Bộ đề ôn luyện kỳ thi Toán Quốc Tế HKIMO 2021 Khối 2 + 3

Tài liệu ôn tập khối lớp 2 và khối lớp 3 ôn luyện cho kỳ thi Olympic Toán Học Quốc tế HKIMO. Nội dung thi là các dạng toán logic theo chuẩn chương trình học của Quốc Tế và các trường song ngữ, các trường Quốc tế tại Việt Nam.

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BỘ ĐỀ ÔN LUYỆN OLYMPIC TOÁN HỌC QUỐC TẾ HKIMO 2020

4 Alice needs 10 minutes to finish a lap Then she needs to rest 1 minute How

many minute(s) does she take to finish 10 laps?

5 According to the pattern shown below, how many ◎ is / are there in the 9th group?

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Arithmetic

6 Find the value of 1  3  5  7  9 11 13 15

7 Find the value of 3  3  6 2  9 1 18 2

8 Find the value of 123  294  377+206

9 What is the number that should be filled in the blank if the equation below is

correct?

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10 Refer to the puzzle, find the value of B

Number Theory

11 Alice has 31 pencils and Peter has 92 pencils How many pencil(s) does Alice

have to ask Peter to give him to make Peter has 11 less pencils than Alice?

12 15 students have even number of scores of mathematics test in total 7 children

have odd number of scores and 3 children has even number of scores Determine the sum of scores of the remaining children is odd or even

13 The numbers below follow the arithmetic sequence, what is the 9th number?

198、 187、 176、 165、 154、 …

14 After Alice gives 8 pencils to Peter and takes 6 pencils from Mary, they will

have equal number of pencils How many pencil(s) did Mary have more than Peter originally?

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15 Fill the lines with ‘ + ’ and ‘  ’ to make the equation below correct

Geometry

16 How many square(s) is / are there in the figure below?

17 A prism has 16 faces, how many vertice(s) does this prism have?

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19 At least how many square(s) can be seen if viewing the figure below from top?

20 At most how many line(s) can be formed by using 6 points on a plane?

Combinatorics

21 How many 3-digit number(s) having the units digit that is smaller than 5 is / are

there?

22 What is the greatest 4-digit number by using 2, 4, 6 and 8 that is divisible by 4?

(Each number can only be used once)

23 Pick 2 from 10 children to take part in interview How many different

combination(s) is / are there?

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24 How many odd number(s) is / are there in the following numbers from the 4th

to the 18th ?

1, 2, 3, 5, 8, 13,…

25 Alice has 5 $1 coins, 4 $2 coins and 5 $5 coin, how many value(s) of a product

can she buy without any changes?

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ĐỀ 2:

Logical Thinking

1 According to the pattern shown below, what is the number in the blank?

1 、 1 、 3 、 5 、 9 、 15 、、 …

2 Yesterday will be Thursday Which day of the week will 87 days later be?

3 The age of Alice 11 years later is equal to the age of Peter 5 years later How old

is Peter when Alice is 18 years old?

4 37 students line up where Alice is the 18th starting from the front How many student(s) is / are behind her?

5 According to the pattern shown below, how many ◎ is / are there in the 6th group?

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Arithmetic

6 Find the value of 179  219 121 181  281 119

7 Find the value of 17118  3117 17 51

8 Find the value of 500  2  500  4  500 5  500 10  500 50

9 Find the value of 5 15  25  35  45  55

10 Find the value of 1017 8 129 8

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Number Theory

11 Define the operation symbol a  b  (a  2) (b 3) , find the value of 2  5

12 Alice and Peter have 164 candies in total Alice has 24 candies more than

Peter How many candies does Alice have?

13 The numbers below follow the arithmetic sequence, what is the sum of the 7th term and the 9th term?

8、 14、 20、 26、 32、 …

14 What is the sum of the largest and the smallest 3-digit multiple of 13?

15 The sum of 3 consecutive odd numbers is 27 Find the product of all the

numbers

Geometry

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17 A prism has 36 edges, how many face(s) does this prism have?

18 A square whose sides are 10cm long is cut into 25 squares of side length 2cm

What is the difference in perimeters between 25 small squares and the larger

21 After Alice takes 11 peanuts and 6 peanuts from Peter and Mary respectively,

they will have equal number of peanuts How many peanut(s) did Peter have more than Alice originally?

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22 Choose 3 digits from 2, 4, 6, 8, 9 to form 3-digit numbers How many

number(s) that can be odd number greater than 300 is / are there? (The repetition of digits is allowed)

23 Numbers are drawn from the 32 integers 10 to 41 At least how many

number(s) is / are drawn at random to ensure that there are two numbers whose product is divisible by 4?

24 35 students are either wearing L, M or S size uniforms At least how many

student(s) is / are wearing the same size of uniforms?

