Alg. Sheet (1) Department : Math Form : 3 rd prep. Sheet

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2 Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (, ) (, - ) ) ( 6, ) (, - ) 4) (, ) ( 5, 4 ) [] If {, }, Y {, 4, 5} find Y nd represent it y : ) An rrow digrm ) Grphicl digrm [] If {, }, find nd represent it y n rrow digrm  Complete the following : ) If {,, }, Y {4}, then Y.. ) If {5, 6}, Y {}, then Y ) If {, }, then Ø 4) {, } {4, 5}. 5) If {(, ), (, ), (, ), (, )}, then 6) If Y {(, 5), (, 5)}, then (, ).. 7) If (, ) ( 8, Y ), then Y..  Choose the correct nswer from those given : ) If : ( 5, x 8 ) ( y, - 5 ), then x y ) 4 ) 5 c) 6 d)7 ) {} {} ) {9} ) {} c) {(, )} d) 9 ١

3 ) If n (), n ( Y), then n (Y).. ) 4 ) 9 c) 5 d) 6 4) If n ( ) 4, n ( Y) 8, then n (Y ) ) ) 4 c) 6 d) 64 5) If {, 4}, then n ( Ø ) ) zero ) c) d) Ø  If {, -}, Y {4, 0}, Z {4, 5, -}, find : ) Y ) Y Z c) d) n ( Z) e) n (Y ) f) n (Z )  If {, }, Y {, 4, 5}, find ) Y nd represent it y n rrow digrm nd Crtesin digrm. ) n ( Y) c) n (Y ) d) ( Y) Y  If {, 4}, Y {4, 5} nd Z {6, 5}, then find : ) (Y Z) ) ( Y) Z c) ( Y) Y (Y Z)  If {}, Y {, }, Z {, 5, 6} Represent ech of, Y nd Z y venn digrm, then find : First : ) Y ) Y Z c) Z d) Y Second : ( Y) U (Y Z) Third : (Y Z) Fourth : ( Y) ( Z) Fifth : (Z Y) ( U Y ) ٢

4 Sheet () [] Choose the correct nswer from those given : ) If the point (, ) lies on Y xis, then.. ) zero ) c) d) ) If the point (5, 7) is locted on the xis, then.. ) ) 5 c) 7 d) ) If the point (-4, Y) lies on the xis, then Y ) - ) c) -8 d) -9 4) If the point ( 4, ) where Z is locted on the third qudrnt then equls ) ) c) 4 d) 6 Sheet () [] Choose the correct nswer from those given : ) If F is function from the set to the set Y, then : is clled ) the rnge of the function F ) the domin of the function F c) The codomin of the function F d) the rule of the function F ) If F is function from the set to the set Y, then : Y is clled.. ) the domin of the function. ) the codomin of the function. c) the rnge of the function. d) the rule of the function. ) If {, }, then the rrow digrm which represents function on is. () () (c) (d) 4) The opposite digrm represents A function on, its rnge is ) {} ) {,, c} c) {, } d) {, c} c ٣

5 [] If {, 4, 5}, Y {4, 6, 8, 0} nd R is reltion from to Y where " R " mens " " for ech, Write the set of the reltion R nd show tht R is function, then write its rnge. [] If {4, 6, 8, 0}, Y {,, 4, 5} nd R is reltion from to Y, where R mens for ech, Y Write R nd represent it y n rrow digrm.  If {,, 4, 5}, Y {,,, 4, 5, 6} nd R is reltion from to Y, where R mens 7 for ech of, Y Write R nd represent it y n rrow digrm nd lso y Crtesin digrm.  If {,, }, Y {,, 7} nd R is reltion from to Y, where R mens prime numer for ech, Y Write R nd represent it y n rrow digrm. is R function?  If {-, -,, }, Y { 8,,,, 8 } nd R is reltion from to Y, where R mens for ech, Y Write R nd represent it y n rrow digrm nd lso Crtesin digrm.  If {, 5, 8} nd Y {0, 6, 4, 0} nd R is reltion from to Y where R mens is fctor of for ech, Y Write R nd represent it y n rrow digrm nd y Crtesin digrm. is R function? nd why?  If {,, 4}, Y {6, 8, 0,, 5} nd R is reltion from to Y, where R mens is fctor of for ech, Y write the reltion R. ٤

