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ĐỀ THI VÒNG QUỐC GIA

G7 – HKIMO 2017-2018

Question 2. Andy goes north for 20km, then goes east for 15km. How far is he now from the original position?

North: Phía Bắc; East: Phía Đông; Original position: Vị trí ban đầu.

Question 3. How many times does hour hand and minute hand of a clock form a right angle in a day?

Hour hand: Kim giờ; Minute hand: Kim phút; Right angle: Góc vuông.

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Question 4. Amy is reading a novel. She read 1 page in the first day, 2 pages the second day, 3 pages the third day, etc, until the total pages she read are multiples of 56. How many pages does she read until then?

Total: Tổng cộng; Multiple: Bội.

Question 5. There are 4 pairs of white chopsticks, 6 pairs of yellow chopsticks and 3 pairs of brown chopsticks mixed. If you want to get 1 pair of chopsticks of each colour, at least how many piece(s) of chopstick(s) is / are needed to be taken at random?

At least: Ít nhất; At random: Ngẫu nhiên.

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Question 6. Find the value of y if (2y+24)+(9y-79)=0.

Value: Giá trị.

Question 7. If x and y are positive integers and 2x+4y=48,

find the maximum value of x+y.

Positive integer: Số nguyên dương; Maximum value: Giá trị

lớn nhất.

Question 8.

How many integral solution(s) is / are there for x if 777>9x+25>-29?

Integral solution: Nghiệm nguyên.

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Question 11. Find the sum of all positive factor(s) of 7777.

Sum: Tổng; Positive factor: Ước số dương.

Question 12. From 1 to 2018, how many integers are divisible by 3 and 4, but not divisible by 8?

Integer: Số nguyên; Divisible by: Chia hết cho.

Question 15. The difference between two square numbers is 348. What is minimum value of the larger square?

Difference: Hiệu; Square: Số chính phương; Minimum value: Giá trị nhỏ nhất; Larger: Lớn hơn.

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Question 16. A cube with side length 12 is cut into cubes with side length 1. Find the increase in total surface area of the cubes.

Cube: Khối lập phương; Side length: Độ dài cạnh; Increase: Tăng; Total surface area: Diện tích toàn phần.

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Question 18. Small cubes with side length 1 are stacked according to the pattern shown below. If there are 31 layers, find the volume.

Cube: Khối lập phương; Side length: Độ dài cạnh; Stack: Xếp chồng lên nhau; Pattern: Quy luật; Layers: Tầng; Volume: Thể tích.

Question 19. The hypotenuse of a right-angled triangle is 10, find the maximum area of the triangle.

Hypotenuse: Cạnh huyền; Right-angled triangle: Tam giác vuông; Maximum: Lớn nhất; Area: Diện tích.

Question 20. An interior angle of a n-sided regular polygon is 5 times of an exterior angle. Find n.

Interior angle: Góc trong; n-sided regular polygon: Đa giác đều n cạnh; Exterior angle: Góc ngoài.

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Question 21. For a n-digit number which leftmost digit is 2, if the leftmost digit is now put at the rightmost, the new number formed is 3 times the original. Find the minimum value of n.

n-digit number: Số có n chữ số; Leftmost digit: Chữ số ngoài cùng bên trái; Rightmost: Ngoài cùng bên phải; 3 times: Gấp 3 lần; Minimum value: Giá trị nhỏ nhất.

Question 23. In how many possible ways can 9 identical balls be distributed to 4 distinct boxes so that there are no empty boxes?

Identical: Giống nhau; Distinct: Khác nhau.

Question 24. Use 1, 2, 4, 5, 7, 8 to form six-digit numbers. The odd digits cannot be next to each other and the even digits cannot be next to each other. How many number(s) can be formed in this way?

Six-digit number: Số có 6 chữ số; Odd digit: Chữ số lẻ; Even digit: Chữ số chẵn.

Question 25. Amy goes from point A to point B. For each step, she can only move up or move right. How many way(s) is / are there?

Move up: Đi lên trên; Move right: Đi sang phải; Pass through: Đi qua.

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