Kangourou Sans Fronti`e resMathematics Promotion Society Math Kangaroo in USAMath Kangaroo2012in USAInternational Competition in MathematicsThursday,March15,2012Levels1and2This test consists of24questions on4pages.You have75minutes to complete it.Calculators are not allowed!Please enter your answers on the answer form provided.Please put your name and ID number on the line below.3Point Problems1.How many animals are there in the picture to the right?A)3B)4C)5D)6E)72.Which piecefits in the empty place in the puzzle on the right?A)B)C)D)3.How many legs do these animals have altogether?A)5B)10C)12D)14E)204.Helena wrote the word KANGAROO twice.How many times did she write the letter A?A)1B)2C)3D)4E)65.Luke repeats the same four stickers on astrip. Which is the tenth sticker put down by Luke?A)B)C)D)E)6.On Friday Dan starts to paint the word BANANA.Each day he paints one letter.On what day will he paint the last letter?A)Monday B)Tuesday C)Wednesday D)Thursday E)Friday7.Which of the bolded paths is the longest?A)A B)B C)C D)D E)E8.Katja is in a boat on a lake.Which of the pictures does she see in thelake?A)B)C)D)E) 4Point Problems9.13children are playing hide and seek.One of them is the“seeker.”After a while9children have been found.How many children are still hiding?A)3B)4C)5D)9E)2210.Father hangs the laundry outside on a clothesline.He wants to use as few pins as possible.For3towels he needs 4pins,as shown.How many pins does he need for9towels?A)9B)10C)12D)16E)1811.Today Betty added her age and her sister’s age and obtained10as the sum.What will the sum of their ages be one year from today?A)5B)10C)11D)12E)2012.The clock shows the time when Stephen leaves school.Lunch at school starts3hours before school ends.At what time does lunch start?A)1B)2C)5D)11E)1213.A dragon has3heads.Every time a hero cuts off1head,3new heads grow.The hero cuts1 head offand then he cuts1head offagain.How many heads does the dragon have now?A)4B)5C)6D)7E)814.Stars,clovers,gifts and trees repeat regularly on a game board. Some juice was spilled on the board.As a result some of the pictures can’t be seen(these are the white spaces in the picture).How many stars were on the board before the juice was spilled?A)3B)6C)8D)9E)2015.Eve brings12pieces of candy,Alice brings9pieces of candy and Irene doesn’t bring any candy. They put all the pieces of candy together on a table and divide them equally among themselves. How many pieces of candy does each of the girls get?A)3B)7C)8D)9E)1216.Tim is looking at seven silk paintings on a wall.On the left he sees the dragon and on the right thebutterfly.Which animal is to the left of the tiger and the lion,and to the right of the apricot?A)B)C)D)E) 5Point Problems17.Winnie the Pooh bought4apple pies and Eeyore bought6cheesecakes.They each paid the same amount of money and together they paid24euros.How many euros does1cheesecake cost?A)2B)4C)6D)10E)1218.Sparrow Jack jumps on a fence from one post to another.Each jump takes him1second.He makes 4jumps ahead,then1jump back and again4jumps ahead and1back,and so on.In how many seconds does Jack get from START toFINISH?A)10B)11C)12D)13E)1419.Grandmother made11cookies.She decorated5cookies with raisins and then7cookies with nuts.At least how many cookies were decorated with both raisins and nuts?A)1B)2C)5D)7E)1220.At a school party Dan,Jack and Ben each received a bag with10pieces of candy.Each of the boys ate just1piece of candy and gave1piece of candy to the teacher.How many pieces of candy do they have left altogether?A)8B)10C)24D)27E)3021.What number is covered by theflower?A)1B)2C)3D)4E)5=32435=422.Ann has a lot of these tiles:How many of the following shapes can Ann makeby gluing together two of thesetiles?A)0B)1C)2D)3E)423.In a box there are three boxes,and each one of these boxes contains three smaller boxes.How many boxes are there in total?A)9B)10C)12D)13E)1524.There are coins on the board.We want to have2coins in each column and2coins in each row.How many coins need to be removed?A)0B)1C)2D)3E)4Kangourou Sans Fronti`e res Math Kangaroo in USA Math Kangaroo2014in USAInternational Competition in MathematicsThursday,March20,2014Levels1and2This test consists of24questions on4pages.You have75minutes to complete it.Calculators are not allowed!Please enter your answers on the answer form provided.Please put your name and ID number on the line below.Problems3points each#1.The ladybug will sit on aflower that hasfive petals and three leaves.On which of theflowers below will the ladybug sit?