6  If {6, 4,, 0, -, -4, -6 }, nd R is reltion on where R mens is the dditive inverse of for ech, Write R nd represent it y n rrow digrm nd show with reson if R is function or not? nd if R is function, mention its rnge.  If {0,,, } nd R is reltion on where R mens is the multiplictive inverse of for ech,. write R nd represent it y n rrow digrm nd show if R is function or not. [] If {,, 4, 6, 0} nd R is reltion on where R mens is multiple of for ech,. Write R nd represent it y n rrow digrm nd lso y Crtesin digrm. is R is function? nd why? ٥

7 Sheet (4) [] Choose the correct nswer from those given : ) The function F where () 4 is polynomil function of.degree ) first ) second c) third d) fourth ) The function F : F () ( 5 ) is polynomil function of..degree. ) zero ) second c) third d) fourth ) The function F : F () (- ) is polynomil of the.degree. ) first ) second c) third d) fourth 4) The function F : F () (-) is polynomil of the.degree. ) first ) second c) third d) fourth 5) If : F (), then : F () ) ) 6 c) 9 d) 6) If : F () 6, F (), then.. ) ) - c) 4 d) 6 7) If : F () 5 nd F (), then. ) ) 8 c) d) 6 [] Complete the following : ) If (, y) the set of the function F where F (), then y.. ) If (, ) the set of the function F where F (), then [] If : F () 5 ) Mention the degree of F ) Prove tht : F () F ( ) ٦

8 Sheet (5) [] Complete the following : ) The function F : R R where F () 5 is represented y stright line prllel to.nd intersects y-xis t the point. ) If F (), then F (5) F (-5) ) If F () 5, then F(5) F(0) 4) The liner function given y the rule is represented grphiclly y stright line intersecting the -xis t the point.. 5) The liner function given y the rule Y 6 is represent grphiclly y stright line intersecting the -xis t the point 6) The point of the vertex of the curve of the function F : F () 4 5 is 7) If ( -, y) elongs to the curve of the function F : F (), then : Y... ٧

9 Represent Grphiclly [] Represent the following function grphiclly, where R : ) F () 5 ) F () - 4 [] Represent ech of the following liner function grphiclly nd find the point of intersection of the stright line which represents ech of them with the coordinte xes, where R : ) F : F () ) F : F () - [] Represent ech of the following function grphiclly nd from the grph, deduce the coordintes of the vertex of the curve nd the eqution of the line of symmetry nd the mximum or minimum vlue of the function, where R : ) F : F () tking [ - 4, ].  Complete the following : ) If : {,, 5}, F : R nd F (), then the rnge of F. ) The liner function F : F () 7 is represented y stright line cuts -xis t the point ) The liner function F : F () is represented y stright line cuts y-xis t the point. ٨

10 Unit () Sheet (6) [] Complete the following : ) The proportion is. ) If,, c nd d re proportionl quntities, then c is clled ) If the quntities,, c nd d re proportionl, then :. 4) The fourth proportionl for the numers 4, nd 6 is 5) The second proportionl for the numers, 4 nd 6 is 6) The third proportionl for the numers 8, 6 nd is.. 7) The first proportionl for the numers 5, 7 nd 45 is. 8) If, 4, nd re proportionl, then :.. 9) If 7 Y, then : Y 0) If 5 4 0, then :.. ) If then : ) If where R nd R, then :. ) If, then : Y 5 Y 4) If, then :... [] Choose the correct nswer from those given : ) If 5, then :. ) 5 6 ) 6 5 c) d) ) If : 5,,, 7 re four proportionl quntities, then :.. ) 7 6 ) 5 c) 5 d) ٩

11 ) If ) 8, then : ) 8 c) - 8 d) 8 [] Find the vlue of in ech of the following, If : ) ( ) : ( 5) : 4 ) ( 8) : ( ) : ) If Y Y 4, find the rtio : Y 4) If 4 Y Y, find : Y 5) If 4, then find the vlue of : 4 ) ) Y 6) If, find the vlue of the rtio : Y 6Y 7) find the numer tht if it is dded to ech of the numers, 5, 8 nd, it ecomes proportionl. 8) Prove tht :,, c nd d re proportionl quntities if : ) c d d ) c c d 9) If : : c 5 : 7 : nd 7.6, find the vlue of ech of :, nd c. 0) If 4 c, find : : c  Answer the following : ) Find the numer which if it is dded to the two terms of the rtio 7 : it will e : ) Find the numer tht if we sutrct thrice of it from ech of the two terms of the rtio 49, the rtio ecomes 69 ) Find the numer which if its squre is dded to ech of the two terms of rtio 7 : it ecomes 4 : 5 4) Find the positive numer which if we dd its squre to ech of the two terms of rtio 5 : it ecomes : 5 ٠

