Grade 8 IMO – Tuyển chọn câu hỏi luyện thi IMO Lớp 8

Grade 8 IMO

Week 1

Choose correct answer(s) from the given choices

(1) If you add a number x with another number that is 7 times the value of x, and then take the cube of the sum, what will be the result?

a. 595x^3              b. 512x^3
c. 53x^2                d. 49x^3

(2) Tiffany had a piece of wire. She cut it into 5 equal parts and gave 1 to her sister Kate.
Kate used 1/6 of it and had 2.9 cm of the wire left. Find the length of the wire that Tiffany had.

a. 174 cm         b. 1740 cm
c. 1.74 cm        d. 17.4 cm

(3) Which is the smallest number that should be multiplied with to give a perfect cube?

a. 8        b. 3
c. 6        d. 0

Fill in the blanks

(4) The area of the octagon ABCDEFGH having each side equal to 25 cm, CH = DG = 39 cm and EL ⊥ DG such that EL = 24 cm is ……………. cm²

Answer the questions

(5) In a camp, there was enough food for 270 men for 40 days. After 30 days, 210 men left
the camp. How long would the remaining food last at the same rate?

(6) 4 workers can build a 72 feet tower in 6 days. At the same rate, how long will it take for 6 workers to build a 126 feet tower?

(7) Which is the smallest fraction that must be added to the square root of 11\frac{1}{9} so that the resulting number is a positive whole number?

(8) Name a solid with four triangular faces.

(9) Which is the smallest number that can be multiplied to 5400 to give a perfect square?

(10) Caleb scored 76% in an exam with 608 marks. If Kayden got 504 marks in the same exam, find the percentage obtained by Kayden.

Week 2

Choose correct answer(s) from the given choices

(1) If 2³ × (-4)^x = -32, then find the value of .

a. 2        b. 3
c. 1         d. -1

(2) If angles P, Q, R  and S of the quadrilateral PQRS taken in order are in ratio 13 : 7 : 8 : 12, then what kind of shape does PQRS represent?

a. Rhombus       b. Square
c. Trapezium    d. None of above

(3) Isaac alone can do a piece of work in 32 days and Muhammad alone can do the same work in 28 days. If Muhammad works for 7 days and then leaves, then in how many days can Isaac alone finish the remaining work

a. 24 days         b. 23 days
c. 31 days          d. 26 days

Fill in the blanks

(4) The solid shown is formed by taking a 6 cm × 6 cm × 6 cm cube and drilling a 2 cm × 2 cm square hole from the center of each face to the center of the opposite face. The volume of the solid is ………. cm³

(5) A person lent a certain amount of 13% money at an interest rate of per annum compounded annually and received a total amount of $76614 after years. The amount of money lent by him was $ ………….

(6) The number of people living in a small town is found to be a perfect cube. We know that the number of men in the town is 36090, and the number of women in the town is 47422. By an odd coincidence, we count and find that the number of children in the town is also a perfect cube. If we give you a hint that this number is more than 13820, then the smallest possible number of children in the town is …………..

(7) The denominator of a rational number is greater than its numerator by 9 If 9 is subtracted from the numerator and 8 is added to its denominator, the new number becomes 1/14. The original number is

Answer the questions

(8) Eva plants a jasmine on her 15th birthday. If the plant has one jasmine to start with and the number of jasmines triples every week then how many jasmines will be there after x weeks?

(9) We use n! to mean the following expression n × n-1 × n-2 × n-3 × … × 2 × 1 (the product of all numbers from 1 to n) In the range of numbers 12 <= x <= 44, how many numbers are there such that (x -1)! is not divisible by x?

(10) Which is the smallest fraction that must be subtracted from the square root of 121/25 so that the resulting number is a positive whole number?

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