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Trang 1SAMPLE TEST FOR TIMO
1 There are 16 pieces of white chopsticks, 27 pieces of yellow chopsticks and 46
pieces of blue chopsticks mixed together If you want to get 2 pairs of white
chopsticks and 3 pairs of chopsticks with other different colours in the dark, at least how many pieces of chopsticks are needed to be taken?
At least: Ít nhất
2 There are some chickens and rabbits in a cage The number of chickens is 4 times as the number of rabbits They have 240 legs in total How many chicken(s) is / are there?
4 times: gấp 4 lần; In total: Tổng số
3 It requires 16 minutes to cut a piece of wood into 9 sections If the time required to cut into each section is the same, how many minute(s) is / are required to cut the wood into 11 sections?
4 Find the average of the following 8 numbers
2019、2065、2046、1985、2034、1922、46、1827
Average: Trung bình cộng
5 Leo needs 18 days to finish a project Bruce needs 21 days to finish the same
project If Leo, Bruce and Mary do the project together, it takes 9 days How many days does Mary take to finish the project alone?
Arithmetic
Trang 26 Find the value of 1 4 7 31 34
7 Find the value of 1369 1722 1364 1717
8 Find the value of 1 1 1 1
9-digit number: Số có 9 chữ số; Divisible: Chia hết; Sum: Tổng
12 Find the last digit of A if A 5 12 19 26 5 7 99 5 7 100
Last digit: Chữ số tận cùng
13 Find the numbers of all positive factors of 996
Positive factors: Ước dương
14 The remainder of dividing a positive integer K by 17 is 11 What is the remainder of
dividing 6K 16 by 17?
Remainder: Số dư; Divide: Chia; Positive integer: Số nguyên dương
15 The sum of 25 consecutive numbers is 900 Find the second largest number
Sum: Tổng; Consecutive: Liên tiếp
Trang 418 The figure below is a square overlapped by two right-angled triangles and one
quarter circle Find the area of the shaded region (Take 22
Trang 520 The perimeter of a circle is 18.84 If the diameter of the circle is the same as the diagonal of a square, what is the area of the square? (Take 3.14)
Perimeter: Chu vi; Circle: Hình tròn; Diameter: Đường kính; Diagonal: Đường chéo; Square: Hình vuông; Area: Diện tích
Combinatorics
21 Choose 3 digits, without repetition, from 1, 2, 3, 6, 7, 8 to construct 3-digit numbers
Of these 3-digit numbers, how many of them are divisible by 4?
Digit: Chữ số ; Without repetition: Không lặp lại; Divisible: Chia hết
22 A flight of stairs has 11 steps Peter can go up for 1 step or 3 steps each time The 6thstep cannot be stepped on as it is destroyed How many way(s) is / are there for Peter
to go up the stairs?
23 What is the nearest time while the hour hand and the minute hand are perpendicular
to each other between 6pm and 7pm?
Perpendicular: Vuông góc
24 In how many possible way(s) can 10 identical balls be distributed to 3 distinct boxes
so that every box contains at least one ball?
Distinct: Phân biệt (Khác nhau)
25 6 identical black books and 8 identical white books are put from left to right How many different permutation(s) is / are there?
Permutations: Hoán vị (Cách sắp xếp)
Trang 6ĐỀ 2: (Đề TIMO Khối 7 Vòng Chung Kết Quốc Gia 2019 – 2020)
Logical Thinking
1 There are 22 pieces of white chopsticks, 18 pieces of yellow chopsticks and 39
pieces of blue chopsticks mixed together If you want to get 2 pairs of blue
chopsticks and 2 pairs of chopsticks with other colours in the dark, at least how many pieces of chopsticks are needed to be taken?
2 A, B, C, D and E are passing balls Starting from A, 5th time pass will return to B Within the pass, there is at least 1 time to A, how many passing methods are there?
3 If abcd badc 17743, calculatea b c d
Calculate: Tính
4 There are some chickens and rabbits in a cage The number of chickens is 5 times as the number of rabbits The total legs of chicken’s is 72 more than that of rabbit’s How many rabbit(s) is / are there?
