Prepare for AMO 2019 – Grade 4 – Đề luyện thi toán tiếng anh AMO 2019 – Khối 4

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Đề luyện thi toán tiếng anh AMO 2019 – Khối 4

Prepare for AMO 2019 – Grade 4

Week 1

Exercise 1. Find the missing term in the following sequence:

1,2,4,8,16,(),(),…

Exercise 2. Find the missing number.

Exercise 3. What two numbers should replace the question marks?

10, 30, 32, 96, 98, 294, 296, ?, ?

Exercise 4. Compute the following sums:

1 + 2 + 3 + 4 + … +18 + 19 + 20.

Exercise 5. Given a sequence: 2, 0, 1, 9, 2, 0, 1, 9, 2, 0, 1, 9, 2, ….

1. What is the 37th number?
2. What is the sum of the first 50 term?

Exercise 6. There are 14 rows of seat in a school hall. There are 70 seats in the last row. If there is
an increase of 3 seats, staring from the first row, how many seats are there in the school hall?

Exercise 7. Six people entered a block building contest. Lynda built her pile of blocks twice as high
as Selwyn’s. Michelle created a pile that was three times higher than Lynda’s pile. Warren built his
pile one block higher than Michelle’s. Jane’s pile of blocks was six higher than Warren’s. If Adrian
piled up 27 blocks, which was two blocks higher than Jane’s pile, how high was each person’s pile?
How many blocks would be needed altogether?

Exercise 8. Mark, Neil, Frances and Patrick entered a skipping competition. Patrick skipped eight
more times than Mark before his foot caught on the rope. Mark jumped three more times than Neal. Neal skipped half as many times as Frances. Frances skipped eighty times. How many times
did Patrick skip?

Exercise 9. When Ariella climbs aboard there are already some people sitting the bus. At the next
bus stop an additional five people get on and two people get off. Two stops later seven people
climb on board. All 15 people get off the bus at the ferry. How many were on the bus when Ariella
climbed on?

Week 2

Exercise 1. A road is 650m long. If trees are planted on both its sides at intervals of 10m. How
many trees are planted on the both sides of the road if both ends of the road are also planted with
trees?

Exercise 2. 28 trees are planted in a straight line. The distance between two adjacent trees is 13m. What is the exact distance between the first and the last tree in this line?

Exercise 3. There are 61 trees planted along the road with trees planted at opposite ends. The distance between every two adjacent trees is 8 m. If some lamp posts are to be placed along the opposite side of the road at regular intervals of 10 m, how many lamp posts are placed if both ends of the road are to be placed with lamp posts?

Exercise 4. Count the number of triangles in the figure.

Exercise 5. Find the number of rectangles in the figure below.

Exercise 6. Find the number of cubes in the given figure.

Exercise 7. Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?

Exercise 8. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is
the age of the youngest child?

Exercise 9. The sum of the present ages of a son and his father is 60 years. Six years ago, father’s
age was five times the age of the son. After 6 years, what will be son’s age?

Week 3

Exercise 1. There are 61 mangoes in carton X and 59 mangoes in carton Y. How many mangoes must be transferred from carton X to carton Y so that the number of mangoes in carton Y is 3 times the number of mangoes in carton X?

Exercise 2. It is not in the square. It is an even number.

It is greater than any number in the triangle.

What number is it in the rectangle ?

Exercise 3. Becky is meeting her friend at the library at 8:45 p.m. It takes her 25 minutes to get to the library. What time will she need to leave her house to arrive on time?

Exercise 4. Alan, Ben, Chris, Dave and Emma were eating a big cake. After eating, there was one slice left, and they decided to leave it for Frank but someone ate it! Frank knew that these 5 people were each telling one truth and one lie:

Alan says: “It wasn’t Emma. It was Ben.”

Ben says: “It wasn’t Chris. It wasn’t Emma.”

Chris says: “It was Emma. It wasn’t Alan.”

Dave says: “It was Chris. It was Ben.”

Emma says: “It was Dave. It wasn’t Alan.”

Who ate the last slice of cake?

In your answer sheet, write 001 for Alan, 002 for Ben, 003 for Chris, 004 for Dave, 005 for Emma.

Exercise 5. Thomas has $9 more than Tom. Alice has $20 fewer than Tom. The total amount of
money they have is $199. How much money does Thomas have?

Exercise 6. Aldith, Bogdan and Chedomir are gathered in a medieval tavern. One of them is a knight who always tells the truth, one of them is a knave who always lies, and one of them is a jester who can either tell the truth or lie.

Aldith says: “Iam not a knave.”

Bogdan says: “Jam a knave.”

Chedomir says: “J am not a knave.”

Who is the jester?

In your answer sheet, write 001 for Aldith, 002 for Bogdan, 003 for Chedomir.

Exercise 7. It takes John 25 minutes to walk to the car park and 45 minutes to drive to work. At
what time should he get out of the house in order to get to work at 9:00 a.m

Exercise 8. In a basketball game, Marc, Jackson, and Cole scored 106 points altogether. Marc scored 15 more points than Jackson. Jackson scored 7 fewer than Cole. How many points did Cole score?

Exercise 9. Erin got in her car and started driving toward her grandmother’s house. After driving for 2 hours, Erin took a break for 45 minutes to have a snack. Then Erin drove 1 hour and 15 minutes and finally arrived at her grandmother’s house at 11:30 a.m. What time did Erin start
driving?

Week 4

Exercise 1. There are chickens and rabbits in a cage. Look at the top of the cage – there are totally
35 heads. Look at the bottom of the cage – there are 94 legs. How many rabbits are there in the
cage?

Exercise 2. There are 45 cars and motorbike in a car park. There are a total of 132 wheels. How
many motorbikes are there?

Exercise 3. The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

Exercise 4. Five families are building project homes in an isolated area. Roads will have to be built
to connect each house with all the other houses. How many roads have to be built?

Exercise 5. In the Year Four classroom the desks are organised in equal rows. Jane sits in the desk that is fourth from the front and third from the back. There are four desks on the right but only one to the left of Jane ’s desk. How many desks are in the room?

Exercise 6. Each student in Grade Four was given 20 raffle tickets to sell to raise funds for their school. The price of each ticket is $1.50. If there are 30 students in grade 4, and they all sold all of their tickets, how many dollars was raised altogether?

Exercise 7. Praveen purchased 3 pens at the rate of $14.2 each, 6 books at the rate of $64.1 each, 7 maps at the rate of $8.8 each and 9 notebooks at the rate of $7.8 each. How many dollars did she spend in all?

Exercise 8. Julie had $500. She spent 20% of it on clothes and then 25% of the remaining money
on CDs. How many dollars did Julie spend?

Exercise 9. Jack had $10.00. He bought a pair of socks for $2.30 and a pair of gloves for $5.50. How
many cents did he have left?

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