Prepare for AMO 2019 – Grade 5 – Đề luyện thi toán tiếng anh AMO 2019 – Khối 5
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Đề luyện thi toán tiếng anh AMO 2019 – Khối 5
Prepare for AMO 2019 – Grade 5
Week 1
Exercise 1. An operation is defined as:
3 * 4 = 2
5 * 3 = 7
8 * 2 = 14
Find the value of A = 9 * 3
Exercise 2. Henry is 4 years old and his mother is 28 years old. What will be the age of his mother when she is three times as old as Henry?
Exercise 3. A product of a number and itself is call a square number. Each pattern below is formed by identical squares. Which pattern will that be there are 169 squares?
Exercise 4. Find the number represented by ….. in:
10 + 9 + 8 x 7: ….. + 6 – 5 x 4 – 3 x 2 = 1.
Exercise 5. A new operation is defined as:
3 ⊕ 4 = 3 + 4 + 5 + 6 = 18
5 ⊕ 6 = 5 + 6 + 7 + 8 + 9 + 10 = 45
Find the value of m, if m ⊕ 5 = 485
Exercise 6. The sum of a father’s age and his son’s age is 68. The father’s age was 3 times his son’s age eight years ago. How old are they now?
Exercise 7. Jonathan is 10 years old. His brother, Joseph, is 14 years old. How old will each boy be when the sum of their ages is 50?
Exercise 8. Study the pattern below
(a) How many hexagons are there in figures 10?
(b) Which figures will that be when there are 78 hexagons?
Exercise 9. A pattern of hexagons is formed in two rows using identical sticks.
How many hexagons can be formed using 411 sticks?
Week 2
Exercise 1. Find the missing numbers in the parentheses provided.
Exercise 2. Find the value of
T = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 +13 +14 +15 + 16 + 17.
Exercise 3. Find the value of z.
3, 5, 9, 15, 23, 33, 45, z, 75…
Exercise 4. Given a sequence
3, 3, 1, 9, 4, 3, 3, 1, 9, 4, 3, 3, 1, 9, 4, …
(a) What is the 36th number?
(b) What is the sum of the first 50 terms?
Exercise 5. There are 20 players in a chess tournament.Each player must play exactly one match against the rest of the players. How many matches are there in the competition?
Exercise 6. Rose saved $25 in the first month, $40 in the second month, $55 in the third, and so on. The amount of money she saved in the last month was $190. How much money did Rose saved in total?
Exercise 7. There are a total of 24 cows and chickens on a farm. Given that total number of legs on the farm is 78, find the number of cows and the number of chickens.
Exercise 8. For every 5 chickens a farmer has, he has 3 goats. Altogether, there are 132 legs. How many chickens and goats are there?
Exercise 9. A spider has 8 legs and a dragonfly has 6 legs. There are 14 spiders and dragonflies altogether. There are 100 legs in all. Find the number of spiders and the number of dragonflies.
Week 3
Exercise 1. A van was travelling from Town A to Town B. If it increased its speed by 15 km/h, it would take 4 hours, instead of 5 hours, to reach Town B. Find the distance between the two towns.
Exercise 2. Alan and Ben were having a ninety-meter race. When Alan was 26m away from the finishing point, Ben was 8m ahead of him. How far was Alan from the finishing line when Ben finished the race
Exercise 3. Peter was walking from the library to the mall. At the same time, Jane was walking from the mall to the library on the same road. They met 5 minutes later. Given that their walking speeds were 60m/min and 50 m/min respectively, what was the distance between the library and the mall?
Exercise 4. In a building, there are 25 steps in the staircase leading from one storey to another.
How many steps are there from the second to the tenth storey in that building? (Assume the number of steps in the staircase is the same)
Exercise 5. The stretch of road leading to Cindy’s house is to be planted with some trees at regular intervals of 15m, and trees are planted at opposite ends of the road. If the road is 900m long, how many trees are to be planted along that stretch of road?
Exercise 6. Lamp posts are planted at regular intervals of 30 m along a 1800-metre road. If the lamp posts are placed at opposite ends of the road, how many lamp posts are placed along the road?
Exercise 7. How many ways are there to go from point A to point B following the movements of → and ↓?
Exercise 8. An expo hall is divided into 24 rooms as shown. In how many ways can you walk from Room A to Room B while passing through Room P? [Hint: Follow the movements of → and ↓]
Exercise 9. How many shortest paths are there from A to B that pass through P without passing through Q?
Week 4
Exercise 1. Where
. What is value of x?
Exercise 2. The Cheshire Senior Center is hosting the bingo night; $2400 in prize money will be given away. The first winner of the night will receive 1/3 of the money. The next ten winners will receive 1/10 of the remaining amount. How many dollars will each of the ten winners receive?
Exercise 3. Joey, Aaron, Barbara, and Stu have been collecting pennies and putting them in identical containers. Joey’s container is 3/4 full, Aaron’s is 3/5 full, Barbara’s is 2/3, and Stu’s is 2/5 full. Find the sum of the numerator and the denominator of the person has the most pennies?
Exercise 4. What percent of the figure below is shaded?
Exercise 5. Michelle purchases a vocation home with her sisters. Michelle has $40,000 invested in
the property, which is worth $400,000. What percent of the property does Machelle own?
Exercise 6. Kyra’s weekly wages are $800. A Social Security tax of 5% and a State Disability Insurance of 2% are taken out of her wages. What is her weekly paycheck, assuming there are no other deductions?
Exercise 7. Among Kim and two other friends, Bernice is the lightest and Sabrina is the heaviest.
The table below shows the total weight of two girls weighing themselves.
| 1st reading | 45kg |
| 2nd reading | 55kg |
| 3rd reading | 50kg |
Find the weight of Sabrina ?
Exercise 8. Mr Wood and Mr Smith each have two children below 9 years old. Below shows some information about their children.
- Mike is 3 years younger than his brother.
- Royston is the oldest among the four children.
- Sean’s age is half of Mr Wood’s child’s age.
- Jack is 1 year older than Mr Smith’s younger child.
- Each family had only one child three years ago.
If the ages of the children are different, can you find Jack’s age?
Exercise 9. Four teams are competing against one another for District Volleyball Championship.
Every team must play exactly once against the other three teams. So far, Team A has played 3 matches, Team B has played 2 matches and Team D has played 1 match. How many matches has Team C played?
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