In total: Tổng số; More than: Nhiều hơn
5 According to the pattern shown below, what is the number in the blank?
Pattern: Quy luật
1 、 1 、 4 、 13 、 43 、 142 、 、…
Algebra
6 Factorize x22x63
Factorize: Phân tích thành nhân tử
7 How many negative integral solution(s) is / are there for x if 8x92 16 ?
Negative integral solutions: Nghiệm nguyên âm
Trang 78 Given that a is a negative real number and a 1 If 10 8
1
a a
, find the
minimum value of a
Negative real number: Số thực âm; Minimum value: Giá trị nhỏ nhất
9 Find the value of x if (96 23 ) (11 x x48)0
10 Given a and b are real numbers and satisfy equations a b 6 and ab6, find the
12 Find the sum of all positive factors of 786
Sum: Tổng; Positive factors: Ước số dương
14 Find the unit digit of A if A 13 132133134 13241325
Unit digit: Chữ số hàng đơn vị
15 The difference between two square numbers is 253 Find the value of the larger square given that it is a 3-digit number
Difference: Hiệu; Square numbers: Số chính phương; 3-digit number: Số có 3 chữ
số
Geometry
Trang 816 M( 18, 22) is the mid-point of A x( ,8) and B(10, )y Find the value of xy
Mid-point: Trung điểm
17 A interior angle of a regular n-sided polygon is 17 times of an exterior angle Find n Interior angle: Góc trong; Regular n-sided polygon: Đa giác đều n cạnh; Exterior angle: Góc ngoài
18 Small cubes with side length 1 are combined according to the pattern shown below Find the total volume of the 12th generation
Cubes: Khối lập phương; Side length: Độ dài cạnh; Pattern: Quy luật; Total
volume: Tổng thể tích
19 A solid cuboid is formed by merging 770 cubes with side length 1cm Find the
minimum value of the total surface area of the cuboid
Solid cuboid: Hình hộp chữ nhật đặc; Merge: Ghép; Side length: Độ dài cạnh;
Minimim value: Giá trị nhỏ nhất; Total surface area: Diện tích toàn phần
1 st generation 2 nd generation 3 rd generation
Trang 920 The figure below is a rectangle overlapped by a quarter of a circle and a triangle Find the area of the shaded region (Take 22
Digits: Chữ số; Without repetition: Không lặp lại; Odd: Lẻ
22 What is the nearest time while the hour hand and the minute hand are perpendicular
to each other between 10am and 11am?
Trang 1024 In how many possible ways can 9 identical flowers be distributed to 3 distinct vases with at least one in each vase?
Identical: y hệt nhau; Distributed: Được chia; Distinct: Phân biệt (Khác nhau)
25 7 identical black books and 10 identical white books are put from left to right How many different permutation(s) is / are there?
Identical: y hệt nhau; Permutation: Cách sắp xếp
ĐỀ 3: (Đề TIMO Khối 6 Vòng Chung Kết Quốc Tế 2015 – 2016)
Logical Thinking
1 Peter cuts a circle into parts by straight lines At least how many straight lines are
required to ensure he can get 14 parts?
Circle: Hình tròn; Straight lines: Đường thẳng; Parts: phần
2 Split 3, 12, 14, 26, and 91 into 2 groups of numbers such that they have equal product
Find the sum of the numbers of the group that contains 14
Split: Chia; Equal product: Tích bằng nhau; Sum: Tổng
3 There are some $1 and $2 coins The number of $1 coins is twice that of $2 coins The
total value of coins is $100 Find the number of $1 coins
Twice: Gấp đôi; Total value: Tổng giá trị
Trang 114 John wrote a 3-digit number on a piece of paper and asked Peter to guess it
Peter asked: “Is the number divisible by 21?”
John replied: “It is divisible by 21.”
Peter asked: “Is the number divisible by 9?”
John replied: “It is divisible by 9.”
Peter asked again: “Is it a square number?”
John said: “Yes, it is a square number.”
What is the number written by John?
