ĐỀ THI VÒNG QUỐC GIA
G7 – HKIMO 2016-2017
Question 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..
Question 2. According to the pattern shown below, what is the next number?
Pattern: Quy luật; Next: Tiếp theo.
1、2、3、6、11、20、37、68、...
Question 4. There are six teams named A, B, C, D, E and F, participating a tournament. In 5 days, each team will play one game in each day. They play with another team once in the tournament. So, 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?
Participate: Tham gia; Tournament: Giải đấu; Games: Trận đấu; Win: Thắng; Defeated: Thua
Question 5. There are 7 people arguing which day of week is today. Their statements are quoted 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 among them only one statement is correct, which day of week is today?
Statement: Phát biểu; Yesterday: Hôm qua; Wednesday: Thứ Tư; Tomorrow: Ngày mai; Tuesday: Thứ Ba; The day after tomorrow: Ngày kia; Today: Hôm nay; Monday: Thứ Hai; Sunday: Chủ nhật; Saturday: Thứ Bảy.
Question 6. Given a is a real number and |a+2|+|a+3|=7, find the sum of all value of a.
Real number: Số thực; Sum: Tổng; Value: Giá trị.
Question 7. Find the value of
1×2×3+2×3×4+3×4×5+...+10×11×12.
Value: Giá trị.
Question 9. Given a is a positive integer and 3a+7≤a+19, how many possible values for a?
Positive integer: Số nguyên dương; Value: Giá trị.
Question 14. How many simplified fractions whose denominator is 2015 are there?
Simplified fraction: Phân số tối giản dương nhỏ hơn 1; Denominator: Mẫu.
Question 16. Combine 2015 equilateral triangles with side length 1 unit to form a quadrilateral. Find the maximum perimeter of that quadrilateral.
Equilateral triangle: Tam giác đều; Side length: Độ dài cạnh; Unit: Đơn vị; Quadrilateral: Tứ giác; Maximum: Lớn nhất; Perimeter: Chu vi.
Question 18. In the diagram, ABCE is a square of side length 20 units. If CD:DE=EF:FA=1:2, find the length of AG. Square: Hình vuông; Side length: Độ dài cạnh; Unit: Đơn vị.
Question 21. A collection of integers chosen from 1 to 2015 has the property that none of its members are 10 times of another. What is the maximum number of members such a collection can have?
Collection: Tập hợp; Integer: Số nguyên; Member: Phần tử; Maximum number: Số lớn nhất.
Question 22. Basketball team has 15 members. How many ways are there to send 5 teammates to participate in a competition in which one of them is the captain?
Teammate: Thành viên; Captain: Đội trưởng.
Question 23. In how many possible ways can 10 identical balls be distributed to 3 distinct boxes so that there are no empty boxes?
Identical: Giống nhau; Distinct: Khác nhau.
Question 25. Choosing from digits 0, 2, 4, 6 and 8 to form numbers, how many positive integers less than 10000 can be formed? (Each digit cannot be used more than once)
Digit: Chữ số; Positive integer: Số nguyên dương; Less than: Ít hơn; More than: Nhiều hơn; Once: Một lần.