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Total questions: 109
Worksheet time: 4hrs 59mins
Islands and bridges
The settlements of the Beavers are divided over different islands. They want to build
bridges, so trading goods will become easier. Beaver Beatrix has made a plan, which you can see below. The islands are represented by dots, the bridges by lines.
The other beavers would prefer a different plan though, on which the islands are
represented by lines and the bridges by dots.
Log Jam
The beavers collected 50 logs on Beaver Island. They want to bring these logs to
their home through the river system. At various points in the river system, they lose a certain number of logs. The beavers begin on Beaver Island (at the left side of the diagram) and wish to get home (which is on the right side of the diagram). On the river there are numbers, which show how many logs the beavers would lose, if the beavers use this river on their route home.
What is the fewest logs the beavers could lose?
20 logs
23 logs
15 logs
19 logs
Mirrored or not?
Sandy and her friend Horatio got new computers last week.
The computers have a built-in camera at the top of the screen.
When Sandy is chatting with her friend, the chatting software has two windows: a big one which is showing Horatio chatting and a small one showing herself chatting. The chatting software has two possible settings for showing the video streams:
"mirror mode" - right eye on the right side of the screen and "picture mode" - right eye on the left side of the screen. Look at this picture of Sandy and Horatio chatting:
Which settings does the chatting software have on Sandy's computer?
Sandy's video stream in picture mode Horatio's video stream in picture mode
Sandy's video stream in picture mode Horatio's video stream in mirror mode
Sandy's video stream in mirror mode Horatio's video stream in picture mode
Sandy's video stream in mirror mode Horatio's video stream in mirror mode
Missing piece
Beaver Bruce has received a secret message sent on a 6 x 6 grid. Unfortunately, part of
the message has been destroyed by a spill of red juice.
This case was foreseen (Bruce spills a lot of juice) and there are additional squares in the message that can help Bruce determine the secret message. Each square in the rightmost column (column 6) is coloured such that the number of black squares in each row is even. Similarly, each square in the bottommost row (row 6) is coloured such that the number of black squares in each column is even. Which of the following images could be the pattern
underneath the red spill?
Neighbourhoods
Neighbourhoods in areas on maps can be presented as a diagram. In such a neighbourhood
diagram each neighbourhood is represented by a node.
A line between two nodes means that the two neighbourhoods share one or more borders.
The diagram on the right shows the connections between seven neighbourhoods in a certain area.
Which of the following maps is described by this diagram?
No Anonymity Anymore
The medical records of patients contain personal data, which should not be made public.
For the publication of a research project, the hospital has made some data public, without
mentioning the names of the patients. The table on the left shows a part of this list.
Because of the upcoming elections, the city with postcode M1 1AA publishes a list with all
constituents at the same time. This table on the right shows the constituents who are born on January 1st.
Thanks to these two tables, you know for sure that one of the persons on the right has a
disease and you also know which disease it is.
What is the name of this person?
George Smiths
Roman Petersons
Eve Miller
Isabele Bourne
Packing Logs
Beatrix has a backpack that holds a maximum of 7 kg of wood. Large 3 kg logs are worth 5 coins each. Medium 2 kg logs are worth 3 coins each. Small 1 kg logs are worth half a coin. How many logs of each size should Beatrix pack in her backpack to maximise the total worth?
One large logs and two medium logs
Two large logs and one small logs
Three medium logs and one small logs
one large logs, one medium logs, and three small logs
Planting Flowers
A big and a small beaver are planting flowers in the garden. The small beaver has shorter arms and legs than the big beaver. Therefore, his steps are smaller and the flowers he plants are closer to each other.
The beavers start back to back and are looking in opposite directions.
They both follow these directions:
Repeat two times:
Plant a flower on your right
Go one step forward
Plant a flower on your left
Go one step forward.
#
What will the garden look like after this?
Playing Cards
The beavers want to make playing cards out of five pieces of cardboard.
The pieces of cardboard have different sizes: A4, A5, A6, A7 and A8.
A4 is twice as big as A5, A5 is twice as big as A6 and so on.