12 5) Wht is the numer which is sutrcted from the ntecedent of the rtio 5 : nd dded to its consequent to ecome : 4 6) Two integers, the rtio etween them is : 7 nd if we sutrcted 5 from ech term, the rtio etween ech of them ecomes :, find the two umers. 7) The rtio etween two integers is, if we dd 4 to the smll numer nd sutrct 4 form the gret numer, the rtio will ecome 8 : 9 find the two numers. 8) Two integers, the rtio etween them is :, if you dd to the first 7 nd sutrct from the second, the rtio etween them ecomes 5 : find the two numers. Sheet (7) [] Complete the following : c c ) If, then : d 5 d c e ) If, then : d f 5 d f 4 7 ) If Y Y c e, then : 5 c... c e 4) If, then : d f f.. [] If,, c nd d re proportionl quntities, prove tht : ) ) ) d 5 c 5 d c 5 c c ( c d 5 d c ) d 4) 5c 5d where,, c nd d re positive quntities. 5 c 5) 5 d c d ١

13 ٢ [] If d c f e prove tht : ) d c 5 5 f d e c ) f d e c f e 8 8  If Y 4 Y 4, prove tht : Y 5 Y 5  If 9 y x 7 y z, prove tht : z y x 6 x z  If c c y c z, prove tht : y y z  If c y c z, then prove tht : c y 4 4 z y 6  If y y, prove tht : y  If y y y c 4 5, prove tht : c  If 7 c, find the vlue of : c [] If 7 y 5 y z 8 z, prove tht : z z y 5 [] If y 4, z 5 nd y z 49, find the vlue of ech of :, y nd z

14 Sheet (8) [] Find the middle proportion etween : ), 7 ), 8 [] If is the middle proportion etween nd c, prove tht : ) ) ( ) c c c c ) c c [] If,, c nd d re in continued proportion, prove tht : ) ) ) 4) c 5c 5d cd c 4c c 4d 4c 4d c c d c c d ٣

15 [] Complete the following : ) If α y then :. Sheet (9) ) If z m where m is constnt, then : z α.... ) If y α, then : y 4) If vries inversely s y, then y... 5) If y 5, then : y α 5 6) If y α, then : y vries inversely s 7) If y 0, then : α.. 8) If y 5, then : α.. 9) If y α nd y s 8, then : y when 0) If y α nd y s 0, then : y.. when ) If y α nd y s 4, then : y y ) If α nd y 6 s 4, then :.. ( in simples form ) [] If y vries directly s nd y 0 s 7 Find : when y 40 [] If vries inversely s nd s 8, find : ) The vlue of s.5 ) The vlue of s  If y α nd y 4 when 4, find : ) The reltion etween nd Y ) The vlue of y when 60 ٤

16  If α nd y when, find : ) The reltion etween nd y B) The vlue of y when.5  If y α nd y 46 s, find the reltion etween nd find the vlue of y s  If y α, find the reltion etween nd y where y s  If y α nd 8 s y, find s y.5  If y α ( ), find the reltion etween nd y if when y  If y 7 z z y, prove tht : y α z [] If : 4 9, prove tht : vries s [] Connecting with physics : A cr moves with uniform velocity where the distnce vries directly with the time (t). If the cr covered distnce of 50 km. in 6 hours, find the distnce covered y tht cr in 0 hours? [] Connecting with stronomy ; If the weight of ody on the moon (W) is directly proportionl with its weight on the ground ( R ). If the ody weight 84 kg., on the ground nd its weight on the moon is 4 kg.. Wht will its weight e on the moon if its weight on the ground is 44 kg.? ٥

