# 3 x x 3x x. 3x x x 6 x 3. PAKTURK 8 th National Interschool Maths Olympiad, h h

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1 PAKTURK 8 th Ntionl Interschool Mths Olmpid,.9. Q: Evlute Q: Evlute bc bc. b. c bc.9.9b.9.9bc Q: Find the vlue of h in the eqution h bc. bc bc. b. c bc bc bc bc h 7 7 h Q: Which of the following is not fctor of b b 6 9 h b b b b b Q: Age of fther is nd his son is ers old. After how mn ers the ge of fther will be triple of his son : b then nswer b

2 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q6: Find the multiplictive inverse of if /76 / Q8: ISMOISMOISMO... find the 767 th letter or digit in the sequence? I M nd 7th term is Q9: ABCD is squre nd equilterl tringle. Find BCE is n 76 Q7: Ech of the nine pths in prk is m long. Ann wnts to go from A to B without going long n pth more thn once. Wht is the length of the longest route she cn choose? 6 9m 8m 7m 6m

3 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: Which of the following is lws n even number where n is positive integer? 7(n+) 7(n+) 7(n+) 7(7n+) 7n 7n n Q: Evlute Q: If 6 nd thn 6 6 6? 6 Q: If Frhn leves now nd drive t 8km/h, he cn be in Lhore in time for his ppointment. On the other hnd, if he ets first nd leves in hlf n hour, he will hve to drive t km/h to mke his ppointment. How fr is he to Lhore? km km km km Q: I think of number, subtrct 7 from it, divide the result b, nd then dd. If this gives finl result of, find the originl number d 8t t. 8t t t 8t t t.hrs Q: A wter tnk cn be filled b one pipe in hours nd it cn be emptied b nother pipe in hours. If both pipes re open, how long will it tke to fill the tnk? d 8t 8. km hrs

4 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q6: Evlute. Q9: If [ AK [ AC,[ BF //[ CE nd, m ACD m DCE m FKB then, 9.. m FDC? Q7: If nd the,... n? n n nn nn nn... n n n Q8: If n, then find the mimum nd minimum vlue of n? (n is n integer) 9 nd - nd -6 9 nd -6 nd - Q: Evlute ? - - n ? n 6 n min n... 9 n n m n 9 9 9

5 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: If is the result of then, which of the followings in terms of 9 7 Emple: ++=6 or ++++= The numbers which re squres of nturl numbers re clled perfect squres. Which of the following numbers is neither tringulr nor perfect squre? Emple: 6 is squre of Q: Sibtin evlutes. for nd 7 Which of the following epressions hs the sme vlue when nd Q: In the figure, rectngulr prism hs been removed from lrger prism with dimensions cm, cm nd cm. Find the vlume of the remining solid in cubic centimeters. 8 6 Q: Informtion: The numbers which cn be written s the sum of the integers from to n for n=,,,,... re clled tringulr numbers. cm

6 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: Find the re of given figure if BD is cm Are of ABCD cm, Are of AKFE cm 6 6 6, Are of LMNC cm 9, shded re cm , cm 6cm cm 6cm Q7: The figure shosw cube. Wht is the mesure of ngle EFL? Are of ABD cm, Are of BDC 6 cm, totl re cm cm cm, 6 7 Q6: In the figure, ABCD, AKFE nd LMNC re squres. Find the re of the shded region Q8: Find the vlume in cubic centimeters of the solid with the given dimensions. cm 99cm 78cm 86cm

7 PAKTURK 8 th Ntionl Interschool Mths Olmpid, AD 69 AD 69 AD cm 66cm 68cm 7cm 7cm Q: Simplif b. b V cm b b b b Q9: Wht is the mesurement of the ngle between the hour-hnd nd the minute- hnd t the time :? 6 8 b b b b. b b Angle between to is. If ever 6 minutes it moves then in minutes it will move. Totl mkes + =. Q: Find the distnce between A nd D Q: There re two different ws from the cit A, to the cit B. There re different ws from the cit B, to the cit C. There re two different ws from the cit A to the cit C tht re not pssing through the cit B. How mn different ws re there from the cit A to the cith C? 6 8 cm cm cm cm

8 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: In the given figure, wht is the vlue of ngle o? 7m m m m 9 7 Are of Shded Region=Are of Rectngle-(Are of smll circles+are of big circle) cm Q: In the figure, O is the center of the circle. Find the re of the shded region. Q: The figure below shows circulr pools in rectngulr grden. The dimeters of the circles re 6 m nd m nd the side lengths of the grden re m nd m. The rest of the grden is covered in grss. How much of the grden is covered in grss? cm 6cm cm 8cm Are of tringle(with perpendiculr sides)= 8 8 cm

9 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q6: Find the perimeter of the shded region Q8: A gs sttion gives % discount on gsoline. The net month it gives nother % discount on the new price. Find the totl percentge of discount on the originl price. 6% % 6% 66% st : then 66cm 7cm 78cm 8cm 6% discount Perimeter of the shded region= cm Q9: In school referendum % of techers nd 98% of students s YES. All the students nd techers prticipte in the referendum. Referendum results s 9% YES. Find the rtio of the number of students to the number of the techers. 8 Q7: Find the re of trpezoid Let Techers : nd Students : be cm. cm 7 cm 7 cm 8 8 : : Are of trpezium=/ Sum of prllel sides height cm

10 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q: Wht is M PN \? Q: A regulr hegon is divided in to 6 equilterl tringles. If one side of the hegon is 6 cm wht is the totl perimeter of tringles? 6 cm 7 cm 8 cm cm {,,} {,,,} {,,,,9} {,,,,6,7,8,9} M \ P N,,,,,9 \,,,,9 Q: One of the students sks the ge of Khwrizmi. His nswer is : "When I ws t our ge ou were ers old nd when ou re t m ge, I will be 66 ers old." Accordingl, wht is the student's current ge? 8 6 Totl Perimeter: 8One side of tringle= 86=8cm.? Q: -7 Pst Present Future Student -k Khwrizmi -k +k=66 -k=+m nd -k+m= then m=k, -k=+m nd -k=+k, -k= nd +k=66 solutions =8 nd k=8 then Student s current ge=-k=8-8=

11 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q:...? Q6: If. b nd. b.7 then, evlute b..7 Q: Onder, Tner nd Serht re plnning to go to trip. The shre the cost of the trip in the rtio ::6 respectivel. If hlf of Serht`s shre is 6 Rs, how much less is Onder going to p thn Tner? Q7: If the numbers in the figure re ordered with rule then which number will come in plce of question mrk? Rs. Rs. Rs. Rs. Serht s shre: 6=Rs., Totl shre is: 6Totl Serht ' s Totl Rs. Onder ' s Rs.8 Tner ' s Rs. 8 Tner ' s Onder ' s 8 Rs.

12 PAKTURK 8 th Ntionl Interschool Mths Olmpid, Q8: During n rt lesson, Mudessir creted repeted pttern on piece of pper s shown below, The re of the shded prt is... Q: If b c 8 9 b c 8 then, find the vlue of. b c cm cm cm cm Are of tringles: Q9: cm, is the vlue of nd then, wht b c 8 b c b c b c 8 8 b c 6

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