AMO Grade 7 – Tuyển chọn câu hỏi AMO – Lớp 7

AMO Grade 7

Week 1

Answer the questions

(1) In the image given below, if the radius of all the large circles is r, then what is the radius of the inner smaller circle?

(2) If A ♦ B means (A + B)/2, what is the value of 3 ♦ (1 ♦ 9)?

(3) Find the order of rotational symmetry in the given image.

(4) A square park of an area 900 sq. m has to be fenced. The fencing will require the use of a wire that can
enclose the park 4 times and each circuit of the wire would be 3 % greater than the perimeter of the park. What length of the wire is needed for this?

(5) If the hour hand of a clock is 1.4 cm long, find the distance covered by the tip of hour hand in 100 days.
(assume π = 22/7)

(6) What percentage of the following letters cannot be drawn using straight lines ?

K V W B C Q

(7) A number multiplied by 10 and 15 is added to the product. If the result is 165, what was the original
number?

(8) Find the next number in the sequence.

7, 8, 14, 15, 21, 22, ….

(9) Among five friends, Ethan is taller than Charlotte, but not as tall as Janelle. Giselle is taller than Isabelle
but shorter than Charlotte. Who is the shortest in the group ?

(10) Pointing towards a man swimming in the pool, Daniel says, “His son is my son’s uncle”. How is the man
related to Daniel?

(11) Find the missing term.

(12) A train traveling at the speed of 30 kmph leaves the station at 3 pm. Another train leaves the station at 5pm. If the second train travels at a speed of 70 kmph, then at what time will it catch up with the first train

(13) The radius of the unshaded circles is 4 cm, 4 cm, and 2 cm, respectively. Find the area of the shaded region. (For this question assume π = 3)

Choose correct answer(s) from the given choices

(14) 4% of 1.26 is same as :

a. 40% of 126            b. 0.4% of 0.126
c. 0.4% of 12.6          d. None of these

(15) If diameter of a circle is doubled, what would be the ratio of new circumference to new diameter?
a. 2 π          b. π + 2      c. π/2         d. π

Week 2

Choose correct answer(s) from the given choices

(1) Using the rule between IN and OUT, find the missing number.

IN	25	19	26	24	27	12	8	7
OUT	150	133	208	?	270	132	96	91

a) 168         b) 240     c) 192        d) 216

(2) Find the order of rotational symmetry in the given image.

a) 4       b) 5         c) 3          d) 7

(3) Find the sum of the following angles : ∠pqr + ∠qrs + ∠rsp+ ∠spq

a) 540 °          b) 360 °              c) 270 °               d) 180 °

Fill in the blanks

(4) The radius of a wheel of a rickshaw is 28 cm. If the wheel makes 50 rotation in one minute, the rickshaw will cover a distance of 2640 meters in minutes. (assume π = 22/7)

(5) The average of any four consecutive odd integers is always ……….

(6) The number of

which can fit in the given shape are

(7) AP and BP are bisectors of ∠CAB and ∠CBD, respectively. ∠APB = ………… °

Answer the questions

(8) Find the missing angle.

(9) Some n integers have been selected randomly from the integers 1, 2, 3, …, 320. 2 integers a and b are chosen from the selected n integers such that a and b are relatively prime. What should be the minimum value of n that ensures there exist 2 such integers a and b

Week 3

Choose correct answer(s) from the given choices

(1) Tiffany remembers that her father’s birthday is after 8th but before 13th of April. Her sister Megan remembers that her father’s birthday is before 17th and after 11th of April. On which date of April is their father’s birthday?

a. 12th                  b. Can not be determined
c. 11th                   d. 13th

(2) There are red and green balls in a bag. Two-third of the balls are red. If we now add 8 red and 8 green to the bag, which of following is correct?

a. There are same number of red and green balls.
b. There are more green balls than red balls.
c. Cannot be determined from given information.
d. There are more red balls than green balls.

(3) A dog takes 3 rounds of the field shown in the picture.

The number expression given below shows the distance covered by the dog.

3 × P = Q m = R km

Find the value of P, Q and R where P is the perimeter of the field, Q is the total distance traveled by the dog in meters and R is the total distance traveled by the dog in kilometers.

a. 900 m, 300 m, 0.9 km             b. 300 m, 0.9 m, 300 km
c. 300 m, 900 m, 0.9 km             d. 0.9 m, 300 m, 900 km

(4) In a triangle, the third angle is half the first angle, and the first angle is two-third of the second angle. What is the value of the third angle ?

a. 45°             b. 30°
c. 90°             d. 60°

Fill in the blanks

(5) Teacher asks students to fix flags around the periphery of a circular ground of radius 56 meters. If each flag is fixed 4 meters apart, flags would be required to cover the periphery of the ground. (assume π = 22/7)

(6) The number of lines of symmetry in the box given below is …………. (Input numbers only)

(7) The length of the longest straight line that can be drawn on a paper of size 27 cm X 36 cm is ……… cm.

Answer the questions

(8) Let be the number

Find the remainder when n is divided by 11.

(9) Two wheels of radius 7 cm are connected by a belt as shown below. If the distance between the wheels is 5 cm, find the length of the belt (Assume π = 22/7).

