Đề thi thử toán AMO lớp 6 năm 2019

According to the table, how many more micrograms of penicillin are present in 10 milliliters of blood drawn from the patient 5 minutes after the injection than are present in 8 millilite[r]

AMO MOCK TEST #2

Grade 6

INSTRUCTIONS

1 Please DO NOT OPEN the contest booklet until the Proctor has given

per-mission to start

2 TIME: 1 hour 30 minutes

3 Attempt all 25 questions Each question scores 1 point No points are

de-ducted for incorrect answers

4 Write your answers neatly on the answer sheet

5 PROCTORING : No one may help any student in any way during the contest

6 No calculators are allowed

7 All students must fill in your Name and School

8 MINIMUM TIME: Students must stay in the exam hall at least 1h 15 min

9 Students must show detailed working and put answers on the answer sheet

10 No spare papers can be used in writing this contest Enough space is provided

for your working of each question

Remark: Counting numbers are whole numbers except 0, i.e 1, 2, 3, 4, 5,

Question 1 Counting by 3 means adding three to previous number (or

we can say that jump by 3 numbers) Here each number is three more than the previous number In counting by three’s, if the first number is 1,

1, 4, 7, 10, 13, 16, 19,

what is the 100th number in the sequence?

Question 2 If 1

3 =

1

A +

1

B where A and B are different counting num-bers, find the value of (A + B)

2

Question 3 For all integers P and Q, P ⊗ Qis defined as P ⊗ Q =

P × Q

2 What is the value of 8 ⊗ (1 ⊗ 6)?

Question 4 The numbers 2, 4, 6 and 8 are a set of four consecutive

even numbers Suppose the sum of five consecutive even numbers is

320 What is the smallest of the five numbers?

Question 5 Each of the smallest boxes in the below figure is a square.

How many different squares can be formed by using the lines in the below figure?

Question 6 A dealer packages marbles in two different box sizes:

small and large boxes One small box holds 5 marbles and a large box holds 12 marbles If the dealer has packaged 99 marbles and used more than 10 boxes, how many boxes has he used in total?

4

Question 7 Soshana looks in a mirror and sees the reflection of a

clock behind her as shown in the figure on the left How many minutes

later will the reflection in the mirror of the same clock next show the

image shown in the figure on the right?

Question 8 Let A and B be the following sets:

A = {21, 22, 23, 24, 25, 26}

B = {12, 13, 14, 15, 16}

Let C be the set of all possible positive differences when an number

from set A is subtracted by an number from set B How many elements

are contained in set C?

Question 9 Two 9cm × 13cm rectangles overlap as shown to form a

9cm × 22cm rectangle What is the area of the overlapping rectangular region?

Question 10 For the first half of the season, Alpha team won 25 of their meets For the second half of the season, they won 37 of their meets If both halves of the season had the same number of games, what is the fewest possible number of wins that they have?

6

Question 11 The small boxes in figures A and B below are congruent

squares If the perimeter of figure A is 48cm, what is the perimeter of

figure B?

Question 12 In the figure shown, the “H” has been formed by

remov-ing two 2×4 rectangles from the top middle and bottom middle of a 6×10

rectangle The “H” is to be completely tiled with 1 × 1 tiles, which come

in boxes of 6 tiles What is the fewest number of boxes of tiles that must

be bought to tile the “H”?

Question 13 Thirteen dots are arranged on a square grid in the

pat-tern below How many different squares can be formed by connecting

at least four of these dots?

Question 14. 13 plums have the same mass as 2 apples and 1 pear 4

plums and 1 apple have the same mass as 1pear How many plums have the mass of 1 pear?

8

Question 15 The complete outside including the bottom of a wooden 4

-cm cube is painted red The painted cube is then cut into 1cm cubes as

in the below figure How many of the 1-cm cubes do not have red paint

on any face?

Question 16 In the "magic square" at the right, the four numbers in

each column, in each row, and in each of the two diagonals, have the

same sum What is the value of N?

10 13

N 12 1

2 15 8

14 9

Question 17 A train can hold 78 passengers The train starts out empty and picks up 1 passenger at the first stop, 2 passengers at the second stop, 3passengers at the third stop, and so forth Given that no one

leaves the train during the trip, after how many stops will the train be full?

Question 18 Find the least value of whole number N, with N > 10, so that the expression 2N − 7 is both a perfect square and a perfect cube

10

Question 19 The numbers from 1through 9 are placed in the grid,

exactly one number per box without repeats The numbers shown at

the end of each row are the products of all numbers in that row The

numbers shown at the bottom of each column are the products of all

numbers in that column What is the sum of the numbers in the four

corners of the 3 by 3 grid?

14 144 180

15 64 378

Question 20 If a kindergarten teacher places her children 4 on each

bench, there will be 3 children who will not have a place However, if

5 children are placed on each bench, there will be 2empty places on

the last bench What is the smallest number of children the class could

have?

Question 21 A six-digit number A4273B is divisible by 72 without re-mainder Find the product of two digits, A and B

Question 22 The sum of the digits of the number 1689 is 24 How many

4-digit numbers, less than 3000, have the sum of their digits equal to 24?

12

Question 23. 21 ten-cent coins are put into four piles so that each pile

has a different number of coins What is the smallest possible number

of coins that could be in the largest pile?

Question 24 In the addition problem below, each letter represents

a digit and different letters represent different digits What three-digit

number does RID represent?

I N

+ R I D

D E E R

Question 25 When a patient receives a penicillin injection, the kidneys

begin removing the penicillin from the body The table below shows the penicillin concentration in a patient’s bloodstream at 5-minute intervals for the 20 minutes immediately following a one-time penicillin injection

Minutes after Penicillin concentration injection (micrograms per milliliter)

According to the table, how many more micrograms of penicillin are present in 10 milliliters of blood drawn from the patient 5 minutes after the injection than are present in 8 milliliters of blood drawn 10 minutes after the injection?

14