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2013_MATHCOUNTS_Chapter_Countdown_Round

发布时间:2013-12-22 14:41:39  

(CDs)1.??_____________How??many??CDs??can??Edward??buy??for??$14??each??and??spend??the??same??amount??he??would??spend??to??buy??60??CDs??for??$7??each???

What??is??the??smallest??prime??that??is??a??factor??of??the??sum??5!??+??1?

What??is??the??value??of??x??if??3x??+??7??=??22?

The??sum??of??the??first??n??odd??positive??integers??is??64.??What??is??the??value??of??n?

A??bookstore??employee??is??given??a??20%??discount??off??the??retail??price??of??any??book.??Assuming??there??is??no??tax,??how??many??dollars??does??she??pay??for??a??book??with??a??retail??price??of??$55?2.??_____________3.??_____________4.??_____________(dollars)5.??_____________

(degrees)6.??_____________If??an??isosceles??triangle??has??base??angles??that??are??each??twice??the??measure??of??the??smaller??angle,??what??is??the??degree??measure??of??one??of??the??base??angles???

Tim’s??math??homework??is??on??five??consecutive??pages??in??the??math??textbook,??and??the??sum??of??those??page??numbers??is??630.??What??is??the??page??number??of??the??next??page??after??these??five??homework??pages?

The??intersection??of??a??circular??region??of??radius??3??inches??and??a??circular??region??of??radius??2??inches??has??area??π??in2.??In??square??inches,??what??is??the??area??of??the??total??region??covered??by??the??two??circular??regions???Express??your??answer??in??terms??of??π.??

What??is??the??value??of??the??product??47??×??53???

What??is??the??ratio??of??the??number??of??degrees??in??the??interior??angle??of??a??regular??pentagon??to??the??number??of??degrees??in??the??interior??angle??of??a??regular??hexagon???Express??your??answer??as??a??common??fraction.

??Marielle??buys??an??equal??number??of??50¢??and??75¢??candy??bars??and??spends??$10,??not??including??tax.??How??many??candy??bars??did??she??buy??altogether???

A??restaurant??automatically??adds??an??18%??tip??to??the??bill.??If??the??tip??was??$9,??what??was??the??bill??before??the??tip??was??added,??in??dollars?

Copyright MATHCOUNTS, Inc. 2012. All rights reserved. 2013 Chapter Countdown Round(page)7.??_____________(in2)8.??_____________9.??_____________10.??_____________(candy11.??_____________bars)(dollars)12.??_____________

(miles)24.??_____________How??many??miles??are??traveled??driving??at??30??mi/h??for??30??minutes?

What??is??the??median??of??the??set??of??all??positive??factors??of??100?????

41-What??is??the??value??of??the??quotient?????-If??a2?????b2??=??10??and??a?????b??=??2,??what??is??the??value??of??a??+??b?

When??the??positive??integer??x??is??divided??by??each??of??4,??5??and??6,??it??has??a??remainder??of??3.??What??is??the??sum??of??the??three??smallest??possible??values??of??x?????

The??sum??of??the??interior??angles??of??a??convex??polygon??is??900°.??How??many??sides??does??the??polygon??have???

How??many??positive??integers??between??100??and??200??are??divisible??by??14?????

What??is??the??least??value??of??n??for??which??a??regular??n-gon??has??at??least??17??diagonals?

What??is??the??value??of??the??difference??20182???????20132?

11111What??is??the??denominator??when??++++??is??written??as??a??common??23456fraction?

What??is??the??range??of??the??set??{121,??142,??163,??184,??106}?25.??_____________26.??_____________27.??_____________28.??_____________(sides)29.??_____________(integers)30.??_____________31.??_____________32.??_____________33.??_____________34.??_____________

35.??_____________99??1??2??3??1?1?1???1???????????What??is??the??value??of??the??quotient???????(years36.??_____________??old)John??is??3??years??older??than??Peter.??Ten??years??ago??the??sum??of??their??ages??was??59.??In??years,??how??old??is??John??now?

Copyright MATHCOUNTS, Inc. 2012. All rights reserved. 2013 Chapter Countdown Round

49.??_____________In??the??game??Yahtzee?,??five??standard??dice??are??tossed.??What??is??the??probability??that??all??five??dice??show??even??numbers??or??all??five??show??odd??numbers???Express??your??answer??as??a??common??fraction.

What??is??the??value??of??0.+0.+0.+0.???Express??your??answer??as??a??common??fraction.??????

Five??couples??went??to??the??movies??together.??They??all??sit??in??ten??adjacent??seats??in??the??same??row.??How??many??different??ways??can??they??be??seated??if??each??couple??sits??together???

What??is??the??value??of??8??÷??8?????8??+??8??×??8?????

What??is??the??product??of??the??least??common??multiple??and??the??greatest??common??factor??of??84??and??105?

Kevin??has??twice??as??many??cookies??as??Aidan??and??half??as??many??cookies??as??Beth.??If??Aidan??and??Beth??have??35??cookies??together,??how??many??cookies??does??Kevin??have?