They need 12 playing cards of size A8 and they don't want to waste any paper.
Which pieces of cardboard should they use?
A4 and A5
A6 and A7
A5 And A6
It is not possible
Programmed Robot
A robot is programmed to find a target (the green field marked with X) on a map of square
fields. The robot has its movements programmed as follows:
• The robot moves straight forward until it reaches an obstacle (black field) or the edge of the map.
• When reaching an obstacle or the edge of the map, the robot turns right by 90°.
• When the robot moves out of a field, the field becomes a black obstacle.
The arrows on the maps below show the starting position as well as the starting direction of the robot.
On which map does the robot NOT eventually reach the target (green field marked with X)?
RGB Grid
The RGB colour model is often used in electronics and computing. Squares (often called pixels) are coloured either red, green or blue.
A pattern is used to fully colour an 8 x 11 grid. Part of this colouring is shown below. The pattern is alternating bluegreen in the first row, alternating green-red in the second row, alternating blue-green in the third row, etc.
What coloured squares fit the pattern in the bottom right corner of the grid?
Rivers and Dams
In the Beaver valley, a river splits several times on its way from the source to a nearby lake. Using smartly built dams, the beavers can regulate the amount of water in each arm
of the river for maximum efficiency.
At a fork, the amount of water is divided over the two arms of the river. In the image above,
the amount of water that can flow through the different arms (arrows) per second is shown.
How should the beavers regulate the arms X, Y and Z to get as much water in the
river per second as possible?
X=1, Y=0, Z=5
X=1, Y=2, Z=3
X=2, Y=2, Z=2
X=4, Y=3, Z=2
Sailing Home
Sailor Beaver is going home. The flag marks the spot where he must drop anchor.
It is getting dark so he wants to get there as quickly as possible by taking the shortest course home but he does not want to crash into the islands. He takes out his compass and plots the course home.
He must follow the shipping lanes, shown as broken lines on the map and he may change direction only on the black dots. He writes down the course he must follow. For example “2N” means go two black dots North, "3SW;2S" means go three black dots South West. Change direction, go 2 black dots South.
His boat is on a black dot as shown on the map. Which instructions will lead the ship to its goal as fast as possible without crashing into an island?
4NW; 1W
2NW; 2N; 1NW; 1W; 15W
2NW; 2W; 2N; 1W
2NW; 2W; 1NW; 1N
Short story
Here's a short story for you:
"On his way home, Hans finds a cat in front of his house. Because it's raining cats and
dogs, he decides to take it inside. The cat gets comfortable at the chimney and falls
asleep. When Hans' mother arrives home, she accidentally bumps into the cat. The cat
gets scared and scratches her leg."
This story can be summarised using abbreviations. Everything that can't be shortened, is left out.
take(H,C); sleep(C); scratch(C,M)
sleep(C); take(H,C); scratch(H,M)
take(C); sleep(H,C); scratch(M,C)
take(C); sleep(C); scratch(H,H)
Sorting tree trunks
Robot Alan is sorting tree trunks. Unfortunately, we forgot how he was programmed exactly.
On the ground, there are several tree trunks of different lengths.
Alan chooses a tree trunk following a certain formula, lays it on top of the ramp and lets it roll down.
He repeats this, until there are no more tree trunks on the ground.
See the result:
Which formula does Alan use to decide in which order the tree trunks have to be placed on the ramp?
Take the longest tree trunk
Take the shortest tree trunk
Take the second longest tree trunk. If only one tree trunk remain, take that one
Take the second shortest tree trunk. If only one tree trunk left, take that one
Beatrix has a backpack that holds a maximum of 7 kg of wood. Large 3 kg logs are worth 5 coins each. Medium 2 kg logs are worth 3 coins each. Small 1 kg logs are worth half a coin.
How many logs of each size should Beatrix pack in her backpack to maximise the total worth?
One large log and two medium logs
Two large logs and one small log
Three medium logs and one small log
one large log, two medium logs and one small log
Stage Coaches
In the Wild West, where the cowboy beavers live, the Bebras Stage Coach Company built a network of stage coach routes between eight settlements.