(A)(B)(C)(D)(E)#2.If you start at the arrow and move along the line,in what order do youmeet the shapes?(A) , ,•(B) ,•, (C)•, , (D) , ,•(E) ,•,#3.How many more small gray squares are there than(A)6(B)7(C)8(D)9(E)10#4.Put the animals in order from the smallest to the largest.Give the number of the animal in the middle.(A)1(B)2(C)3(D)4(E)5#5.Ann has twelve of these tiles.She makes a design that is onecontinuous line.Ann starts at the left side of the grid,as shown in the picture.How does the line end on the right side of the grid?(A)(B)(C)(D)(E)#6.Which of the pictures below is the shadow of the girl?(A)(B)(C)(D)(E)#7.A square was made out of25small squares,but some of these small squares are nowmissing.How many small squares are missing?(A)6(B)7(C)8(D)10(E)12#8.How many ducks balance the crocodile?(A)(B)(C)(D)(E)Problems4points each#9.When the ant goes from home following thesearrows:→3,↑3,→3,↑1on the board to the right,it comes tothe ladybug.Which animal will it come to if it goes fromhome following these arrows:→2,↓2,→3,↑3,→2,↑2?(A)(B)(C)(D)(E)#10.The kangaroo is inside how many circles?(A)1(B)2(C)3(D)4(E)5Math Kangaroo 2014March 20,2014Levels 1and 2#11.A square was cut into 4parts as shown in the picture to the right.Whichof the following shapes cannot be made using only these 4parts?(A)(B )(C)(D )(E)#12.Which of the shapes shown below will fit this shape exactly to make a rectangle?(A)(B)(C)(D)(E)#13.Walking from K to O along the lines,pick up the lettersKANGAROO in the correct order.What is the length of the shortestwalk in meters (1m =1meter)?(A )16m (B )17m (C )18m (D )19m (E )20m #14.How many numbers that are greater than 10and less than or equalto 31can be written with only the digits 1,2and 3?You can repeat digits.(A )2(B )4(C )6(D )7(E )8#15.Seven sticks lie on top of each other.Stick 2is atthe bottom.Stick 6is at the top.Which stick is in themiddle?(A )1(B )3(C )4(D )5(E )7#16.How many frogs did the three pelicans catchaltogether?(A )1(B )2(C )4(D )9(E )12Problems 5points each#17.The chess board is damaged.How many black squares are missingon the right side of the line?(A )11(B )12(C )13(D )14(E )15#19.What shouldyou put in the square on the bottomto get a correctdiagram?(A)−38(B )÷8(C )−45(D )×6(E )÷6#20.Put the digits 2,3,4and 5in the squares and calculate the sum to get the largest possible value.What is that value?(A )68(B )77(C )86(D )95(E )97#21.The central cell of the square was removed.We cut the rest of the squareinto identical pieces.Which type of piece is it not possible to get?(A )(B )(C )(D )(E )#22.To get the product of 2×3×15,Bill has to press the keys of his calculator seven times:.Bill wants to multiply all the numbers from 3to 21using his calcu-lator.At least how many times will he press the keys of his calculator?(A )19(B )31(C )37(D )50(E )60#23.Fred has 4red cubes,3blue cubes,2green cubes and 1yellow cube.Hebuilds a tower (see the picture)in such a way that no two adjacent cubes have thesame color.What color is the cube with the question mark?(A )red (B )blue (C )green (D )yellow(E )It is impossible to determine.#24.Cogwheel A turns around completely once.At which place is x now?x C A (A )a (B )b (C )c (D )d (E )eKangourou Sans Fronti`e res Math Kangaroo in USA Math Kangaroo2015in USAInternational Competition in MathematicsThursday,March19,2015This test consists of24questions on4pages.You have75minutes to complete it.Calculators are not allowed!Please enter your answers on the answer form provided.Please put your name and ID number on the line below.Levels1and23points#1.Look closely at these four pictures.Whichfigure is missing from one of the pictures?(A)(B)(C)(D)(E)#2.Find the piece missing from the house on the right.(A)(B)(C)(D)(E)#3.There arefive ladybugs shown to the left.How many spots are there onall the ladybugs together?(A)17(B)18(C)19(D)20(E)21Math Kangaroo 2015March 19,2015Levels 1and 2#4.Which of the following pictures can be rotated so that it will be the same as the picture shown on the right?