pcket contins prctice questions (with nswers roken down y chpter. If you tke the time to prepre for this em, you my e plesntly surprised with how mny questions you re le to complete on the midterm. Plese tke moment to fmilirize yourself with the Formul Sheet it s on the very lst pge of this pcket. You should only use clcultor to nswer the questions mrked with the clcultor symol: SCHEDULE Dte Session Session Tuesdy, Jnury th Wednesdy, Jnury th Thursdy, Jnury th Fridy, Jnury 6th / /6 6/7 8/9 7/8 9/0
2 CHAPTER P REVIEW PROBLEMS Simplify ech of the following. There should e no negtive eponents in your finl nswer c 7. m m 8. 7y 0 9. k k n n v. 6v m m. 7 m 6. 8 Simplify ech of the following. Assume tht ll vriles represent positive numers c y y k k Rtionlize the denomintor: 0 8. Rtionlize the denomintor: 9. Write 9,70,000, 000 in scientific nottion. 0. Write in scientific nottion. Rewrite m s rdicl. Then simplify 8.. Rewrite 8 h using rtionl eponents. Study Tip Studying for 0-0 minutes t time (with 0 minute reks in etween is the most effective wy to retin informtion.
3 Simplify ech of the following epressions nd report your nswer in stndrd form.. v 6v v v 8v y n n 9. c 6 y y 8. c Use the figure elow to nswer questions #.. Epress the perimeter of the rectngle in terms of.. Epress the re of the rectngle in terms of.. Epress the re of the tringle in terms of.. Epress the re of the shded region in terms of. 6. The length of rectngle is more thn twice its width. The width is douled while the length is decresed y. Using s the vrile, epress the chnge in re in terms of. Fctor ech of the following epressions completely. You my need to use more thn one fctoring strtegy within one prolem k k y Wht s the first rule of fctoring?. 6 y y Add, sutrct, multiply, or divide ech of the following rtionl epressions
4 CHAPTER P ANSWERS undefined c k n 0.. v m. m c 9. y 6y 0. y. k. 0 k ; m. h. v v v y y 8y y 6 y 9. 6 n n c c units. squre units. squre units. 8 0 squre units squre units k 0. y9 6y y k y y
5 CHAPTER REVIEW PROBLEMS LINEAR, LITERAL, AND ABSOLUTE VALUE EQUATIONS: Solve ech of the following equtions for.. 6( ( RATIONAL EQUATIONS: Solve ech of the following equtions for QUADRATIC EQUATIONS: Solve ech of the following equtions for. Use ny method. 0.. ( INTERVAL NOTATION PRACTICE: Rewrite using intervl nottion or LINEAR INEQUALITIES: Solve ech inequlity nd write your result using intervl nottion. 9. or ABSOLUTE VALUE INEQUALITIES: nottion. Solve ech inequlity nd write your result using intervl QUADRATIC (AND HIGHER INEQUALITIES: Solve nd write your result using intervl nottion Use the grph shown to stte where y ( ( ( 0. ( ( ( ( 0
6 MODELING WITH LINEAR AND QUADRATIC EQUATIONS: Answer ech of the following.. The sum of consecutive even integers is 60. Wht re the integers?. The sum of consecutive integers is 6. Wht re the integers? 6. One positive numer is times nother numer. The difference etween the two numers is 8. Wht re they? 7. The width of Mr. Oliveri s rectngulr room is 7 more thn twice its length. Its perimeter is 7 feet. Wht re the dimensions of the room? 8. To get n A in Mr. Geist s mth clss, you must hve n verge of t lest 90 on five tests of 00 points ech. The scores on your first three tests were 79, 97, 8, nd 9. Wht must you get on the lst test to get n A? 9. The length of rectngle is one less thn three times its width. The re is squre feet. Find the dimensions of the rectngle. 0. The squre nd rectngle shown elow hve the sme re. Write qudrtic eqution to model this sitution. Then solve it y fctoring. Wht re the dimensions of the rectngle? Wht is the re of the squre? feet feet feet 8 feet. An inheritnce of $0,000 is divided into two investments erning 8% nd 0% simple interest. Your ojective is to otin totl nnul interest income of $,00 from the investments. Wht is the smllest mount you cn invest t 0% to meet your ojective?. Wht quntity of 0% HCl solution should Dr. Boctor dd to 60% HCl solution to produce qurts of % HCl solution?