17 Sheet (0) Importnt Rules : ) The stndrd devition of set of vlues. σ Σ (x x ) n ) The stndrd devition of frequency distriution. σ k Σ (x x ) Σ K ) The stndrd devition of frequency distriution of sets. σ k Σ (x x ) Σ K A) Complete the following : - The resources of collecting dt re nd.. - The personl interview is. resource of collecting dt. - Centrl gency for pulic moiliztion nd sttistics is resource of collecting dt. 4- The suitle method for checking the production of fctory is 5-. Is secondry resource of collecting dt. 6- Choosing smple from the society s lyers in sttistics is clled smple. 7- Dispersion mesurements re.. nd.. 8- The simplest mesure of the dispersion is. 9- The difference etween the gretest vlue nd the smllest vlue in set of vlues is clled 0- The positive squre root of the verge of squres of devition of the vlues from their men is clled.. - If the stndrd devition equls zero, then... - The dispersion to ny set eqully vlues equls. - The men of the set of the vlues : 7, 5, 9, nd is. 4- The rnge of the set of the vlues : 6, 5, 9, 4 nd is. 5- The most repeted vlue in set of vlues represents. ٦

18 6- If the men of numers : k, k, k, k nd k 5 is, then k. 7- If Σ ( x x ) 6 of set of vlues nd the numer of these vlues 9, then the stndrd devition.. B) Clculte the stndrd devition of the vlues : 8, 9, 7, 6 nd 5. C) The following tles shows the distriution of ges of 0 persons in yers : The ge Totl Numer of persons Find the stndrd devition of the ges. D)The following is the frequency distriution of weekly incentives of 00 workers in fctory : Incentives in pounds Numer of workers Find the stndrd devition of this distriution. ٧

19 ٨

20 [] In the opposite figure : If ABC is right-ngled tringle t B, then : sin A.. Geom. Sheet () A 5cm. C cm. B [] In the opposite figure : ABC is right-ngled tringle t B, AB cm, AC 5 cm, Then : sin C cos C C 5cm. A cm. B [] If the rtio etween the mesures of two supplementry ngles is : 5, find the mesure of ech one y degree mesure.  In the opposite figure : ABC is right-ngled tringle t B in which : AB 8 cm, AC 7 cm. Find ech of : Sin C, tn A, cos A, cos C, tn C, sin A C 7cm A 8cm B  YZ is right-ngled tringle t Z where Z 7 cm. nd Y 5 cm. Find the vlue of ech of the following : ) tn tn Y ) sin sin Y  YZ is right-ngled tringle t Y, if YZ Y Find the vlue of ech of : tn Z, tn, cos Z, cos  ABC is right-ngled tringle t B, if AB AC Find : the min trigonometricl of the ngle C. ٩

21  In the opposite figure : ABC is right-ngled tringle t B, AB 6 cm, tn C, find : 4 ) The length of ech of BC nd AC ) Sin A cos A C A 6 cm B ٠

22 Sheet () [] Complete the following : ) sin 45. ) cos 60 sin 0 ) sin 0 cos 60 - tn ) sin 60 cos 0 tn 60. 5) sin 45 cos 45 6) tn 60 cos 60 - tn 45. 7) tn 45 sin 0. 8) 4 cos 0 tn 60 [] Without using the clcultor, prove ech of the following : ) sin 60 sin 0 cos 0 ) cos 60 cos 0 - ) cos 45 - sin 45 4) cos 60 cos 0 - sin 0 tn 0 5) tn 60 tn 0 [] Choose the correct nswer from those given : ) If cos C where C is n cute ngle, then : m ( C).. ) 0 ) 60 c) 45 d) 90 ) If sin where is n cute ngle, then : m ( ).. ) 0 ) 60 c) 45 d) 90 ) If tn where is n cute ngle, then : tn ) ) c) d) 4) If is the mesure of n cute ngle nd sin, then : sin.. ) ) 4 c) d) ١

23 5) If sin tn 60 where is n cute ngle, then : m ( ).. ) 0 ) 45 c) 60 d) 40 6) If tn where is n cute ngle, then : m ( ).. ) 5 ) 0 c) 60 d) 45 7) If sin, then : (where is n cute ngle ). ) 0 ) 0 c) 45 d) 60 8) If cos where is n cute ngle, then : m ( ).. ) 0 ) 45 c) 60 d) 0 9) If cos ( 0 ) where ( 0 ) is n cute ngle, then. ) 0 ) 40 c) 50 d) 70 0) If tn ( - 5 ) where ( - 5 ) is n cute ngle, then :. ) 5 )65 c) 60 d) 0 ) If sin ( 5 ) where ( 5 ) is the mesure of n cute ngle, ) then : tn ( 0 ). ) tn 75 ) c) cos 75 sin75 ) ) c) tn 5 d) sin 5 cos 5 Sin 75 cos 75 d)  Find the vlue of in ech of the following : ) tn 4 sin 0 cos 60 where is n cute ngle. ) sin sin 60 cos 0 - cos 60 sin 0 where is n cute ngle. ) sin sin 0 cos 60 cos 0 sin 60 where is n cute ngle. ٢