(10) In triangle ΔPQR, ∠Q = 70° and bisectors of angles R and P meet at point S. Find ∠RSP.

Week 4

Choose correct answer(s) from the given choices

(1) Gabrielle is facing South. She turns 90° in anticlockwise direction and then turns 45° in clockwise direction. Which direction is her back facing now?

a. South-West
b. South-East
c. North-West
d. North-East

(2) The algebraic expression of the statement “Three-fifth of y multiplied by the difference of p and q” (Assume that p is less than q) ?

a. \frac{3}{5} y(q – p)

b. \frac{3}{5} y(p – q)

c. \frac{3}{5} (yq – p)

d. \frac{3}{5} y(p/q)

(3) Find the arithmetic mean of first 15 multiples of 5.

a. 45    b. 35    c. 40      d. 42.5

(4) ♥ ♣ ♦ ♠ ♥ ♣ ♦ ♠

What will be the shape at the 17th position?

a. ♥       b. ♠     c. ♣       d. ♦

Fill in the blanks

(5) The value of the missing angle = ………. °

Answer the questions

(6) In ΔABC, D is a point on the side BC such that AB = AD = DC. If ∠BAD = 20° , find ∠BAC.

(7) In ΔPQR, QR = PQ and ∠P=65°, find the value of ∠R.

(8) An article with price tag of $1400 is sold at 15% discount. Due to festival season, the shopkeeper provides an additional discount of 10% on the discounted price. Find the selling price of the article.

(9) Isabelle remembers that her father’s birthday is after 12th but before 17th of May. Her sister Hayley remembers that her father’s birthday is before 21st and after 15th of May. On which date of May is their father’s birthday?

(10) ♣ + ♣ + ♣ + ♣ = 20
♣ + ♥ = 12
Find the value of  ♣ + ♥ + ♥.

Week 5

Choose correct answer(s) from the given choices

(1) PQRS is a parallelogram. Find the ratio of the area of the parallelogram PQRS to the area of the triangle PQR.

a. 1:2       b. 3:1
c. 1:3       d. 2:1

(2) The chart shows the production of different apparels in a garment factory. If the production of jackets was 5000 pieces, find the total production.

a. 10200 pieces     b. 10000 pieces
c. 9800 pieces.      d. 9900 pieces

(3) Few cadets are standing in a row. Joshua is at the 20th position from the front, and Kate
is standing at the 20th position from the back. If Joshua and Kate interchange their positions, Kate becomes 29th from the back. How many cadets are there in the row?

a. 51         b. 50
c. 48         d. 46

(4) In a triangle, the second angle is three times the first angle, and the first angle is half the third angle. What is the value of the third angle ?

a. 60°      b. 45°
c. 30°      d. 90°

Fill in the blanks

(5) If today is Tuesday, the day after 33 days will be ………….

Answer the questions

(6) Tristan and Giselle are running on a circular track. Tristan is running on the outer edge of the track and covers a distance of 844.8 meters in one round. Giselle is running on the inner edge of the track and covers a distance of 712.8 meters in one round. Find the width of the track. (Assume π = 22/7)

(7) There are three small circles in a big circle and there are three smaller circles in every small circle. How many circles are there in all?

(8) A clock shows 7:30 as the time. Nur rotated the clock (without touching the hands of the clock) such that the hour hand points to South-East, in what direction does the minute hand point?

(9) In a class of 18 students, the average marks in a test was 62. If Olivia got 60 marks and Ashley got 112 marks, what were the average of the other 16 students?

(10) If the distance between B and D is 58 cm, find the distance between A and C.

Week 6

Choose correct answer(s) from the given choices

(1) The number of hours left in a day is half the number of hours already passed. How many hours are left in the day?

a. 12 hours       b. 10 hours
c. 6 hours         d. 8 hours

(2) Muhammad is Hayley’s brother, Hayley is Joshua’s sister, and Joshua is Aaron’s father. Who is Aaron to Muhammad?

a. Uncle         b. Aunt
c. Brother      d. Niece

(3) A dog is walking around the periphery of a right-angled triangle shown in the picture. Find the distance traveled by the dog in 7 rounds.
(All units are in meters)

a. 3455 m        b. 3458 m
c. 3461 m        d. 3464 m

(4) 45% of 30% of 200 = ?

a. 24.3       b. 32.4
c. 29.7       d. 27

(5) $5 + (100% of $5) + (5% of $100) = ?

a. $555       b. $10
c. $505       d. $15

Fill in the blanks

(6) The number of three-digit integers less than 501 have exactly two different digits in their representation (for example, 232 or 466 is …………

(7) The radius of a wheel of a rickshaw is 37.1 cm. If the wheel makes 150 rotation in one minute, the rickshaw will cover a distance of 24486 meters in ……….. minutes. (assume π = 22/7)

(8) If the distance between B and D is 205 meters, the distance between A and C is …………. meters.

(9) If AB and PQ are parallel, the value of ∠Y is ………… °.

Answer the questions

(10) Find the area of un-shaded part (area of each small square is 1 cm²).

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