In the plan of transportation, you can see at which days of the week the stage coaches will depart at the different settlements. A stage coach departs early in the morning and arrives at the next settlement in the evening of the same day.
What is the fastest way to get a package from settlement 1 to settlement 8?
1-2-5-8
1-3-6-8
1-2-6-8
1-4-7-8
Turning numbers
In the game of "Turning Numbers" you can scramble the numbers 1 to 9.
At the start of every game, the numbers are orientated as shown in the picture on the left.
When you push button A, B, C or D, the numbers around make a quarter turn.
For example: when you push button A, the numbers will be placed as shown in the image on the right side.
You start a new round and push the following buttons:
D, C, B, B.
Where will the number 4 be at the end?
Turning Glasses
There are five drinking glasses on the table. One of them is turned upside down.
In this game, you have to get all glasses upright again. But: you have to turn exactly three glasses every turn.
How many turns do you need at least to get all the glasses standing upright?
2 turns
5 turns
3 turns
impossible
Vigenère encryption
Beavers Beatrix and Bruce encrypt their private messages, so others cannot read them. They use the same key for encrypting and decrypting the messages.
The key they use is CAB.
Beatrix encrypts a message to Bruce:
Because the C is the third letter in the alphabet, the first letter in the message (W) is replaced by the letter which comes three places after it in the alphabet (Z). Because the A is the first letter in the alphabet, the second letter in the message (H) is replaced by the letter which comes one place after it in the alphabet (I). And so on, until the complete message has been encrypted.
Bruce
answers: DUGOFXHO
When do they meet?
(a)
Watering a tree
The beaver has made a pipe system for watering his apple tree.
Valves 1, 2, 3 and 4 can be opened or closed independently.
In which case does the water reach the
apple tree?
Valve 1 closed 2 opened 3 closed 4 closed
Valve 1 opened 2 closed 3 closed 4 opened
Valve 1 opened 2 opened 3 closed 4 closed
Valve 1 closed 2 closed 3 closed 4 opened
Wood streams
In forest (A) is an area where the beavers fell trees for their dams. They transport the tree
trunks to their new project - the biggest dam of all times (D) - through an infrastructure of
channels. The arrows represent the channels, the dots are points where the water splits up or comes together. Every channel has a restricted capacity. The numbers next to the channels show how many tree trunks can be transported through the channels in one minute.
How many tree trunks can be transported from A to D at most in one minute?
(a)
The Wrong Hat
Anna, Bert, David and Emily Beaver have two rules for choosing what clothes to wear:
• Normally, they wear a hat of their favourite colour.
• They wear a shirt with a different colour than the hat.
One day, they change hats, just for fun. Now they all wear a hat of another colour than
their favourite one.
Which beaver owns the green hat?
(a)
Tic tac toe
You are playing a game of tic-tac-toe with your friend. First your friend has to place an 'O', then
you place your 'X'. You continue taking turns in this way. The player who places their three
marks in a horizontal, vertical or diagonal line wins.
It is your turn to put an 'X' in the grid below:
Click on the grid to place your 'X’ so that you have the best chance of winning.
(a)
Toothbrushes
It is time for bed! Every beaver should have a toothbrush that matches their size. But look at the picture to see what has happened. “Not so fast!” sighs mother beaver. “Eve and Chad, swap your brushes! Ann and Chad, you too!” But then she does not know how to continue.
Which two beavers still need to swap their toothbrushes so that all the beavers have
the correct brushes?
Ben and Chad
Ann and Eve
Ben and Dan
Nobody
Storm proof network
On a small green island a network of mobile phone towers is setup. Every tower covers a circular area of the island. When the coverage area of two towers overlaps the towers are said to be directly connected. Towers can also be indirectly connected if there is a chain of directly connected towers between the two towers.
The operators want to make the network of towers Storm Proof. This means that even if one tower breaks down all other towers must still be connected, either directly or indirectly. Which system shown below is a way to create a storm proof network on the island?