7 CHAPTER ANSWERS No solution. All rel numers 6. 0, 8. ecluded / etrneous 7. No solution ecluded / etrneous ,., , 6., 7., 7,., 8. 8, 9., 0.,., 7 6., 7,. 8,.,. No solution 6., 7, 7.,, 8., 9., 0. 6,.,,.,,,,.,,.,, 6, 8.,,,, 6. 7 nd ft y7 ft ft y 8 ft 0. 9 ft y ft; 6 ft. $,000 t 0%. 9 qurts of 0% nd qurts of 60% Study Tip Brek the study guide prolems up in to sections, nd do section ech dy. If you hve ny questions, come to etr help nd get them nswered!
8 CHAPTER REVIEW PROBLEMS Fill in the tle of vlues for ech function.., c ( 7, c(. 6 h ( h( Use h ( nd g ( to simplify ech of the following.. h c h. g h ( 6. h g ( 7. h g ( 8. h g (0 9. g h ( 0. g h (. Use m ( 7 6 nd p ( to nswer ech of the following questions.. Find ll vlues of such tht m ( 0. Find ll vlues of such tht m( p(. Find m (0.. Find p m (. Find p m (0 6. Stte the domin of m ( Use 8 f ( to nswer ech of the following questions Find f (0 8. Find ll vlues of such tht f ( 0 9. Find f (6 0. Stte the domin of f ( Use g ( 8 to nswer ech of the following questions.. Find g (0. Find g (. Find ll vlues of such tht g ( 0. Stte the domin of g ( Use c ( nd w( to nswer ech of the following questions.. Find ll vlues of such tht c ( 0 6. Find c (0. 7. Find c w ( 8. Find c w ( 9. Stte the domin of c ( 0. Stte the domin of w (
9 Use n (, k(, nd ( to simplify ech of the following.. n (. n (. n (. n (. n (0 6. n ( 7. n k ( 8. ( k Use the grph of f ( shown elow to fill in the requested informtion using intervl nottion. 9. Domin Rnge Incresing Decresing Where is f ( 0? Grph ech function without using tle of vlues. Stte the domin nd rnge. c. ( 0. ( o. d ( Domin Rnge Domin Domin Rnge Rnge. ( z. e (. d ( Domin Rnge Domin Rnge Domin Rnge
10 Write the eqution for ech of the functions grphed elow The grph of y f ( is shown. Drw ech trnsformtion on the sme coordinte plne s y f (. 9. y f 6 0. y f. y f Fill in the rules for the trnsformtions of f ( y f ( c trnsltion of c units y f ( c trnsltion of c units y f ( c trnsltion of c units y f ( c trnsltion of c units y f ( reflection over the y f ( reflection over the y c f (, c verticl epnsion of y f ( c, c horizontl compression of y c f (, 0 c verticl compression of y f ( c, 0 c horizontl epnsion of Did you memorize these rules?
11 CHAPTER ANSWERS.. c( 8 h( undefined. 6 6 c 0c ,., undefined 0. 66,., 6 7., 7. 8.,..., 6,. solution No undefined 9. 0,, 0., Domin,, Rnge, Incresing, Decresing, Where is f ( 0? 0. D :, R :,. D :, R :,. D :, R :,
12 . D :, R :,. D :, R :,. D :, R :, 6. f ( 7. ( f 8. f ( 9. y f 6 0. y f. y f Good luck on ll of your midterms!
13 W L P W L A L W h h A ADVANCED ALGEBRA / TRIG Midterm Em Formul Sheet SPECIAL PRODUCTS ( ( ( ( ( ( FACTORING SPECIAL POLYNOMIALS ( ( ( ( ( ( ( ( OTHER FORMULAS c T R D r P Interest
14 This chrt is provided for your convenience ONLY. It will not count s credit on the em. You do not need to fill this chrt out if you re cple of completing the prolems without it. Feel free to use the remining spce s scrp pper if needed X X X X X X X X X X 6 X X X X X 7 X X X X X 8 X X X X X 9 X X X X X 0 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
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