加拿大国际袋鼠数学竞赛试题 及答案-2018年_图文

INTERNATIONAL CONTEST-GAME

MATH KANGAROO

CANADA, 2018

INSTRUCTIONS

GRADE 1-2

have 45 minutes to solve 18 multiple choice problems. For each

problem, circle only one of the proposed five choices. If you circle more

than one choice, your response will be marked as wrong.

your answers in the response form. Remember that this is the only

sheet that is marked, so make sure you have all your answers transferred

to the response form before giving it back to the contest supervisor.

problems are arranged in three groups. A correct answer of the first 6

problems is worth 3 points. A correct answer of the problems 7-12 is worth

4 points. A correct answer of the problems 13-18 is worth 5 points. For

each incorrect answer, one point is deducted from your score. Each

unanswered question is worth 0 points. To avoid negative scores, you start

from 18 points. The maximum score possible is 90.

use of external material or aid of any kind is not permitted.

figures are not drawn to scale. They should be used only for illustration

purposes.

er, you have about 2 to 3 minutes for each problem; hence, if a

problem appears to be too difficult, save it for later and move on to another

problem.

the end of the allotted time, please give the response form to the

contest supervisor.

not forget to pick up your Certificate of Participation on your way out!

Good luck!

Canadian Math Kangaroo Contest team

Grade 1-2

2018

Canadian Math Kangaroo Contest

Part A: Each correct answer is worth 3 points

shape cannot be formed using and ?

(A) (B) (C) (D) (E)

least how many 4-ray stars like thisare glued together to

make this shape

(A) 5

3.

(B) 6

?

(C) 7 (D) 8 (E) 9

This pizza was divided into equal slices.

How many slices are missing?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Page 1

Grade 1-2

4.

2018

How many kangaroos must be moved from one park to the other in order to

get the same number of kangaroos in each park?

(A) 4 (B) 5 (C) 6 (D) 8 (E) 9

of these ladybugs has to fly away so that the rest of them have 20

dots in total?

(A) (B) (C) (D) (E)

builds towers in the following pattern

Which one will be the tower number 6?

(A) (B) (C) (D) (E)

Page 2

Grade 1-2

Part B: Each correct answer is worth 4 points

7. If ◊ + ◊ = 4 and ∆ + ∆ + ∆ = 9, what is the value of ◊ + ∆ = ?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

2018

8. Lisa has 4 pieces , but she only needs 3 for

completing her puzzle frame . Which piece will be left over?

(A)

9.

(B) (C) (D) (E)

or

How many right hands are in this picture?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

10. The dog went to its food following a path. In total it made 3 right turns and

2 left turns. Which path did the dog follow?

(A) (B) (C)

(D) (E)

Grade 1-2

11. What number is in the box marked \"?\" ?

2018

(A) 6 (B) 13 (C) 24 (D) 29 (E) Some other number

12. Charles cut a rope in three equal pieces and then made some equal knots

with them. Which figure correctly shows the three pieces with the knots?

(A) (B)

(C) (D)

(E)

Part C: Each correct answer is worth 5 points

many circles and how many squares are covered by the blot in the

picture?

(A) 1 circle and 3 squares

(B) 2 circles and 1 square

(C) 3 circles and 1 square

(D) 1 circles and 2 squares

(E) 2 circles and 2 squares

Grade 1-2

shoots three arrows at a target.

On her first try, she gets 6 points

and the arrows land like this:

2018

6 points

On her second try, she gets 8 points

and the arrows land like this:

8 points

On her third try, the arrows land

like this:

How many points will she get the third time?

(A) 8 (B) 10 (C) 12 (D) 14

? points

(E) 16

many different numbers greater than 10 and smaller than 25 with

distinct digits can we make by using any two of the digits 2, 0, 1, and 8?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

had some sticks of length 5 cm and width 1 cm

With the sticks he constructed the fence below.

.

length

What is the length of the fence?

(A) 20 cm (B) 21 cm (C) 22 cm (D) 23 cm (E) 25 cm

Page 5

Grade 1-2

road from Anna\'s house to Mary\'s house is 16 km long.

The road from Mary\'s house to John\'s house is 20 km long.

The road from the crossroad to Mary\'s house is 9 km long.

2018

How long is the road from Anna’s house to John\'s house?