Space maze
Some space explorers landed on an empty planet. From their ship they could see a maze with
an unknown golden object in it. The explorers dropped their robot into the maze hoping it could take a closer look at the unknown object. Unfortunately the robot broke during the fall and can now only send and receive garbled instruction about where to go. The robot suggests four possible directions it can go. Even though the words in the instructions are garbled, there are still only four different words, each indicating north, west, east or south.
When following the instructions the robot will move into an adjacent square as instructed.
Which instructions should the explorers send the robot in order for it to reach the
golden object?
Ha' poS poS Ha' Ha' nIH
Ha' poS poS Ha' nIH Ha'
Ha' Ha' poS Ha'
Ha' poS nIH vI'ogh Ha' poS
Alice and Tom are playing a game of "True or False" on their colourful, magnetic whiteboard in their classroom. Alice has stuck seven different magnetic shapes on the board. She then makes four statements about the shape, colour, size and position of the shapes. Only one statement is allowed to be true. Tom must figure out which one it is. Which of the following statements is true?
There are two shapes X and Y, so that X is dark blue and Y is pale yellow and X is higher than Y.
For all pairs of shapes X and Y, if X is a square and Y is a circle, then X is higher than Y.
For all pairs of shapes X and Y, if X is small and Y is big, then X is to the right of Y.
For all pairs of shapes X and Y, if X if light yellow and Y is dark blue, then X is below Y.
Height game
Young beavers Amy, Beavy, Cuttree, Diggy and Eary, want to play a game with you. They all stand in a line. Then they each count how many beavers are taller than they are both infront of them and behind. They give you the results on a slip of paper: In what order are the beavers standing?
Diggy, Cuttree, Amy, Beavy, Eary
Amy, Cuttree, Diggy, Eary, Beavy
Diggy, Amy, Cuttree, Beavy, Eary
Diggy, Amy, Eary, Beavy, Cuttree
Meeting point
Three friends Anne, Bernie and Clara live in a city with an underground train system. The map of the system below shows the stations and connections between the stations. The map also indicates how many minutes each connection takes. Anne lives next to Ashbourne station, Bernie's nearest station is Best, and Clara's is Corner. They wish to select a station for a meeting. None of the friends should take more than 15 minutes of travel to reach the meeting point.
Which stations qualify as possible meeting points?
Ashbourne and Corner
Ashbourne and Park
Park and Outbound
Park and Upleft
JOANA COLOCOU 1 TIJOLO EM UM PRATO DA BALANÇA E NO OUTRO PRATO COLOCOU MEIO TIJOLO JUNTO COM 1 QUILO. A BALANÇA FICOU EQUILIBRADA, COMO MOSTRA A FIGURA. QUANTO PESA UM TIJOLO INTEIRO?
MEIO QUILO
1 QUILO
1 QUILO E MEIO
2 QUILOS
4 QUILOS
QUANTOS CONJUNTOS COM 1 LÁPIS, 1 BORRACHA E 1 APONTADOR PODEM SER FORMADOS COM OS OBJETOS DA FIGURA?
8
7
6
5
4
QUAL É A DIFERENÇA ENTRE OS COMPRIMENTOS DO LÁPIS E DO PINCEL?
11 CENTÍMETROS
5 CENTÍMETROS
3 CENTÍMETROS
2 CENTÍMETROS
1 CENTÍMETRO
ANDRÉ JOGOU UM DADO TRÊS VEZES SEGUIDAS E CONTOU 17 PONTOS NAS FACES QUE FICARAM VIRADAS PARA CIMA. QUAL DAS SEGUINTES FACES APARECEU ENTRE AS VIRADAS PARA CIMA?
Face com 1 ponto
Face com 2 pontos
Face com 3 pontos
Face com 4 pontos
Face com 5 pontos
NA FIGURA, VEMOS UMA MESMA LOCOMOTIVA PUXANDO 2 OU 3 VAGÕES IGUAIS. O PRIMEIRO TREM TEM 34 METROS DE COMPRIMENTO NO TOTAL E O SEGUNDO TREM TEM 45 METROS DE COMPRIMENTO NO TOTAL. QUAL É O COMPRIMENTO DA LOCOMOTIVA?