24  ABCD is trpezium in which : AD // BC nd m ( ABC) 90 If AB cm, AD 6 cm, nd BC 5 cm. Find : ) The length of DC ) m ( C) ) sin ( DCB) tn ( ACB) ٣

25 Sheet () [] Complete the following : ) The distnce etween the two points (5, 0), (6, 0) equls ) The distnce etween the two points A (6, 0), B (0, 8) ) The distnce etween the point (-, 4) nd the point of origin 4) If A (, - ), B (-, ), then AB.. 5) If the distnce etween the two points (, 0 ), (0, ) is unit length, then 6) The rdius length of the circle whose centre is (7, 4) nd psses through (, ) equls 7) In the squre ABCD if A (, 5) nd B (4, ), then the re of the squre equls..re unit. 8) In the rhomus ABCD where A ( -, 7), B (-, ), then the perimeter of the rhomus equls..length unit. [] Prove tht : ) The points A ( 4, ), B (, ) nd C (-5, -) re colliner. ) Prove tht the tringle with vertices of points : A (5, -5), B (-, 7) nd C (45, 5) is right-ngled tringle t B, then clculte its re. ) The points A (0, ), B (4, 5), C (, 8) nd D (-, 4) re vertices of rectngle nd find its digonl length. 4) ABCD is qudrilterl where A ( 5, ), B (6,-), C (,-) nd D (0, 4) Prove tht : ABCD is rhomus, then find its re. ٤

26 5) The points A ( -, 5), B (, ) nd C (-4, ) re non-colliner nd if D (-9, 4), Prove tht : The figure ABCD is prllelogrm. 6) ABCD is qudrilterl where A (, 4), B (-, 0), C (-7, 5) nd D ( -, 9) Prove tht : The figure ABCD is squre. 7) The points A (, -), B (-4, 6) nd C (, -) lie on the sme circle whose centre is M (-, ), then find the circumference of the circle where π.4 [] If the distnce etween the two points A (0, K) nd B (4, 0) is 5 length units. Find : The vlue of K.  Find the vlue of in ech of the following cses : ) If the distnce etween the two points (, 7), (-, ) equls 5 length units. ) If the distnce etween the two points (, 7), (, - 5 ) equls length units. ٥

27 Sheet (4) [] Find the coordintes of the midpoint of AB in ech of the following cses : ) A (, 5), B (7, ) ) A (5, - ), B (-, ) ) A (-5, 4), B (5, -4) 4) A (0, 4 ), B (8, 0) [] If the point (, 0) is the midpoint of the line segment whose ends re (, -5) nd (, 5 ), find the vlue of [] If the point (5, ) is the midpoint of AB where its terminls re A ( 5, y ) nd B (-5, -), find the vlue of y.  If the point (5, ) is the midpoint of AB where its terminls re A (5, y) nd B (-5, -), find the vlue of y  Find the vlue of ech of nd y if the point (, -) is the midpoint of the line segment drwn etween the two points (, ), (, y)  Prove tht the points A (, -), B (-5, 0), C (0, -7) nd D (8, -9 ) re the vertices of prllelogrm. ٦

28  If the points A (, ), B (4,-), C (-, -) nd D (-, ) re vertices of the rhomus. Find : ) The coordintes of the point of intersection of the two digonls. ) The re of the rhomus ABCD.  ABCD is squre whose vertices re A ( 0, 5), B (, ), C (0, -) nd D (, y ) respectively. Find the coordintes of the point D.  Prove tht : The points A (6, 0), B (, -4), C (-4, ) re the vertices of right-ngled tringle t B, then find the coordintes of D tht mke the figure ABCD rectngle. ٧