(A) 7 km (B) 9 km (C) 11 km (D) 16 km (E) 18 km

are four ladybugs on a 4×4 board. Two are asleep and do not move.

The other two ladybugs move one square every minute (up, down, left, or

right). Here are pictures of the board for the first four minutes:

Minute 1 Minute 2 Minute 3 Minute 4

Which of these is a picture of the fifth minute (Minute 5)?

(A) (B) (C) (D) (E)

Page 6

International Contest-Game

Math Kangaroo Canada, 2018

Answer Key

Grade 1-2

1

2

3

4

5

6

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

7

8

9

10

11

12

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

13

14

15

16

17

18

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

INTERNATIONAL CONTEST-GAME

MATH KANGAROO

CANADA, 2018

INSTRUCTIONS

GRADE 3-4

have 60 minutes to solve 24 multiple choice problems. For each problem,

circle only one of the proposed five choices. If you circle more than one choice,

your response will be marked as wrong.

your answers in the response form. Remember that this is the only sheet

that is marked, so make sure you have all your answers transferred to the

response form before giving it back to the contest supervisor.

problems are arranged in three groups. A correct answer of the first 8

problems is worth 3 points. A correct answer of the problems 9-16 is worth 4

points. A correct answer of the problems 17-24 is worth 5 points. For each

incorrect answer, one point is deducted from your score. Each unanswered

question is worth 0 points. To avoid negative scores, you start from 24 points. The

maximum score possible is 120.

use of external material or aid of any kind is not permitted.

figures are not drawn to scale. They should be used only for illustration

purposes.

er, you have about 2 to 3 minutes for each problem; hence, if a problem

appears to be too difficult, save it for later and move on to another problem.

the end of the allotted time, please give the response form to the contest

supervisor.

not forget to pick up your Certificate of Participation on your way out!

Good luck!

Canadian Math Kangaroo Contest team

Grade 3-4

2018

Canadian Math Kangaroo Contest

Part A: Each correct answer is worth

3 points

has 10 rubber stamps. Each stamp has one of the digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

She prints the date of St. Patrick’s Day 2018:

1 7

0

3201

8

(E) 10

How many different stamps does she use?

(A) 5 (B) 6 (C) 7 (D) 9

picture shows three flying arrows and nine fixed

balloons. When an arrow hits a balloon, it bursts,

and the arrow flies further in the same direction.

How many balloons will be hit by the arrows?

(A) 2

(D) 5

3.

(B) 3

(E) 6

(C) 4

Susan is six years old. Her sister is one year younger, and her brother is one year

older. What is the sum of the ages of the three siblings?

(A) 10 (B) 15 (C) 18 (D) 21 (E) 30

is a picture of Sophie the ladybug

the ladybugs below is not Sophie?

. She turns around. Which picture of

(A)(B)(C)(D)(E)

folds a sheet of paper in half. Then she cuts a piece out of it

she see when she unfolds the paper?

. What will

(A)(B)(C) (D)(E)

Page 1

Grade 3-4

6.A table is set for 8 people.

2018

How many settings have the fork to the left of the plate and the knife to the right of

the plate?

(A) 5

7.

(B) 4 (C) 6 (D) 2 (E) 3

Emily added two 2-digit numbers correctly on paper. Then she painted out two cells,

as shown below.

What is the sum of two digits in the painted cells?

(A) 5

8.

(B) 7 (C) 8 (D) 9 (E) 13

First, Diana scores 12 points in total with three arrows. On her second turn she

scores 15 points.

12 points

(A) 18 (B) 19 (C) 20

15 points

(D) 21

? points

(E) 22

How many points does she score on her third turn?

Part

B: Each correct answer is worth

4 points

many different numbers greater than 12 and smaller than 58 with distinct digits

can we make by using any two of the digits 0, 1, 2, 5, and 8?

(A) 3 (B) 5 (C) 7 (D) 8 (E) 9

Page 2

Grade 3-4

o makes designs using tiles like this .

2018

How many of the following five designs can he make?

(A) 1 (B) 2 (C) 3 (D) 4

,

(E) 5

, appears exactly once in every of these five figures ,, ,

column and every row of the given table.

Which figure must we put in the cell with the question mark?

