Year 10 Maths. Semester One Revision Booklet.

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1 Yer 0 Mths. Semester One Revision Booklet. Nme

2 YEAR 0 MATHEMATICS REVISION BOOKLET AND STUDY SUGGESTIONS NAME: READ through ALL of this vie prior to strting your revision. It is essentil informtion. Chpters tht re exmine re: Chpter (Liner Reltions), Chpter (Inies n Surs), Chpter 6 (Mesurement) n Chpter 8 (Proility).. Summry Book - You nee to work on your summry ook if it is not up to te. Inlue ifferent types of exmples n formule tht you my nee to refer to. Do not OVER lutter your summry ook. Keep spe etween setions in se you wish to more in lter. You shoul inlue CAS instrutions n exmples. Summry Book rules re:. CAS It nnot hve fol out setions or ts. It is to e oun ook (leture p or exerise ook), it n e spirl oun if you wish. You re expete to know how to use your CAS to ssist you. You must still show ll working on the exm pper where mrks re llote for steps in Setion B (short nswer n extene response). Multiple Choie questions o not require working to e shown, hene CAS n n shoul e use to vntge in the yer 0 exm. You shoul o ny working for multiple hoie questions iretly on the exmintion pper to ssist you. The letter of your hoie will e irle on eh question.. Work through questions from text ook first. You shoul work through eh hpter tht is on the exm. Do the questions tht you i not hve to o in eh setion n the en of hpter questions. ALWAYS hek your nswers on regulr sis. 4. Work through your lss notes tht hve een provie Your lss notes help put ll the methos, priniples n exmples of eh require tehnique together in sequene for you. You shoul re k over these n opy or ut out n pste some of these exmples into your summry ook if esire. 5. Re through the summry provie t the en of eh hpter. The en of hpter summry is n exellent visul isply of how ll the key onepts, formule n methos relte together. It n e overwhelming t first, ut if you go through eh ox refully, it will e gret resoure to help put everything together for tht hpter. 6. Work through the revision questions provie. There re lrge numer of revision questions. You re expete to omplete ll of these thoroughly n in seprte exmintion revision leture ook. Keep your work net n show ll steps s you woul nee to for the exmintion. Chek your nswers regulrly. There re no further revision questions provie. This set is more thn enough, with the ove lso eing omplete s require prior to oing the provie revision questions.

3 YEAR 0 MATHEMATICS Semester, 07 Exmintion Thursy 8 th June 07 (8.5m to 0.5m) Reing Time: Writing Time: 0 minutes.5 hours QUESTION AND ANSWER BOOKLET Numer of questions Setion A: Setion B: Struture of exmintion Numer of questions to e nswere 0 5 Numer of mrks 0 65 Suggeste time 0 minutes 60 minutes STUDENT S NAME: TEACHER S NAME: INSTRUCTIONS: Stuents re permitte to ring into the exmintion room: A CAS lultor, one summry ook of their own notes, pens, penils, highlighters, ersers, shrpeners, rulers Stuents re NOT permitte to ring into the exmintion room: lnk sheets of pper n/or white out liqui/tpe All written responses must e in English, unless otherwise stte For Setion A: Multiple Choie responses re to e irle in this ooklet For Setion B: Stuents re to omplete ll nswers in the spe provie in this ooklet Mterils supplie: Question n nswer ook of 4 pges. Stuents re NOT permitte to ring moile phones n/or ny other unuthorise eletroni evies into the exmintion room.

4 Topi: Proility - Chpter 8 Revision Worksheets (Atthe) A B Solutions (Atthe) Text ook Chpter Summry Pge 6. NOT REQUIRED: Inepenent Events Text ook Chpter Review Pge 6-65 Multiple Choie: 9 Short Answer: (NOT 9) Extene Response: Text ook Semester Review Pge Multiple Choie:,, 5 Short Answer:, (not (iv)), 4, 5, (i) Extene Response: prt,

5 Chpter 8 Proility Worksheet A A letter is hosen from the wor MATHEMATICAL. Fin the proility tht the letter is: T n A not n A n A or T An experiment involves tossing three ise oins n ounting the numer of tils. Here re the results fter running the experiment 00 times. Fin the experimentl proility of otining: Numer of tils 0 Frequeny no tils tils fewer thn tils t lest tils A numer is hosen from the set of positive integers etween n 0 inlusive. A is the set of integers less thn 5 n B is the set of even numers etween n 0 inlusive. Represent the two events A n B in Venn igrm. List the following sets: i A B _ ii A B _

