Đề thi thử toán AMO lớp 9 năm 2018- Đề số 2| KÌ THI OLYMPIAD

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<b>AMO MOCK TEST #2 - GRADE 9</b>

<b>Time allowed: 90 minutes</b>

<b>INSTRUCTIONS</b>Please read all the instructions below carefully.

1. Please<b>DO NOT OPEN</b>the contest booklet until the Proctor has given permission to start.

2. Attempt all 15 questions. Each question scores 1 point. No points are deducted for incorrect answers.
3.<b>No calculators</b>are allowed, but dictionaries are.

<b>MARKS</b>

<b>Question 1.</b>The graph shows the temperature forecast and the actual temperature of a city on ten days.
Find the maximum deviation of actual temperature from the forecast, in degree Celcius.

Submit your answer at />

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<b>Question 2.</b>Given that

1
10+

9

1
9+1

+ 1

a+ 1

b+ 1

b+1

b

=1.

Notethataandbarewholenumbers,findthevalueofa+b.

<b>Question 3.</b>A water tank has two types of taps (type-A and type-B). A tap of type-A can fill the tank in
10 minutes, while a tap of type-B can fill the same tank in 20 minutes. If there are 3 type-A taps and 4
type-B taps that can be used to fill the tank, how many minutes will it take to fill an empty tank?

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<b>Question 4.</b>A four digit numberabcdis a multiple of 11 withb+c =aand the two digit numberbcis a
square number. What is the greatest value ofa+b+d?

<b>Question 5.</b>A group of workers is paving a road. If they pave 200mof the road a day, they will need 3
more days to finish the work. If they pave 240mof the road a day, they will finish the work 2 days in
advance. How long is the road, in meter?

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<b>Question 6.</b>Mrs. Darlie has a silver ring, a golden ring and a diamond ring. She put them on her left
hand. Each ring can be on any of the five fingers. When there are two or three rings on the same finger,
if the order in which they are put is different, that count as a different way. How many different ways
for Lea to put on these rings ?

<b>Question 7.</b>

16 21 26 31 36
21 28 35 42 49
21 ? 45 57 69

48 46 ? 38 34
16 42 68 ? 120
What is the total value of numbers in “?” boxes ?

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<b>Question 8.</b> In a collection of black, yellow, and orange marbles, there are 35% more black marbles
than yellow marbles, and there are 60% more orange marbles than black marbles. If there are 135 black
marbles, what is the total number of marbles?

<b>Question 9.</b>The cost price of a TV set is $4800. It is marked at 20% above its cost price but later sold at
75% of its selling price. What is the amount of loss, in dollar?

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<b>Question 10.</b>In the diagram,BE= AC,_CAE[ =30◦ and [_AEB =70◦. Find [_ABC_{, in degree.}

70◦
30◦

B E C

B0
B₁0

A

<b>Question 11.</b> The product of David’s grandfather and David’s father ages is 2268. The product of
David’s grandfather, David’s father and David is a square number. How old is David’s grandfather?

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<b>Question 12.</b>LetP(x)be a polynomial with degree 3 such thatP(1) =3,P(2) =3,P(3) = 7,P(4) =21.
Find the value ofP(5).

<b>Question 13.</b>Observe the figures below. What is the value of missing numberx?

35 ₂₉

68 74

17 94

158 81

46 23

87 x

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<b>Question 14.</b>There are some aunts running on a piece of wood AB, starting from either A or B. Each ant
needs 13 minutes to climb from A to B. If there is one running from A to B and one running from B to A
at the same time, they will meet each other at C. From C, they change their direction and come back to
their beginning. How many seconds at least needed to ensure that there is no ant on the piece of wood ?

<b>Question 15.</b> The table below shows the number of pair of shoes sold in a day. Note that there are 6
kinds of shoes in sizes: 36, 37, 38, 39, 40, 41 and 42.

<b>Size</b> 36 37 38 39 40 41 42

<b>Number</b> 14 28 30 13 X Y 20

The mean pairs of shoes sold in that day was 19. The median pairs of shoes was 16. Find the number of
shoes in size 40 sold in that day.

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<b>Question 16.</b> ABCDis a rectangle which is divided into 4 triangles as the figure below. The areas of

AMB, AMDand DMCare 20cm2, 38cm2, 120cm2respectively. What is the area ofBMCincm2?

38

20

120

x

A _B

C
D

M

<b>Question 17.</b>Children A, B and C take an examination. Total score of A and B is 6 less than that of C.
Total score of B and C is 16 more than that of A. Total score of C and A is 8 more than that of B. What is
the product of the scores of A, B, and C ?

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<b>Question 18.</b>If the weight of a cuboid of size 20cm×5cm×20cm is 20kg, then find the weight of an
another cuboid of same material with the size 20cm×5cm×19cm, in kilogram.

<b>Question 19.</b>Givenaandbare different two non-negative integers such that
1

a +

1

b =3.

What is the value ofa+b?

<b>Question 20.</b>A civil engineer figures out that if the efficiency of a road work can be increased by 40%
then the number of working days can be reduced by 20 days. How many days was the road work
scheduled to take in original plan ?

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<b>Question 21.</b> If Nur writes all the numbers from 5 to 75, which are divisible by 5. What will be the
number at 7th position?

<b>Question 22.</b> The average weight of Alison and Belinda is 26kg. The average weight of Alison and Carol
is 22kg. The average weight of Belinda and Carol is 24kg. Find the weight of Carol.

<b>Question 23.</b> There is a flight of 6 steps in a staircase. John can take single or double steps each time
when he climbs the staircase. In how many ways can he complete the climbing ?

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<b>Question 24.</b> Mr. David starts from town A at 0h to come to town C. 2 hours later, Mr. Wilson starts
from town B and come to town C with the same direction as Mr. David. Given that town B is 20km
to the right of town A. Consider that their speed are constant. The line graph I and II below show the
relationship between the distance Mr. David and Mr. Wilson travel and the time each needs to complete
that distance respectively.

What is the sum of Mr. David’s speed and Mr. Wilson’s speed ?

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<b>Question 25.</b>When converting from a decimal number to a binary number, we have:
1=1,

2=10,

3=11,
4 =100,
5 =101,
6 =110,
7 =111,
8=1000,
9=1001,
10 =1010.

What is the value of a binary number 1010110 in decimal number ?

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<b>ANSWER KEY</b>

1. 2 14. 780

2.

1

0 15. 12

3. 2 16. 147

4. 19 17. 60

5. 32 18. 19

6. 210 19. 16

7. 169 20. 70

8. 72 21. 35

9. 648 22. 262

10. 40 23. 13

11. 63 24. 120

12. 51 25. 86

13. 744

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