(A) (B) (C) (D) (E)

glues 10 cubes together to make the structure shown.

He paints the whole structure, even the bottom.

How many cubes are painted on exactly four of their faces?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

. opposite faces of a cube are identical, being dark, bright or patterned

Which picture below is the unfolded net of this cube?

(A)(B)(C)(D)(E)

Page 3

Grade 3-4

cuts two types of pieces out of grid paper.

2018

What is the smallest number of pieces identical to the ones shown that Tom needs to

build the boat in the picture?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

rooms in Kanga\'s house are numbered. Baby Roo enters

the main door, passes through some rooms and leaves the

house. The numbers of the rooms that he visits are always

increasing. Through which door does he leave the house?

(A) A (B) B (C) C (D) D (E) E

rabbit had 20 carrots. She ate two carrots every day. She ate the twelfth carrot

on Wednesday. On which day did she start eating the carrots?

(A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday

Part C: Each correct answer is worth

5 points

belt shown in the drawing can be fastened in five ways.

How much longer is the belt fastened in one hole than the belt fastened in all five

holes?

(A) 4 cm (B) 8 cm (C) 10 cm (D) 16 cm (E) 20 cm

Page 4

Grade 3-4

2018

an ancient writing the symbolsrepresent the

numbers 1, 2, 3, 4, and 5. Nobody knows which symbol represents which number.

We know that

Which symbol represents the number 3?

(A) (B) (C) (D) (E)

19.A stained-glass tile is flipped along the black line. The figure shows the tile after the

first flip.

What will the stained-glass tile look like after the third flip (at the far right)?

(A)(B)(C)(D)(E)

large rectangle is made up of squares of varied sizes. The three smallest squares

each have an area of 1, as shown.

What is the area of the largest square?

(A) 81 (B) 100 (C) 110 (D) 121 (E) 144

Page 5

Grade 3-4

2018

ducklings walk behind the mother duck in a row from the oldest to the youngest

like this: Dina and Becca walk right one after the other, Mingo walks behind Lisa but

in front of Becca, Becca walks directly in front of Pip. What is the name of the

youngest duckling?

(A) Dina (B) Pip (C) Becca (D) Lisa (E) Mingo

balls each weigh 10, 20, 30 and 40 grams. Which ball weighs 30 grams?

(A) A (B) B (C) C (D) D (E) it could be A or B

wants to write the numbers from 1 to 7 in the grid shown.

Two consecutive numbers cannot be written in two neighbouring

cells. Neighbouring cells meet at the edge or at a corner. What

numbers can she write in the cell marked with a question mark?

(A) all seven numbers (B) only odd numbers

(C) only even numbers (D) only number 4

(E) only the numbers 1 or 7

?

distance from Anna\'s to Mary\'s house is 16 kilometers along the shown road.

The distance from Mary\'s to Nick\'s house is 20 kilometers.

The distance from Nick\'s to John\'s house is 19 kilometers.

How far is Anna\'s house from John\'s?

(A) 15 (B) 16 (C) 18 (D) 19 (E) 20

Page 6

International Contest-Game

Math Kangaroo Canada, 2018

Answer Key

Grade 3-4

1

2

3

4

5

6

7

8

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

9

10

11

12

13

14

15

16

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

17

18

19

20

21

22

23

24

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

INTERNATIONAL CONTEST-GAME

MATH KANGAROO

CANADA, 2018

INSTRUCTIONS

GRADE 5-12

have 75 minutes to solve 30 multiple choice problems. For each

problem, circle only one of the proposed five choices. If you circle more

than one choice, your response will be marked as wrong.

your answers in the response form. Remember that this is the

only sheet that is marked, so make sure you have all your answers

transferred to that form before giving it back to the contest supervisor.

problems are arranged in three groups. A correct answer of the first

10 problems is worth 3 points. A correct answer of problems 11 -20 is

worth 4 points. A correct answer of problems 21-30 is worth 5 points. For

each incorrect answer, one point is deducted from your score. Each

unanswered question is worth 0 points. To avoid negative scores, you

start from 30 points. The maximum score possible is 150.

use of external material or aid of any kind is not permitted.

figures are not drawn to scale. They should be used only for

illustration purposes.

er, you have about 2 to 3 minutes for each problem; hence, if a

problem appears to be too difficult, save it for later and move on to

another problem.

the end of the allotted time, please give the response form to the

contest supervisor.

not forget to pick up your Certificate of Participation on your way out!