Divisible: Chia hết; Square number: Số chính phương
5 A class has 40 students 26 students join the badminton club, 25 students join the judo
club and 20 students join the dance club Each student joins at least one club Given that
23 students join two clubs, how many students join all three clubs?
Arithmetic
6 Find the value of 1 5 25 125 625 3125
7 Find the value of 2015210152
8 Find the value of 1 1 2 3 144 233 377
(Remark: Starting from the third number, each number is the sum of the previous two numbers.)
Sum: Tổng; Previous two numbers: Hai số đằng trước
9 Find the value of 2 2 2 2 2 2 2 2 2
3 15 35 63 99 143 195 255 323
10 Convert 0.148
into the simplest fraction
Convert: Đổi; Simplest fraction: Phân số tối giản
Trang 12Number Theory
11 Find the sum of all positive factors of 2015
Sum: Tổng; Positive factos: Ước số dương
12 If a 5-digit number 2015A is divisible by 8, find the value of A
Divisible: Chia hết
13 Counting from 1 to 999, how many numbers are divisible by 6 or 9?
Divisible: Chia hết
14 When a 4-digit integer is divided by 5, 13, or 31, the remainder in each division is 2
Find the least possible value of that integer
4-digit integer: Số nguyên có 4 chữ số; Remainder: Số dư; Division: Phép chia; Least possible value: Giá trị nhỏ nhất có thể
15 Find the smallest 3-digit number that can be divisible by 3 different prime numbers?
Prime numbers: Số nguyên tố
Trang 1317 The side length of square ABCF is 18cm Extend BC to D and connect AD It is
known that the area of triangle AEF is 90cm2 less than that of triangle DCE Find the length of CD (in terms of cm)
Side length: Độ dài cạnh; Square: Diện tích; Extend: Kéo dài; Connect: Nối; Area: Diện tích; Triangle: Tam giác; Less than: Nhỏ hơn
18 Rectangle ABCD is divided into 8 parts whose areas are shown below Find the area
Trang 1419 Paint a cube with edge length of 4cm with red colour If it is divided into smaller
cubes with edge length of 1cm afterwards, find the numbers of small cubes with only 1 face being painted
Cube: Lập phương; Edge length: Độ dài cạnh; Face: Mặt của hình lập phương
20 Given a cuboid If its length is increased by 4cm, its volume is increased by 720cm3
If its width is decreased by 2cm, its volume is decreased by 264cm3; if its height is
increased by 4cm, its volume is increased by 660cm3 Find the surface area and the
volume of the original cuboid
Cuboid: Hình hộp chữ nhật; Length: Chiều dài; Width: Chiều rộng; Height: Chiều cao; Increased: Được tăng thêm; Volume: Thể tích;; Surface area: Diện tích toàn phần
Combinatorics
21 Counting from 1 to 10000, how many numbers are there that have exactly two digits
“5” and only one digit “4”?
Digit: Chữ số
22 How many 4-digit numbers whose product of all the digits is an odd number are
there?
Product: Tích; Digit: Chữ số; Odd: Lẻ
23 There are 11 boys and 4 girls in a class Choose 3 boys and 2 girls to form a study
group How many ways to form such a group are there?
Trang 1524 The attached figure is made up of 5 grids A colour is filled into each grid, and two
adjacent grids do not share the same colour If there are in total 4 colours to choose from
to fill in the grids, how many ways are there to colour the figure?
Grid: Ô; Adjacent: Kề nhau
Question 24
25 Arrange 5 letters A, B, C, D and E in a row If the pair A and B and the pair C and E
must be adjacent regardless of order, find the number of permutations
Row: Hàng; Adjacent: Kề nhau; Permutation: Cách sắp xếp
ĐỀ 4: (Đề TIMO Khối 7 Vòng Chung Kết Quốc Tế 2015 – 2016)
Logical Thinking
1 Amy bought flowers from a market It is known that a rose, a lily and a tulip cost $16,
$8 and $1 respectively She used $300 to buy 30 flowers and bought at least 1 for each type How many roses did she buy?