(A)(B)(C)(D)(E)#5.What does the tower shown to the right look like from above?(A)(B)(C)(D)(E)943728#6.The diagram to the left shows six numbers.What is the sum of thenumbers outside the square?(A )12(B )11(C )23(D )33(E )10#7.Half of a movie lasts half an hour.How long does the whole movie last?(A )15minutes(B )half an hour (C )1hour(D )2hours (E )40minutes #together into five long strips.Which connected strip is the shortest?(A )A(B )B (C )C (D )D (E )E4points#9.There are 11flags on a straight race track.The first flag is at the start,and the last flag is at the finish.The distance between each flag is 4meters.How long is the track?(A )12meters (B )24meters (C )36meters (D )40meters (E )44meters #10.Marko has 9pieces of candy and Tomo has 17pieces of candy.How many pieces of candy does Tomo need to give to Marko so that each boy has the same number of pieces of candy?(A )2(B )3(C )4(D )5(E )6#12.When written as5/5/2015,the date Mayfifth,2015,has three5’s.The next earliest date that will have three5’s is:(A)May tenth,2015(B)Apriltwenty-fifth,2015(C)May twenty-fifth,2015(D)Januaryfifth,2055(E)Mayfifteenth,2015#13.Emil placed the numbers1,2,3,4,and5correctly inthe boxes in the diagram on the right.What number did heplace in the box with the question mark?(A)1(B)2(C)3(D)4(E)5#14.Vera invited13guests to her birthday party.She had2pizzas,and each of them was cut into8 slices.Each person at the party ate one slice of pizza.How many slices of pizza were left over?(A)5(B)4(C)3(D)2(E)1#15.Don has two identical bricks(see picture to the right).Whichfigure can he notbuild using these two bricks?(A)(B)(C)(D)(E)#16.Which piece is missing from the puzzle to the right?(A)(B)(C)(D)(E)5points#17.In one jump,Jake the Kangaroo jumps from one circle to a neighboringcircle along a line,as shown in the picture to the right.He cannot jump intoany circle more than once.He starts at circle S and needs to make exactly4jumps to get to circle F.In how many different ways can Jake do this?(A)3(B)4(C)5(D)6(E)7S F#18.A ship was attacked by pirates.One by one,the pirates climbed a rope to get to the ship.The pirate captain was the eighth pirate to climb,and there were as many pirates in front of him as behind him.How many pirates climbed the rope?(A)7(B)8(C)12(D)15(E)16Math Kangaroo2015March19,2015Levels1and2 #19.For3days,Joy the cat was catching mice.Each day Joy caught2mice more than the previous day.On the third day Joy caught twice as many mice as on thefirst day.In total,how many mice did Joy catch during the three days?(A)12(B)15(C)18(D)20(E)24#20.The numbers3,5,7,8and9were written in the squares of the cross(see thefigure to the right)so that the sum of the numbers in the row is equal to the sum ofthe numbers in the column.Which number was written in the central square?(A)3(B)5(C)7(D)8(E)9#21.My grandmother has a dog named Atos,as well as some ducks,hens and geese.She has40animals altogether.She has four times as many geese as ducks.Atos and the hens make up one half of all her animals.My grandmother has:(A)19hens and5ducks(B)20hens and4ducks(C)19hens and15geese(D)19hens and16geese(E)20hens and16geese#22.One of the six stickers shown below was placed on each of the six faces of a die.The next picture shows the die in two positions.Which picture is on the face opposite the face with the kangaroo sticker?(A)(B)(C)(D)(E)#23.Sylvia,Tara,Una and Wanda went out for dessert.They stood in line one after another.Each one of them ordered one of the following desserts:ice cream,waffle,bun,and cake,and each one ordered a different item.We know that:•Thefirst girl did not buy the ice cream or the waffle.•Una was not last in line,and she bought the cake.•Sylvia,who was standing behind Tara and in front of Una,did not buy the waffle.Which of the following is true?(A)Wanda wasfirst in line.(B)Tara bought the ice cream.(C)Wanda bought the waffle. (D)Una was second in line.(E)Sylvia bought the bun.#24.We left for a summer camp yesterday at4:32PM and got to our destination today at6:11AM. How long did we travel?(A)13hours39minutes(B)14hours39minutes(C)14hours21minutes(D)13hours21minutes(E)2hours21minutes。