29 Sheet (5) [] Complete the following : ) In the opposite figure : The slope of the stright line L equls.. y L θ y ) The condition of prllelism of two stright lines whose slopes re m, nd m is. While the condition of their perpendiculrity is ) The slope of the stright line prllel to -xis.. 4) The slop of the stright line prllel to y-xis.. 5) The slope of the stright line which mkes with the positive direction of -xis positive ngle of mesure 45 equls. 6) If AB // CD nd the slope of AB, then : the slope of CD equls.. 7) If AB CD nd the slope of AB, then the slope of CD equls. 8) The slope of the stright line which is prllel to the stright line pssing through the two points (, ) nd (-, ) equls. 9) If ABCD is squre whose digonls AC nd BD where A (, 5) nd C (5, -), then the slope of BD. 0) If the stright line AB is prllel to the -xis where A (8, ) nd B (, K), then K ) If the stright line CD is prllel to the y-xis where C ( M, 4) nd D (-5, 7), then M. [] Prove tht : The stright line which psses through the two points (4, ) nd (5, 6) is prllel to the stright line which psses through the two points (0, 5) nd (-, ). [] Prove tht : The stright line pssing through the two points A (-, 4) nd C (-, -) is perpendiculr to the stright line pssing through the two points B (, ) nd D (-, ) ٨

30  Find the slope of the stright line which is perpendiculr to the stright line which psses through the two points A (, - ), B (, 5).  Prove tht : The stright line pssing through the two points (. - ) nd (6, ) is prllel to the stright line tht mkes n ngle of mesure 45 with the positive direction of the -xis.  The tringle whose vertices re A (, -), B (, ) nd C (5, ) is right-ngled tringle t A, find the vlue of.  If the stright line AB // the y-xis, where A (, 7) nd B (, 5), then find the vlue of.  If the stright line CD // the -xis where C (4, ) nd D (-5, y), find the vlue of y  If A (-, - ), B (, ) nd C (6, 0), prove tht tringle ABC is right-ngled tringle t B.  Prove tht : The point A (-, ), B (0, 5), C (4, ) nd D (5, 6) re the vertices of the prllelogrm ABDC. [] Prove tht : The point A (5, ), B (, 5), C (-, ) nd D (, -) re vertices of the rectngle ABCD. ٩

31 [] Prove tht : The point A (, ), B (6, 4), C (7, 9) nd D (, 8) re vertices of the rhomus ABCD. [] Prove tht : The points A (-, -), B (, ), C (6, 0) nd D (, -4 ) re vertices of squre. ٠

32 Sheet (6) [] Find the slope nd the intercepted prt of y-xis y ech of the following stright lines : ) y 5 ) y 8 [] Find the eqution of the stright line if : ) Its slope nd intercepts from the positive prt of y-xis 7 units. ) Its slope - nd intercepts from the positive prt of y-xis units. [] Find the eqution of the stright line if : ) Which psses through the point nd mkes with the positive direction of -xis positive ngle of mesure 5. ) Which cuts prt of length units from the negtive prt of y-xis nd is prllel to the line whose eqution : y 6. ) Which is perpendiculr to the stright line : 4 y 7 0 nd intercepts from the positive prt of y-xis prt of length 6 units. 4) Which psses through the point (, -) nd its slope equls. 5) Pssing through the point (-, ) nd perpendiculr to the stright line whose eqution : y 5 6) Pssing through the point (, -5) nd it is prllel to the stright line : y 7 0 7) Which psses through the point (, ) nd prllel to the stright line pssing through the two points ( 5,6) nd (-, ). 8) Which psses through the two points (, - ) nd (, ) 9) The perpendiculr to AB from its midpoint where A (, ) nd B (, 5). ١

33  In the opposite figure : A prticle moves with constnt speed (v) where the distnce (d) is mesured y meter nd time (t) y second. find the following : ) The distnce t the eginning of moving. ) The velocity of the prticle. ) The eqution of the stright line which represent the movement of the prticle. 4) The time in which the prticle covers distnce of 5 meters from the eginning of the movement.  The opposite grph : Represents the motion of prticle moving with uniform velocity (v) where the distnce (d) is mesured in meter nd the time (t) in seconds. Find : ) The distnce t the eginning of the motion. ) The velocity of the prticle. D (m.) 0 T (sec.) D (meter) ) The eqution of the stright line representing the motion of the prticle. 4) The covered distnce fter 4 seconds from the eginning of the motion. 5) The time in which the prticle covers distnce of.5 meters from the eginning of the motion T (second ٢