6 (ont.) If numer from the first 0 positive integers is rnomly selete, fin the proility tht the following events our. i A _ ii A B _ iii A B _ Are the events A n B mutully exlusive? Why/why not? 4 From lss of 0 stuents, 7 like soer, 4 like AFL n 9 like oth soer n AFL. Illustrte this informtion in Venn igrm. Stte the numer of stuents who like: i AFL only ii neither soer nor AFL Fin the proility tht person hosen t rnom will like: i AFL ii AFL only iii oth soer n AFL 5 This Venn igrm shows the istriution of elements in sets A n B. Trnsfer the informtion in the Venn igrm into two-wy tle. A A B B

7 5 (ont.) Fin: i n(a B) ii n(a B) iii n(a B ) iv n(a B ) v n(a) vi n(b ) vii n(a B) Fin: i Pr(A B) ii Pr(A ) iii Pr(A B ) 6 A r is selete from pk of 5 plying rs. Let A e the event the r is hert n B e the event the r is queen. Fin: i n(a) ii n(b) iii n(a B) Fin: i Pr(A) ii Pr(A ) iii Pr(A B) Use the ition rule to fin Pr(A B). Fin the proility tht the r is queen or not hert. 7 Two events A n B re suh tht Pr(A) = 0.45, Pr(B) = 0.7 n Pr(A B) = 0.8. Fin: Pr(A B) Pr(A B )

8 Chpter 8 Proility Worksheet B Consier the following Venn igrm isplying the numer of elements elonging to the events A n B. Fin the following proilities: Pr(A) Pr(A B) Pr(A B) Pr(B A) From the 0 memers of ski lu, 6 like skiing, like snoworing n 8 like oth skiing n snoworing. A ski lu memer is hosen t rnom. Let A e the event the person likes skiing n B e the event the person likes snoworing. Represent the informtion in two-wy tle. A A B B Fin the proility tht the person only likes snoworing. Fin the proility tht the person likes snoworing given tht they like skiing. Fin the proility tht the person likes skiing given tht they like snoworing.

9 Two four-sie ie, numere to 4, re rolle. List the smple spe using tle. Die 4 Die Fin the proility of otining the outome (, ). 4 Fin: i Pr (sum of t lest 6) ii Pr (sum not equl to 6) Fin the proility of sum of 7, given tht the sum is t lest 6. 4 Two letters re hosen from the wor NINE without replement Construt tle to list the smple spe. Letter N I N E N Letter I N E Fin the proility of: i otining the outome (N, E) ii seleting N n E iii seleting two Ns iv seleting two Ns given tht t lest one N is selete 5 Boxes A n B ontin 4 ounters eh. Box A ontins re n yellow ounters n ox B ontins re n yellow ounters. A ox is hosen t rnom n then single ounter is selete. Fin the proility of seleting re ounter from: i ox A ii ox B

10 5 (ont.) Represent the options ville s tree igrm tht shows ll possile outomes n relte proilities. Wht is the proility of seleting ox B n re ounter? Wht is the proility of seleting re ounter? 6 A g ontins re (R) n 4 white (W) mrles n two mrles re selete without replement. Drw tree igrm showing ll outomes n proilities. Fin the proility of seleting: i re mrle n then white mrle ii re mrles iii extly re mrle

11 6 (ont.) If the experiment ws repete with replement, fin the nswers to eh question in prt. i re mrle n then white mrle ii re mrles iii extly re mrle Chpter 8 Proility Worksheet A nswers i {, 4} ii {,,, 4, 6, 8, 0} i 5 ii 5 The sets A n B re not mutully exlusive sine A B. iii i 5 ii 8 i 7 5 ii 6 iii 0 5 A A B 5 6 B

12 i 5 ii 6 iii 4 iv v 9 vi 7 vii 5 i 5 8 ii 6 i ii 4 iii i ii 4 Worksheet B nswers iii iii A A B 8 4 B Die 4 (, ) (, ) (, ) (, 4) Die (, ) (, ) (, ) (, 4) (, ) (, ) (, ) (, 4) 4 (4, ) (4, ) (4, ) (4, 4) 6 i 8 ii 6

