# Grade 9 IMO – Tuyển chọn câu hỏi luyện thi IMO Lớp 9

Table Of Contents

Grade 9 IMO

## Week 1

### Choose correct answer(s) from the given choices

(1) Aidan got an average score of 81.75 in 4 tests. He got 83 as the average of the highest 3 scores, and his lowest two scores are the same numbers. What is the average of his highest two scores?

a. 85 b. 84.5

c. 85.5 d. 86

(2) The value of

(3) There are 28 numbers. Each number is subtracted from 30 and the mean of the numbers so obtained is found to be −2.2. Find the mean of the given numbers.

a. 36 b. 32.2

c. 39.1 d. 29.6

(4) Factorize: (2a^{5} − 50a)

a. 2a(a^{2} + 5)(a^{2} + 5) b. 2(a^{2 }− 5)(a^{2} + 5)

c. 2a(a^{2 }− 5)(a^{2} + 5) d. a(a^{2 }− 5)(a^{2} + 5)

(5) The equation of a straight line which is parallel to y-axis, and is at a distance of d from y-axis is

a. x = d b. y = d

c. y – x = d d. y + x = d

### Fill in the blanks

(6) The arithmetic mean of first 19 multiples of 8 is ………..

(7) In △ABC, ∠ACB = 40∘ and the interior angle bisectors of ∠CAB and ∠ABC intersect at P. The value of ∠APB is …….∘.

### Answer the questions

(8) Two circles with radii of 4 and 10 are drawn with the same center. The smaller inner circle is painted green, and the part outside the smaller circle and inside the larger circle is painted purple. What is the ratio of the areas painted purple to the area painted green?

(9) Simplify: (25p^{2} + 90p + 81) ÷ (5p + 9).

(10) A train traveling at 48 kilometers per hour, passes through a tunnel in 4 minutes. A second train, twice as long as the first one, traveling at the same speed, takes 5 minutes to pass through the tunnel. What is the length of the second train?

## Week 2

### Choose correct answer(s) from the given choices

(1) In an examination, Giselle attempted 15 questions correctly and secured 59 marks. If there were two types of questions i.e. of 3 marks and 5 marks, how many questions of 3 marks did she attempt correctly?

a. 8 b. 7

c. 9 d. 6

(2) What is the value of

(3) What is the units digit of the number 8^{2} + 80^{50} + 400^{300} + 4005^{6005}

a. 9 b. 8

c. 5 c.16

(4) If an angle is 66° more than its complement, find the measure of the angle.

a. 78° b. 90°

c. 79° d. 76°

(5) The smaller angle formed between the hands of a clock when it strikes 11 o’clock is:

a. a right angle b. an acute angle

c. an obtuse angle d. a straight angle

### Fill in the blanks

(6) If CD is perpendicular to AB and CE bisects angle ∠ACB, the angle ∠DCE = ………..°.

(7) A cuboid of size 6 cm × 9 cm × 11 cm is melted and re-shaped as cylinder of height 21cm. Find the radius of the cylinder = cm. (Assume π = 22/7)

(8) Simplify:

(9) In the figure below, BAD, BCE, ACF and DEF are straight lines. It is given that BA = BC AD = AF EB = ED, if ∠BAC = z∘, the value z is …….. ^{0}

### Answer the questions

(10) A cone completely made of metal (i.e. it is not hollow) has a base radius of 16 cm, and height of 8 cm. If we melt it and recast it into a sphere, what will be the radius of the sphere?

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