34 ٣

Linear Inequalities: Each of the following carries five marks each: 1. Solve the system of equations graphically. Liner Inequlities: Ech of the following crries five mrks ech:. Solve the system of equtions grphiclly. x + 2y 8, 2x + y 8, x 0, y 0 Solution: Considerx + 2y 8.. () Drw the grph for x + 2y = 8 by line.it

03 Qudrtic Functions Completing the squre: Generl Form f ( x) x + x + c f ( x) ( x + p) + q where,, nd c re constnts nd 0. (i) (ii) (iii) (iv) *Note t A-PDF Wtermrk DEMO: Purchse from www.a-pdf.com to remove the wtermrk Add Mths Formule List: Form 4 (Updte 8/9/08) 0 Functions Asolute Vlue Function Inverse Function If f ( x ), if f ( x ) 0 f ( x) y f

03 Qudrtic Functions Completing the squre: Generl Form f ( x) x + x + c f ( x) ( x + p) + q where,, nd c re constnts nd 0. (i) (ii) (iii) (iv) *Note t A-PDF Wtermrk DEMO: Purchse from www.a-pdf.com to remove the wtermrk Add Mths Formule List: Form 4 (Updte 8/9/08) 0 Functions Asolute Vlue Function Inverse Function If f ( x ), if f ( x ) 0 f ( x) y f

Edexcel GCE Core Mathematics (C2) Required Knowledge Information Sheet. Daniel Hammocks Edexcel GCE Core Mthemtics (C) Required Knowledge Informtion Sheet C Formule Given in Mthemticl Formule nd Sttisticl Tles Booklet Cosine Rule o = + c c cosine (A) Binomil Series o ( + ) n = n + n 1 n 1

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Prerequisite Knowledge Required from O Level Add Math. d n a = c and b = d Prerequisite Knowledge Required from O Level Add Mth ) Surds, Indices & Logrithms Rules for Surds. b= b =. 3. 4. b = b = ( ) = = = 5. + b n = c+ d n = c nd b = d Cution: + +, - Rtionlising the Denomintor

2) Three noncollinear points in Plane M. [A] A, D, E [B] A, B, E [C] A, B, D [D] A, E, H [E] A, H, M [F] H, A, B Review Use the points nd lines in the digrm to identify the following. 1) Three colliner points in Plne M. [],, H [],, [],, [],, [],, M [] H,, M 2) Three noncolliner points in Plne M. [],, [],, [],, [],,

CONIC SECTIONS. Chapter 11 CONIC SECTIONS Chpter. Overview.. Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig..). Fig.. Suppose we rotte the line m round

Mathematics Extension 1 04 Bored of Studies Tril Emintions Mthemtics Etension Written by Crrotsticks & Trebl. Generl Instructions Totl Mrks 70 Reding time 5 minutes. Working time hours. Write using blck or blue pen. Blck pen

MATHEMATICS PART A. 1. ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC FIITJEE Solutions to AIEEE MATHEMATICS PART A. ABC is tringle, right ngled t A. The resultnt of the forces cting long AB, AC with mgnitudes AB nd respectively is the force long AD, where D is the AC foot

Shape and measurement C H A P T E R 5 Shpe nd mesurement Wht is Pythgors theorem? How do we use Pythgors theorem? How do we find the perimeter of shpe? How do we find the re of shpe? How do we find the volume of shpe? How do

I. Equations of a Circle a. At the origin center= r= b. Standard from: center= r= 11.: Circle & Ellipse I cn Write the eqution of circle given specific informtion Grph circle in coordinte plne. Grph n ellipse nd determine ll criticl informtion. Write the eqution of n ellipse from rel

Problem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are: (x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one PROPERTES OF RES Centroid The concept of the centroid is prol lred fmilir to ou For plne shpe with n ovious geometric centre, (rectngle, circle) the centroid is t the centre f n re hs n is of smmetr, the JUST THE MATHS UNIT NUMBE 13.1 INTEGATION APPLICATIONS 1 (Second moments of n re (B)) b A.J.Hobson 13.1.1 The prllel xis theorem 13.1. The perpendiculr xis theorem 13.1.3 The rdius of grtion of n re 13.1.4