13 4 Letter N I N E N (N, I) (N, N) (N, E) Letter I (I, N) (I, N) (I, E) N (N, N) (N, I) (N, E) E (E, N) (E, I) (E, N) i 6 ii iii 6 iv 5 5 i ii i 7 ii 7 iii 4 7 i 49 ii 9 49 iii 4 49

14 Topi: Mesurement - Chpter 6 Revision Worksheets (Atthe) A B C Solutions (Atthe) Text ook Chpter Summry Pge 455. NOT REQUIRED: Limits of Aury Text ook Chpter Review Pge 45 Multiple Choie: Short Answer: Extene Response:, - Text ook Semester Review Pge Multiple Choie: - 5 Short Answer: - 4 Extene Response: prt,

15 Chpter 6 Mesurement Worksheet A Consier the given two-imensionl shpe. Fin the perimeter of the shpe if x = 8.8. Fin x if the perimeter is 9. m. Write n expression for x in terms of the perimeter P. If irle hs rius r m, fin the following, rouning to two eiml ples where neessry. The irumferene of irle if r = 4. A rule for r in terms of the irumferene C. The rius of irle with irumferene of 65 m. Fin the perimeter of these setors y i using ext vlues, n ii rouning to one eiml ple. i i ii ii

16 4 Fin the length of the unknown sie in these right-ngle tringles, orret to two eiml ples. 5 Consier the retngulr prism ABCDEFGH shown elow. Fin BE, leving your nswer in ext form. Fin BH, orret to two eiml ples. Chpter 6 Mesurement Worksheet B Fin the re of these shpes, rouning to two eiml ples where neessry.

17 e f g h Fin the vlue of the pronumerl for these shpes, rouning to two eiml ples where neessry. Are = 7 m Are = 0 m

18 Fin the totl surfe re of these solis, rouning to two eiml ples where neessry. 4 Fin the totl surfe re of this omposite soli, orret to one eiml ple.

19 Chpter 6 Mesurement Worksheet C Fin the volume of these solis, rouning to two eiml ples where neessry. e f

20 Fin the volume of this omposite soli, orret to one eiml ple. Fin the surfe re of sphere with rius 6 m, orret to two eiml ples. Fin the volume of sphere with imeter.74 km, orret to two eiml ples. Fin the rius of sphere with volume 580 mm, orret to two eiml ples. 4 This omposite soli inlues hemisphere n one s shown. Fin the surfe re, orret to two eiml ples. Fin the volume, orret to two eiml ples.

21 Chpter 6 Mesurement Worksheet A nswers 9 m x = 9. x = P m r C 0.5 m i 6 + π mm ii 9. mm i 6 + π m ii 5.7 m m.44 km Worksheet B nswers 49 m m 0.4 km.0 mm e 9.8 m f 6.49 m g 7.5 mm h 7.6 m = 9 r =.09 mm 9. m 44 m 05.6 m m Worksheet C nswers 48 m m.5 m 84 mm e 6. mm f. m m 45.9 m 0.77 km 5.7 mm m m

22 Topi: Liner Reltions - Chpter Revision Worksheets (Atthe) A B C Solutions (Atthe) Text ook Chpter Summry Pge 8. Not Require: Hlf Plnes Text ook Chpter Review Pge 8-87 Multiple Choie: 5 Short Answer: 6 Extene Response: Text ook Semester Review Pge Multiple Choie: - 5 Short Answer: - 7 Extene Response: prt,

23 Chpter Liner reltions Worksheet A Simplify the following y olleting like terms xy x y xy x y Simplify the following. m 8n - pq 5 p q Expn the following using the istriutive lw. Simplify where possile. 4 x y x 5 x 4 Ftorise the following. x x 6 x 5 Evlute these expressions if -, 4 n -. 6 Simplify the following y nelling ommon ftors. -8 6mn mn 4 7x 7

24 7 Simplify the following Simplify the following x x 5 x 4 x 7 9 Solve the following equtions n hek your solution y sustitution. 5x 7 x 4x x 8 - x x Solve the following inequlities n grph their solutions on the numer line provie. 4x -5 x 8 6 5x 9 7x 5

25 Chpter Liner reltions Worksheet B Deie if the point (-, 4) is on the line with the given equtions. y x 7 5x y -9 Fin the grient n y-interept for these liner reltions n sketh their grphs. y - x y x Sketh the grph of the following liner reltions y fining the x- n y-interepts. y x x y

26 4 Sketh the grph of the following liner reltions. x 5 y - y 4x y - x 5 Determine the grient of the line joining the following pirs of points. (6, ) n (9, 8) (-, 5) n (, -7) 6 Fin the eqution of the stright lines shown.