3A??round??birthday??cake??was??divided??into??16??congruent??slices,??and????of??the??cake??

was??eaten.??The??next??day,??five??slices??were??eaten.??How??much??of??the??original??cake??is??left???Express??your??answer??as??a??common??fraction.50.??_____________(ways)51.??_____________52.??_____________53.??_____________(cookies)54.??_____________55.??_____________

56.??_____________

(students)57.??_____________What??is??the??least??of??three??consecutive??integers??whose??product??is??1716?Each??of??the??2898??students??at??Descartes??Middle??School??voted??for??his??or??her??favorite??meal??chosen??from??a??list??of??six??different??meals.??Pia??created??a??circle??graph??to??represent??the??data.??If??a??60-degree??sector??of??the??circle??graph??represents??votes??for??pizza,??how??many??students??voted??for??pizza???

The??cost??of??daily??school??lunch??increased??from??$1.80??to??$2.25.??What??was??the??percent??increase?

When??expressed??as??an??integer,??what??is??the??units??digit??of??2013!???(percent)58.??_____________59.??_____________

Copyright MATHCOUNTS, Inc. 2012. All rights reserved. 2013 Chapter Countdown Round

(dollars)60.??_____________3Sun-Li??sold??candy??bars??for??the??glee??club??for??$0.50??each.??If??she??sold????of??the??candy??bars??that??she??had??and??has??12??candy??bars??left,??how??many??dollars??has??she??

collected??so??far?

61.??_____________

(inches)62.??_____________For??what??value??of??n??is??the??sum??of??the??first??n??positive??integers??equal??to??190?An??isosceles??triangle??with??sides??of??integer??length??has??a??perimeter??of??24??inches.??If??the??ratio??of??two??of??its??sides??is??2:3,??what??is??the??number??of??inches??in??the??length??of??one??of??the??legs?

4g+gIf??g??=??4,??what??is??the??value??of?????4

A??conical??pool??takes??2??hours??to??be??filled??at??a??uniform??rate??to??a??depth??of??6??ft.??How??many??minutes??does??it??take??to??fill??it??to??a??depth??of??3??ft?

For??how??many??integers??x??is??(x?????3)(x??+??4)??<??0?

How??many??diagonals??can??be??drawn??in??a??convex??dodecagon?

Eduardo??is??writing??math??problems.??He??writes??1??problem??on??day??1,??2??problems??on??day??2,??3??problems??on??day??3,??and??so??on.??If??this??pattern??continues,??on??what??day??does??he??write??the??50th??problem?

What??is??the??100th??term??of??the??arithmetic??sequence??3,??11,??19,??27,??…?

Richard??is??thinking??of??three??distinct,??positive??integers.??He??tells??Barbara??their??sum??is??9,??and??he??tells??Lori??that??their??product??is??24.??What??is??the??median??of??Richard’s??three??numbers?

Two??sides??of??a??triangle??measure??9??units??and??11??units.??In??units,??what??is??the??positive??difference??between??the??measures??of??the??smallest??and??the??largest??possible??integral??lengths??of??the??third??side??of??the??triangle?

What??is??the??sum??of??all??positive??integers??from??1??to??30,??inclusive,??that??are??neither??multiples??of??2??nor??perfect??squares?

Copyright MATHCOUNTS, Inc. 2012. All rights reserved. 2013 Chapter Countdown Round63.??_____________(minutes)64.??_____________(integers)65.??_____________(diagonals)66.??_____________(day)67.??_____________68.??_____________69.??_____________(units)70.??_____________71.??_____________

(miles)72.??_____________1In??miles,??how??far??will??Jill??travel??if??she??drives??for??3??hours??at??an??average??speed??of??44??mi/h?

What??is??the??mean??of??the??first??five??triangular??numbers?

Molly??has??eight??U.S.??coins??with??a??total??value??of??78??cents.??She??does??not??have??any??half-dollars.??How??many??dimes??does??Molly??have?

The??domain??of??a??function??f(x)??is??all??real??numbers??and??the??range??of??f(x) is??all??real??numbers??from???1??to??12,??inclusive.??What??is??the??maximum??value??of??g(x)??if??g(x)??=??2f(x –??1)??+??3?

In??an??arithmetic??progression??the??first??term??is??0??and??the??fifth??term??is??5.??What??is??the??third??term???Express??your??answer??as??a??common??fraction.

2xThe??positive??real??numbers??w,??x??and??y??satisfy??the??equation????=??16yw.??If??y??is??tripled??and??w??is??halved,??by??what??percent??must??x??be??increased??so??that??the??new??

values??of??w,??x??and??y??also??satisfy??the??equation?73.??_____________(dimes)74.??_____________75.??_____________76.??_____________(percent)77.??_____________

78.??_____________What??is??the??value??of??6.9??×??1015??÷??(2.3??×??107)??×??7.0??×??10?4???Express??your??answer??in??scientific??notation.

How??many??sides??does??a??regular??polygon??have??if??the??measure??of??an??interior??angle??is??150??degrees?

If??g(x)??=??2x??–??8??and??f(x)??=??3x2??+??17x,??what??is??f(g(3))?(sides)79.??_____________80.??_____________

Copyright MATHCOUNTS, Inc. 2012. All rights reserved. 2013 Chapter Countdown Round

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