Respectively: Lần lượt; At least: Ít nhất
2 According to the pattern shown below, what is the next number?
1、2、3、6、11、20、37、68、…
Pattern: Quy luật
Trang 163 Find the integer part of 1
Integer part: Phần nguyên
4 There are six teams named A, B, C, D, E and F, participating in a tournament In 5
days, each team will play one game on each day They play against another team once in the tournament and there are 3 games every day Given that:
1) Team A wins Team B on the first day
2) Team C is defeated by Team D on the second day
3) Team E wins Team A on the third day
4) Team B wins Team C on the fourth day
Which team does Team A play with on the fifth day？
5 There are 7 people arguing which day of the week is today Their statements are
quoted as below:
A: Yesterday was Wednesday
B: Tomorrow will be Tuesday
C: Tomorrow will be Wednesday
D: The day after tomorrow will be Tuesday
E: Today is Tuesday
F: Today is neither Monday, Tuesday nor Sunday
G: Today is not Saturday
Given that only one statement is correct, which day of the week is today?
Trang 17Arithmetic
6 Given a 2 a 3 7, find the sum of all possible values of a
Sum: Tổng; All possible values: Tất cả các giá trị có thể
7 Find the value of 1 2 3 2 3 4 3 4 5 10 11 12
8 Convert 16
37 into recurring decimals
Convert: Đổi; Recurring decimals: Số thập phân vô hạn tuần hoàn
9 Let a be a positive integer satisfying the constraint 3a 7 a 19 How many possible
values for a are there?
Positive integer: Số nguyên dương; Constraint: Điều kiện
10 Find the value of 1 1 1 1
Remainder: Số dư; Divided: Bị chia
13 Given that x and y are natural numbers and 7 11
x y
When y attains its minimum, find the value of x
Natural numbers: Số tự nhiên; Miminum: Giá trị nhỏ nhất
Trang 1814 How many simplest fractions with denominator 2015 are there, given that it is
positive smaller than 1?
Simplest fraction: Phân số tối giản; Denominator: Mẫu số; Positive: Dương
15 Given positive integers x and y satisfying equations xy x y 19 and 2 2
84
x yxy Find the value of 2 2
x y
Positive integers: Số nguyên dương; Equations: Phương trình
Geometry
16 Combine 2015 equilateral triangles with side length of 1 unit to form a quadrilateral
Find the maximum perimeter of that quadrilateral
Equilateral triangles: Tam giác đều; Side length: Độ dài cạnh; Quadrilateral: Tứ giác; Maximum perimeter: Chu vi lớn nhất
17 ABCDEFGH shown in the graph is a cube If the distance between of A and F is 4 3, find the volume of the cube
Graph: Hình vẽ; Cube: Hình lập phương; Distance: Khoảng cách; Volume: Thể tích
Question 17
Trang 1918 In the diagram given below, ABCD is a square whose side length is 20 units If
CD DEEF FA , find the length of AG
Diagram: Hình vẽ; Square: Hình vuông; Side length: Độ dài cạnh
Question 18
19 A circle is inscribed in a square and another smaller square is inscribed in that circle
If the side length of the larger square is 4cm, find the area of the smaller square in cm2
Circle: Hình tròn; Inscribe: Nội tiếp; Square: Hình vuông; Side length: Độ dài cạnh; Area: Diện tích
20 It is known that the lengths of two legs of a right-angled triangle are in the ratio of
1: 7 If the length of the hypotenuse is 10cm, find the area of the triangle in cm2
Legs: Cạnh góc vuông; Right-angled triangle: Tam giác vuông; Ratio: Tỉ số;
Hypotenuse: Cạnh huyền; Area: Diện tích
Trang 20Combinatorics
21 A set of integers chosen from 1 to 2015 has the property that none of its members are
10 times another What is the maximum number of members such a collection can have?
Set of integers: Tập các số nguyên; Property: Tính chất; 10 times: Gấp 10 lần; Maximum number of members: Số phần tử lớn nhất
22 A basketball team has 15 members How many different ways are there to send 10
teammates to participate in a competition in which one of them is the captain?