25 If Alice goes from point A to point B, each step can only move up or move

right How many way(s) is / are there?

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4 John goes home by taxi and he needs to pay $90 How much does he has to pay

if he goes home by taxi with his father, mother and sister?

5 According to the pattern shown below, how many  is / are there in the 12th

group?

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Arithmetic

6 Find the value of 2 + 8 + 12 + 18 + 22 + 25 + 28 + 35

7 Find the value of 105 : 3 – 105 : 5 + 105 : 7

8 Find the value of 22 – 19 + 16 – 13 + 10 – 7 + 4 - 1

11 Amy has 73 apples and John has 39 apples How many apple(s) does Amy

have to give John to make them have the same number of apples?

12 4 students have 38 balloons in total Two children have even number of

balloons and one child has odd number of balloons Determine the number of

balloons of the remaining child

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143、 139、 135、 131、 127、 …

14 How many 3-digit number(s) having the units digit 1 is / are there?

15 Fill the lines with ‘ + ‘ and ‘ x ‘ to make the equation below correct

Geometry

18 According to the pattern shown below, what is the figure in the space

provided?

19 At least how many square(s) can be seen if viewing the figure below from top?

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20 At most how many rectangle(s) can be formed by drawing 5 straight lines on a

plane?

Combinatorics

21 After Amy gives 3 apples to Andy and 7 apples to Johnny, they will have equal

number of apples How many apple(s) did Amy have more than Johnny originally?

22 What is the smallest 4-digit number by using 3, 5, 6 and 8 that is divisible by

5? (Each number can only be used once)

23 Every 2 of the 6 children shake hand How many times do they shake hands?

24 How many odd number(s) is/are there in the following numbers from the 1th to the 30th ?

1, 2, 3, 5, 8, 13,…

25 Jack has 6$1 coins, 4 $2 coins and 2 $5 coins, how many way(s) can he buy for

a souvenir cost $8 without any changes?

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ĐỀ 4:

1 What is the value of the number to represent “?” in the following table?

2 According to the pattern shown below, how many triangle(s) is / are there from

the 1th to the 99th symbol counting from the left?

3 The age of Samuel 9 years ago is equal to the age of Joseph 2 years later How

much Samuel is older than Joseph when Joseph is 25 years old?

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4 A tree is planted every 15m in a street from one end The street is 255m long

How many trees are there in the street?

5 According to the pattern shown below, how many  is / are there in the 10th

group?

Arithmetic

6 Find the value of 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18

7 Find the value of 81 x 16 + 27 x 52

8 Find the value of 16 x 625 x 4 : 25

9 Find the value of 2018 - 2017 + 2016 - 2015 + 2014 - + 2002 - 2001 + 2000

10 Find the value of 1258 + 369 + 742 + 641

Number Theory

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12 The sum of A and B is 2018 The difference between A and B is 902 Given A is

larger than B, find the value of A

13 The numbers below follow the arithmetic sequence, what is the sum of the 9th

term and the 14th term?

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17 A pyramid has 2018 edges, how many face(s) does this pyramid have?

18 9 squares which perimeters are 48cm form a larger square What is the

perimeter of the larger square?

19 At least how many square(s) can be seen if observing the figure below from the

top?

20 At most how many intersection point(s) are there by drawing 5 straight lines on

a plane?

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Combinatorics

21 After Amy gives 10 apples to Andy and 7 apples to Johnny, they will have

equal number of apples How many apple(s) did Johnny have less than Amy

originally?

22 Choose 3 digits from 1, 3, 4, 5, 9 to form 3-digit numbers How many

number(s) that can be divisible by 5 is / are there? (repetitions of digits are

allowed)

23 Numbers are drawn from the 27 integers 1 to 27 At least how many number(s)

is / are drawn at random to ensure that there are two numbers whose difference is

divisible by 4?

24 At least how many of 37 children that was/were born in the same month?

25 If Andy goes from point A to point B, each step can only move up or move

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4 Jame goes to the supermarket and he need to pay $80 How much does he has to

pay if he goes to the supermarket with 3 friends?

5 According to the pattern shown below, how many is/ are there in the 10thgroup?

Arithmetic

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6 Find the value of 3 + 7 + 15 + 30 + 25 + 18 + 4 + 2 + 6

7 Find the value of 120 ÷2 + 120 ÷5 -120÷10

8 Find the value of 23-8 + 15-4 + 10 -5

11 Anna has 66 apples and John has 24 apples How many apples does Anna have

to give John to make them have the same number of apples?

12 5 students have 65 balloons in total Three children have even number of

ballons and two childrens got odd number of ballons Determine the number of balloons of the remaning child?