Good luck!

Canadian Math Kangaroo Contest team

Grade 5-6

2018

Canadian Math Kangaroo Contest

Part A: Each correct answer is worth 3 points

drawing shows 3flying arrows and 9fixed balloons. When

an arrow hits a balloon, it bursts, and the arrow flies further in

the same direction. How many balloons will not be hit by

arrows?

(A) 3 (B) 2(C) 6

(D) 5(E) 4

The image shows a structure made of three objects.

What does Peter see if he looks at the structure from above?

2.

(A)

3.

(B)(C) (D) (E)

Diana played darts throwing arrows toward a target with three sections. First she got 14 points with two

arrows on the target. The second time she got 16 points. How many points did she get the third time?

14 points

(A) 17

4.

(B) 18 (C) 19

16 points

(D) 20 (E) 22

?

A garden is divided into identical squares. A fast snail and a slow snail move along the perimeter of the

garden starting simultaneously from the corner S but in different directions. The slow snail moves at the

speed of 1 metre per hour (1 m/h) and the fast one at 2 metres per hour (2 m/h).

At what point will the two snails meet?

A B C

1 m/h

(A) A (B) B

2 m/h

(C) C

S

E

(D) D (E) E

D

Page 1

Grade 5-6

5. In which of the four squares is the fraction of the black area the largest?

2018

(A) A

6.

(B) B (C) C (D) D (E) they are all the same

A star is made out of four equilateral triangles and a square. The perimeter of the

square is 36 cm. What is the perimeter of the star?

(A) 144 cm (B) 120 cm (C) 104 cm (D) 90 cm (E) 72 cm

From the list 3, 5, 2, 6, 1, 4, 7 Masha chose 3 different numbers whose sum is 8. From the same list Dasha

chose 3 different numbers whose sum is 7. How many common numbers have been chosen by both girls?

(A) none (B) 1 (C) 2 (D) 3 (E) impossible to determine

7.

move a bead along a piece of wire. What shall we see when the bead

comes to the end of the wire?

(A)

(D)

(B)

(E)

(C)

9. There are 3squares in the figure. The side length of the smallest square is 6 cm.

What is the side length of the biggest square?

(A) 8 (B) 10 (C) 12

(D) 14 (E) 16

the following figure, the circles are light bulbs connected to some other light

bulbs. Initially, all light bulbs are off. When you touch a light bulb, this light bulb

and all its neighbours (e.g., the light bulbs connected to it) are lit.

At least how many light bulbs do you have to touch to turn on all the light bulbs?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

Grade 5-6

Part B: Each correct answer is worth 4 points

square contains one of the numbers 1, 2, 3, 4, or 5, so that both of the

calculations following the arrows are correct. A number may be used more

than once. What number goes into the box with the question mark?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

2018

12. Nine cars arrive at a crossroads and drive off as indicated by the arrows.

Which figure shows these cars after leaving the crossroads?

(A)

13.

(B) (C) (D) (E)

The faces of a cube are painted black, white or grey so that opposite faces are of different colour. Which of

the following is not a possible net of this cube?

(A)

14.

(B) (C) (D) (E)

In a box there are many one-euro, two-euro and five-euro coins. A dispenser draws coins out of the box –

one at a time, and stops when three identical coins are taken out. What is the largest possible amount that

can be withdrawn?

(A) 24 (B) 23 (C) 22 (D) 21 (E) 15

Two girls, Eva and Olga and three boys, Adam, Isaac and Urban play with a ball. When a girl has the ball, she

throws it to the other girl or to a boy. When a boy has the ball, he throws it to another boy but never to the

boy from whom he just received it. Eva starts by throwing the ball to Adam. Who will do the fifth throw?

(A) Adam (B) Eva (C) Isaac (D) Olga (E) Urban

Emily wants to enter a number into each cell of the triangular table. The sum of the

numbers in any two cells with a common edge must be the same. She has already

entered two numbers. What is the sum of all the numbers in the table?

(A) 18 (B) 20 (C) 21 (D) 22 (E) impossible to determine

John coded a correct addition calculation naming the digits