23 Given that x x1, 2, ,x5 are all positive integers, how many solutions are there to the inequality x1 x2 x5 10 ?
Positive integers: Số nguyên dương; Solutions: Nghiệm; Inequality: Bất đẳng thức
24 Five students, A, B, C, D and E are passing a ball given that initially A holds the ball
If A passes the ball to D at the 5th pass, how many possible ways of passing the ball are there?
25 Using 0,2,4,6 and 8 as digits, how many positive integers less than 10000 can be
formed? (Each digit cannot be used more than once to form a number)
Digits: Chữ số; Positive integers: Số nguyên dương; Less than: Nhỏ hơn; More than once: Nhiều hơn một lần
Trang 21ĐỀ 5: (Đề TIMO Khối 6 Vòng Chung Kết Quốc Tế 2016 – 2017)
Logical Thinking
1 There are 4 statements on a piece of paper as shown below, and only one of them is
correct Write down the letter before the correct statement on the answer sheet
2 Split 14, 24, 60, 65, 77, and 143 into 2 groups of 3 numbers such that the product of
numbers in each group is the same Find the sum of the numbers of the group that
contains 14
Split: Chia; Product: Tích; The same: Bằng nhau; Sum: Tổng
3 They caught 12 animals including spiders and crickets with 90 legs in total Find the
number of spiders knowing that a cricket has 6 legs and a spider has 8 legs
In total: Tổng số
Trang 224 John wrote a 3-digit number on a piece of paper and asked Peter to guess it
Peter asked: “Is the number 123?”
John replied: “One of the digits is correct, the position of that digit is also correct.”
Peter asked again: “Is the number 456?”
John replied: “Two digits are correct, but the positions of those digits are both wrong.” Peter asked again: “Is the number 354?”
John said: “All three digits are correct, but the digits are all in the wrong places.”
What is the number written by John?
Digit: Chữ số; Position of the digits: Vị trí của chữ số
5 There are 51 students in Grade 6, among them 22, 19 and 18 students like playing
basketball, volleyball and football respectively There are 5 students like playing
basketball and volleyball; 7 students like playing volleyball and football; 10 students like playing basketball and football 3 students like all three sports Find the number of
students who likes none of the sports
Arithmetic
6 Find the value of 2 6 18 54 162 486 1458 4374 13122 39366 118098
7 Find the value of 128522852
8 Find the value of 1 4 5 9 157 254 411
(Remark: Starting from the third number, each number is the sum of the previous two numbers.)
Sum: Tổng; Previous two numbers: Hai số liền trước
9 Find the value of 1 1 1 1 1 1 1 1 1
2 6 12 20 30 42 56 72 90
Trang 2310 Convert 0.7 8 6
into the simplest fraction
Convert: Đổi; Simplest fraction: Phân số tối giản
Number Theory
11 Find the sum of all positive factors of 2018
Sum: Tổng; All positive factors: Tất cả các ước số dương
12 When a natural number is divided by 20, the remainder is 4 When the number is
divided by 39, the remainder is also 4 When that number is divided by 65, what is the remainder?
Natural number: Số tự nhiên; Divided: Bị chia; Remainder: Số dư
13 Write 9 as the sum of some positive integers (e.g.(8,1) / (2, 7) / (4, 2,3) ) so that the product among those numbers is the largest Find the value of that product
Sum: Tổng; Positive integers: Số nguyên dương; Product: Tích
14 When a 4-digit positive integer is divided by 3, 11, or 61, the remainder of each
division is 2 Find the least possible value of such an integer
4-digit positive integer: Số nguyên dương có 4 chữ số; Divided: Bị chia; Remainder: Số dư; Division: Phép chia; Least possible value: Giá trị nhỏ nhất có thể
15 A book has pages numbered 1, 2, 3, and so on A page was torn from the book and
the sum of all remaining page numbers is 761 What is the page number of the torn page?
Numbered: Được đánh số; Sum: Tổng; Remaining page numbers: Số trang còn lại
Geometry