13 The number below follow the arithmetic sequence, what is the 10th number?

120, 126, 132, 138, 144

14 How many 3 – digit number(s) having the units digit 2 is/ are there?

15 Fill the lines with “+” and “×” to make the equation below correct:

5 6 _7 _8 9 = 95

Geometry

16 How many squares is/ are there in the figure below?

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17 A prism has 6 faces, how many vertices does this prism have?

18 According to the pattern shown below, what is the figure in the space

provided?

19 At least how many squares can be seen if viewing the figure below from top?

20 At most how many rectangles can be formed by drawning 7 straight lines on a

plane?

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Combinatorics

21 After gives 5 apples to Anna and 3 apples to John, they will have equal number

of apples How many apples did John have more than Anna originally?

22 What iss the smallest 4 –digit number by using 5,6,8,2 that is divisible by 5?

(Each number can only be used once)

23 Every 2 of 20 children shake hand How many times do they shake hands?

24 How many even number(s) is/are there in the following numbers?

1, 2, 3, 4, …, 30

25 Anna has 4 $1 coins, 7 $2 coins and 1 $ 5 coins, how many ways can he buy

for a souvenir cost $7 without any changes?

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3 5 years ago, Amy was 14 years old How old will Amy be 4 years later?

2 、 9 、 16 、 23 、 30 、 37、、 …

3 、 3 、 6 、 9 、 15 、 24、、 …

Arithmetic

6 Find the value of 2  4  6 8 10 12 14 16 18

7 Find the value of 1513 153 15 6

8 Find the value of 1 3  5  7  9 11 13 15 17

correct?

113 _  904

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10 Find the value of 20  4  20 5  20 1

Number Theory

11 Amy has 137 apples and John has 37 apples How many apple(s) does Amy

have to give John to make them have the same number of apples?

12 4 students have 40 balloons in total and each of them has a different number of

balloons and at least 1 balloon At most how many balloon(s) does the student with the most balloons have?

21、 31、 41、 51、 61、 …

14 How many 3-digit number(s) that have the unit digit 0 is / are there?

15 What is the largest 2-digit number that can be divisible by 8 and 12?

Geometry

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18 A pyramid has 18 vertices, how many face(s) does this pyramid have?

19 At least how many square(s) can be seen if viewing the figure below from

side?

20 How many line segment(s) can be formed in the figure below?

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Combinatorics

21 Separate 54 candies into six equal groups, how many candy(ies) is / are there in

each group?

22 Choose 2 digits, without repetition, from 1, 4, 6, 8, 9 to form 2-digit numbers

How many even number(s) is / are there?

23 According to the pattern shown below, how many circle(s) is / are there from

1st to 50th symbol counting from the left?

24 What is the smallest 5-digit number by using 3, 1, 0, 5 and 8? (Each number

can only be used once)

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ĐỀ 7:

1 What is the value of the number to represent “?” in the following table?

2 According to the pattern shown below, how many circle(s) from 1st symbol to the 103rd symbol counting from the left?

3 The age of Samuel 7 years later is equal to the age of Joseph 3 years ago Given

that Joseph is 22 years old now, how old is Samuel now?

1 、 4 、 9 、 16 、 25 、 36 、 49、、 …

1 、 3 、 7 、 15 、 31 、 63 、、 …

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Arithmetic

6 Find the value of 2  4  6 8 10 12 14 16 18  20  22

7 Find the value of 2712 15 27  27 23

8 Find the value of 111111

9 Find the value of 1  3  5   23  25  23   5  3 1

10 Find the value of 6253216125

Number Theory

11 Define the operation symbol a  b  a b  ab , find the value of (12  4)

12 The sum of A and B is 2019 The difference between A and B is 405 Given A

is larger than B, find the value of A

21、 34、 47、 60、 73、 …

14 5 students have 50 balloons in total and each of them has a different number of

balloons and at least 1 balloon At most how many balloon(s) does the student with the most balloons have?

15 What is the largest 3-digit number that can be divisible by 8 and 12?

Geometry

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17 A pyramid has 405 vertices, how many edge(s) does this pyramid have?

18 The perimeter of a rectangle is 84 Find the maximum value of the area of this

rectangle

19 At least how many square(s) can be seen if viewing the figure below from

side?

20 There are 6 points on a plane Given that any 3 points are not in collinear How

many quadrilateral(s) can you draw?

Combinatorics

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21 Peter has 4 $5 coins and 6 $10 coins How many $20 notes can he exchange?

22 Choose 3 digits, without repetition, from 2, 3, 4, 5, 6 to form 3-digit numbers

How many odd number(s) is / are there?

23 Separate 108 candies into six equal groups, how many candy(ies) is / are there

in each group?

24 What is the largest 5-digit odd number by using 3, 1, 0, 6 and 9? (Each number

can only be used once)

25 If Andy goes from point A to point B, each step can only move up or move

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