27 Chpter Liner reltions Worksheet C Fin the ext istne etween the pir of points (, ) n (, -5). Fin the mipoint of the line segment joining (, ) n (, -5). Fin the vlues of if the istne etween (, -) n (4, ) is. Deie if the grphs of eh pir of rules will e prllel, perpeniulr or neither. y -x 5 n y x 7 y x 9 n y x 6 4y x 8 n y x 4 Fin the eqution of the line tht is: prllel to y x 5 n psses through (-, ). perpeniulr to y - x 7 n psses through (4, 6). 5 4 Solve the following pirs of simultneous equtions using the metho of sustitution. y 8 6 x n y 4x x 5y -4 n y x 5

28 5 Solve the following pirs of simultneous equtions using the elimintion metho. 9x y n x y 9 x 7y n x 4y 8 6 The sum of the ges of two silings is n the ifferene etween their ges is 7. If Frnk is the oler rother of Beth, etermine their ges. 7 Json uys two highlighters n five pens n pys $6. Ey uys four highlighters n three pens n pys $8. Determine the ost of highlighter n the ost of pen.

29 Chpter Liner reltions Worksheet A nswers 7 6mn 4xy -5p q x y 4x 8y 4x x x x -m x x x x 4 x x x x -4 x 5 0 x - x 4 x 7 Worksheet B nswers Yes, the point is on the line. No, the point is not on the line. -,,

30 y x y - x Worksheet C Answers 5, - or 7 Perpeniulr Neither Prllel y x 7 5 y x 4 4 (, -4) (, -) 5 (, ) (4, -) 6 Beth is 8, Frnk is 5. 7 Highlighters ost $, pens ost $.

31 Topi: Surs n Inies - Chpter Revision Worksheets (Atthe) A B Solutions (Atthe) Text ook Chpter Summry Pge 6 NOT REQUIRED: Rtionl Inies Exponentil Equtions Text ook Chpter Review Pge 4 Multiple Choie: 9, Short Answer: 5, 8-0 Extene Response:,, Text ook Semester Review Pge 80 8 Multiple Choie: - 5 Short Answer: 6, 0 Extene Response: prt,

32 Chpter Inies n surs Worksheet A Simplify the following Simplify the following Simplify the following Expn n simplify the following. ( ) 6 ( 4-6 ) 5 + 0

33 ( 7 -)( 4+ 7 ) ( )( 5 + ) 5 Expn n simplify the following. ( 4+ ) ( 5 - ) ( 6- ) ( 6+ ) ( + 5 )( - 5 ) 6 Rtionlise the enomintor in the following Chpter Inies n surs Worksheet B Simplify the following using the inex lws. m 6 m s t 4s t 5 5

34 e x 5 y x y f x y Evlute using the zero power. 7m 0 6x 0 4x 0 Express eh using positive inies. x 8 y Simplify the following n express your nswers using positive inies. 6 mn 4 m n m n Write eh of these numers s si numerl Write eh of these numers using sientifi nottion

35 Define vriles n form exponentil rules for the following situtions. $ is investe t 6% per nnum. The ontents of leking wter tnk, initilly 800 litres, is eresing t rte of 4% per hour. The vlue of house purhse for $ is expete to grow y % per yer. Let $V e the vlue of the house fter t yers. Write rule onneting V n t. Use your rule to fin the expete vlue of the house fter the following numer of yers. Roun to the nerest ollr. i yers ii 0 yers Use tril n error to estimte when the house will e worth $ million. Roun to one eiml ple.

36 Chpter Inies n surs Worksheet A nswers Worksheet B nswers m 4 8s 5 t e 4x y 7 5 x 8y 4 m 9 4 n f 8x 9 7y A = mount of money t ny time, n = numer of yers of investment, A n A = litres in tnk t ny time, n = numer of hours elpse, A n V t i $ ii $ yers

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