10 METROS
11 METROS
12 METROS
13 METROS
14 METROS
UMA FÁBRICA DE BRINQUEDOS PRODUZIA BOLAS PEQUENAS, MÉDIAS E GRANDES, NAS CORES VERDE, AZUL E AMARELA. ELA DEIXOU DE FABRICAR BOLAS VERDES PEQUENAS E BOLAS AMARELAS DE TODOS OS TAMANHOS. QUANTOS TIPOS DIFERENTES DE BOLAS ELA PRODUZ AGORA?
4
5
6
7
8
ABEL, BETO, CARLOS, DUDU E EMANUEL DISPUTARAM UMA CORRIDA. ABEL CHEGOU EM 2º LUGAR, NEM CARLOS NEM DUDU CHEGARAM EM 3º LUGAR, E BETO CHEGOU LOGO ATRÁS DE EMANUEL. ALÉM DISSO, NÃO HOUVE EMPATES. EM QUE LUGAR EMANUEL CHEGOU?
1º
2º
3º
4º
5º
Num jantar em família foi distribuída fruta para a sobremesa. 1 maçã dava para 2 pessoas. Quantas maças foram precisas para servir 18 pessoas?
15
09
17
10
Miguel mede 1,74 metros, Luis 1,90 centímetros e José faltam 12 centímetros para medir 2 metros. Qual dos três é o mais BAIXO?
LUIZ
MIGUEL
JOSÉ
PAULO
Cinco esquilos A, B, C, D e E estão sentados em fila nas posições mostradas. Em dado momento, os 5 correm para pegar a noz que cada um tem mais perto, e assim que a pegam, vão pegar a próxima noz. Qual dos esquilos consegue coletar 2 nozes?
A
B
C
D
Dentro de quantos círculos está o canguru?
2
4
5
3
Numa apresentação da escola Elite há 24 cadeiras e 33 pessoas. Quantas pessoas ficaram de pé?
10
13
09
12
Qual é a metade de 378 casas?
170
189
300
258
Marque a alternativa com os números MENORES que 478:
378 - 463 - 498 - 370
378 - 487 - 498 - 376
297 - 945 - 470 - 679
467 - 203 - 354 - 470
A Alice desenhou um caminho que liga as joaninhas da figura ao lado, seguindo a ordem crescente do número de pintas das suas asas. Se ela começou na joaninha com uma só pinta, qual foi a figura que ela desenhou?
Tiago empilhou várias argolas e obteve o brinquedo representado na figura ao lado. Quantas argolas ele vê se olhar para o brinquedo de cima?
6
3
4
5
A Uxa, uma bruxa simpática, tem 5 vassouras espalhadas na sua garagem, como se pode ver na figura abaixo. Se ela retirar as vassouras uma a uma sem mexer nas restantes, que vassoura retira em último lugar?
A
B
C
D
E
Qual é a forma obtida quando as cores da figura acima são trocadas?
O caminho da casa de Ana à casa de Bela é de 16 km. O caminho da casa de Bela à casa de Caio é de 20 km. Do cruzamento para a casa de Bela, o caminho tem 9 km. Qual é a distância da casa de Ana à casa de Caio?
8 km
9 km
17 km
18 km
Marisol tem 9 retângulos iguais, com os quais ela forma o maior retângulo mostrado na figura. Se o lado mais longo de cada um dos retângulos pequenos é de 10 cm, qual é o perímetro do retângulo maior?
48
76
80
90
Na sequência a seguir determine o número de esferas que devem aparecer na figura 5.
15
20
25
30
A soma dos pontos nas faces opostas de um dado é igual a 7. Qual das seguintes figuras mostra o dado?
Qual figura mostra uma parte deste colar?
Cada um dos blocos abaixo foi feito colando quatro cubos do mesmo tamanho. Os blocos foram pintados de azul. Em qual dos blocos a área pintada foi a menor?
Mamãe Canguru e seu filhinho Sagu pesam, juntos, 60 quilogramas. A mamãe Canguru, sozinha, pesa 52 quilogramas. Quanto quilogramas pesa Sagu?
