AP STATISTICS SUMMER MATH PACKET

Transcription

1 AP STATISTICS SUMMER MATH PACKET This pcket is review of Algebr I, Algebr II, nd bsic probbility/counting. The problems re designed to help you review topics tht re importnt to your success in the clss.

2 Review of Algebr I nd Algebr II. Solve for the vrible in ech eqution. 4( ) 3 b. d. y 8 e. ( q)3 5q f n n c. 9( p ) 3 p 4 p 6 m Write equtions of the horizontl nd verticl lines tht pss through the point (3, 4). Lbel which eqution is horizontl nd which is verticl. 3. Find the slope nd y-intercept of ech line. y ( 4) b. 3y 4 c y 4. Find the slope nd write the eqution of the line contining the points (6, -) nd (0, 5) b. (8, -5) nd (3, 4) 5. Sketch the grph of the following functions. Be ble to do without clcultor. y 3 4 b. y 6 c. y 3 6. Solve nd grph ech inequlity. 4 b c. 3 3 d. 3y 9 e. 4 y f Solve ech eqution. 8 0 b c Blnk. 9. Blnk. 0. For ech of the problems below, find f[g()] nd g[f()]. Then find g[f(-)] nd f[g(3)] for ech. f() = 3; g() = + 3 b. f() = -; g() = 5. Solve nd check. 9 b. 0

3 . Sketch ech grph. Be ble to do without clcultor. d. y b. 4 y c. y 9 y e. y 3 Logrithmic review: Definition of rithm to bse : Let nd be positive numbers, y nd is defined s follows: y if nd only if. The rithm of with bse is denoted by y Properties of Logrithms: Let, u, nd v be positive numbers such tht, nd let n be ny rel number.. u ( uv) u v. ( ) u v v 3. n u n u Inverse Properties of Eponents nd Logrithms: Let be positive rel number,... Bse Bse e ln e ln e Properties of Eponentil nd Logrithmic Equtions: Let be positive rel number,. y if nd only if = y. y if nd only if = y 3. Evlute ech epression without using clcultor. 5 5 b. 98 c. d. 8 e Solve ech eqution for : 38 b. 3 5 c d. ( ) e. 5( 4) 0

4 5. Simplify ech epression: 4e 4 e 6. Blnk. b. ( ) 5 e c e 7. Epnd ech epression: 3 ( y ) 3 (3 ) b. 0(7 yz ) c. d. ln(3 y ) e. ln y 8. Condense ech epression: y b c. ln 0 ln ln d. (ln ln ) (ln ln 4) 9. Use properties of rithms to solve for : Solve the eponentil eqution: 3 5() 4 3 b. 8 b Solve the rithmic eqution: ln 4 b Sketch the grph of ech function. Be ble to do without clcultor. y ( ) b. y ln( )

5 Review of Bsic Probbility nd Counting. A trffic survey indictes tht of 3756 crs pproching shopping plz, 857 turned into the prking lot. Find the empiricl probbility of cr not entering the prking lot.. Find the probbility of selecting dte in My if one dte is rndomly drwn from the 366 possible dtes in lep yer. 3. Among eight helicopters sent to rescue Americn hostges in Irn, three helicopters filed to operte properly. Given the sme conditions, wht is the empiricl probbility of filure for helicopter? 4. A jury of four men nd eight women hs been selected for se-discrimintion cse. If the foremn of this jury is selected t rndom, find the probbility tht the foremn will be womn. 5. A computer is used to generte rndom telephone numbers. Of the numbers generted nd in service, 56 re unlisted, nd 44 re listed in the telephone directory. If one of these telephone numbers is rndomly selected, wht is the probbility tht it is unlisted? 6. Blood types re determined for smple of people, nd the results re s follows: 8 hve Blood type O, 9 hve Blood type A, nd 8 hve Blood type B. If one person from this smple group is rndomly selected, find the probbility tht the person hs type O blood. 7. In study of the effects of cigrette smoking on children, the dt in the tble below were compiled. If one of these mothers is rndomly selected, find the probbility tht she is in the ctegory of those who smoke two or more pcks dy nd hs hyperctive child. Child is hyperctive Child is not hyperctive Mother smokes pcks/dy Mother smokes < pcks/dy A couple plns to hve two children. List the different possible outcomes ccording to the se of ech child. Assume tht these outcomes re eqully likely. b. Find the probbility of getting two boys. c. Find the probbility of getting ectly one child of ech se. 9. Both prents hve the brown-blue pir of eye-color genes, nd ech prent contributes one gene to child. Assume tht if the child hs t lest one brown gene, tht color will dominte nd the eyes will be brown. (Actully, the determintion of eye color is somewht more comple.) List the different possible outcomes. Assume tht these outcomes re eqully likely.

6 b. Wht is the probbility tht child of these prents will hve the blue-blue pir of genes? c. Wht is the probbility tht child will hve brown eyes? 0. A burger house offers two types of buns, two types of cheese, four vegetble toppings, nd three dressings. How mny different wys could you select bun, cheese, vegetble topping, nd dressing?. A summer reding list contins 8 biogrphies nd 6 science books. In how mny wys could you select biogrphy nd science book? b. In how mny wys could you select biogrphy or science book? c. In how mny wys could you select science book nd then nother science book?. An lgebr clss hs 3 girls nd 8 boys. In how mny wys could you select boy or girl to work the homework problems? b. In how mny wys could you select boy nd then nother boy to work the ssignment? c. In how mny wys could you select girl nd boy to do the ssignment? 3. Using the letters in the word COMPUTER In how mny wys could you pick vowel nd then consonnt? b. In how mny wys could you pick consonnt or vowel? c. In how mny wys could you select vowel nd then nother vowel? For problems 4 nd 5, use Venn Digrm to help you nswer the questions. 4. An dvertising gency finds tht of its 70 clients, 5 use television (T), 00 use rdio (R), 30 use mgzines (M), 75 use television nd rdio, 95 use rdio nd mgzines, 85 use television nd mgzines, nd 70 use ll three. How mny clients do not use television, rdio, or mgzines? b. How mny clients use rdio only? c. How mny clients use television only? 5. A cmpus rdio sttion surveyed 90 students to determine the types of music they liked. The survey reveled tht 4 liked rock, 50 liked country, nd 4 liked clssicl music. Moreover, 4 liked rock nd country, 5 liked rock nd clssicl, liked clssicl nd country, nd 5 liked ll three types of music. How mny students like rock only? b. How mny students like country but not rock? c. How mny students like clssicl nd country, but not rock? d. How mny students like clssicl or country, but not rock? e. How mny students like ectly one of the three types of music? f. How mny students do not like ny of the three types of music? g. How mny students like t lest two of the three types of music?