4
8
12
32
5. Pelo menos quantos cangurus devem ir
de um parque a outro de modo que os dois
parques fiquem com o mesmo número de
cangurus?
4
5
6
8
Tião pinta de azul os quadrados do tabuleiro acima se o resultado da conta dentro deles é 20. Como a pintura do tabuleiro irá ficar?
20 × 19 + 20 + 19 =
389
399
409
419
429
Um trenzinho de brinquedo leva exatamente 1 minuto e 11 segundos para dar uma
volta completa no circuito. Quanto tempo levará para dar seis voltas?
6 minutos e 56 segundos
7 minutos e 16 segundos
7 minutos e 36 segundos
7 minutos e 6 segundos
7 minutos e 26 segundos
Um barbeiro quer escrever a palavra CORTE num quadro de tal modo que o cliente,
olhando no espelho, leia a palavra corretamente. Como o barbeiro deve escrever a
palavra no quadro?
Quantas são as diferentes somas de pontos que você obtém quando lança três dados
simultaneamente?
14
15
16
17
18
Um parque tem cinco portões. Mônica quer entrar por um deles e sair por outro. De
quantas maneiras ela pode entrar e sair do parque?
25
20
16
15
10
Cada quadrado unitário a seguir tem uma certa parte do seu interior pintada de preto.
Qual deles tem a maior área pintada de preto?
Em cada um de três cartões foi escrito um número de cinco
algarismos, conforme mostrado na figura. Três desses alga-
rismos estão cobertos. A soma dos três números escritos é
57263. Quais algarismos estão cobertos?
0, 2 e 2
1, 2 e 9
2, 4 e 9
2, 7 e 8
5, 7 e 8
The number of square units that covers a closed figure is...
Area
Perimenter
square
relative size
A change from one measurement unit to another measurement unit without changing the amount or value...
relative size
conversion
perimeter
area
Lines that meet or cross at a point...
perpendicular lines
parallel lines
intersecting lines
length
How long something is from one point to another...
width
perimeter
line
length
a set of points that form a straight path that goes in opposite directions without ending...
line
width
perimeter
intersecting lines
lines in the same plane, never intersect, and are always the same distance apart...
perpendicular lines
parallel lines
perimeter
line
a measurement of the distance around the outer edge of a figure...
line
parallel lines
area
perimeter
lines that intersect at right angles to each other to form square corners...
perpendicular lines
parallel lines
perimeter
lines
size in relation to a measure...
conversion
area
line
relative size
the distance from side to side...
length
width
perimeter
line
Name the denominator in the fraction.
5
1
8
6
What fraction is the pizza cut into?
halves
fourths
eighths
Which figure shows one-half shaded?
Which figure shows one whole shaded?
2+2−2 x 0
2
6
4
0
3, 5, 2, 5, 4, 7, 1, 0, 6, 4, 8, 5, 3, 2, 4, 5, 9.
How many times were 6-8 goals scored?
5 x 3 =
12
15
8
9
If I have 15 pencils, and I give 3 to my friends. How many will I have left?
45
10
12
30
If you have 8 candy bars, and your mom gives you 6 more, how many will you have?
14
2
48
15
Abu found 19 durians and Mira found 21 durians. How many durians did they find altogether?
30
40
20
2
What is the difference ::
−2.17 + 0.8−1.37
1.37
13.7
0.137
Sally bought 3 nasi lemak and 2 tea for RM10.45.
Jason bought 4 nasi lemak and 3 tea for RM14.30.
How much would 1 nasi lemak and1 tea cost?
RM1.98
RM2.09
RM3.85
RM4.07
52 + 3
25
28
29
30
32 + 5
9
10
11
14
62 − 6
6
36
30
32
72 + 6
55
41
49
56
23
6
7
8
9
5 + 42
28
23
13
21
32+22
18
14
13
16
43
16
64
74
46
33
28
27
26
29
100
10
1
9
8
51+ 40
6
7
2
9
52+3
28
26
29
30
3+23
12
6
8
11
120+2
5
9
14
3
92−1
81
82
80
70
