Instructions:
* Write down your name on every page.
* Answer all 25 questions.
* You have 60 minutes to work on this test.
* Write your answer in the boxes provided.

Math Problems

1. A pole is 156 cm high. It casts a shadow of length 234 cm. Find the length of the shadow cast by a 104 cm-high pole.

2. The square ABCD is divided into 9 smaller squares as shown in the figure. The perimeter of ABCD is 360 m. Find the perimeter of one smaller square.

3. A farmer has some goats and chickens. He counts 110 legs and 76 eyes. How many goats does he have?

4. The table shows Andi’s grades for Test 1 and Test 2 in Mathematics, Language and Science. In which subject does he show the best improvement in terms of percentage, from Test 1 to Test 2?

5. Complete the magic square so that the vertical sums, horizontal sums and diagonal sums are all equal.

6. Nasir draws 5 straight lines on a piece of paper. What is the maximum number of intersection points can Nasir make?

7. Ade and Tomi are talking about money. Ade says, ”If you give me 1, 000 rupiahs, our money will be equal”. Tomi says, ”If you give me 1, 000 rupiahs, my money will be twice as much as your money”. How much money do they have altogether?

8. A swimming pool is 10 m long and 4 m wide. The shallow end is 1 m deep. The bottom slopes evenly to the other end, where it is 2 m deep. Find the volume of the pool in m^3.

9. In the figure below, the number assigned to the edge connecting two circles describes the sum of two numbers in the circles.

Fill all circles with the appropriate numbers following the above rule.

10. The figure below shows paths in a garden. ABCDEF is a regular hexagon with center O. H is the midpoint of side AB. What is the shortest way to go from H to E along the paths?

11. In a birthday party, all the children are given candies. If each child gets 5 candies, there would be 10 candies left. If each child gets 6 candies, 2 more candies are needed. How many candies are there?

12. A natural number has the following conditions:
* When this number is divided by 4, the remainder is 3.
* When this number is divided by 3, the remainder is 2.
* When this number is divided by 2, the remainder is 1.
Find the smallest number that satisfies the above conditions.

13. Jones, Jennifer, Peter and Ruby are playing a game. Jones thinks of a 3-digit number without saying out and the others guess what number it is.
* Jennifer says : ”I guess it is 765”.
* Peter says : ”I think it may be 364”.
* Ruby says : ”Hmmm…. I choose 784”.
Then Jones answers: ” Each of the numbers you guess coincides with the number in my mind in exactly two digits.” What is this number?

14. The distance from Ani’s house to her school is 800 m. If Ani starts walking from her house at 06:35, she arrives at her school at 07:00. Ani’s running speed is five times of her walking speed. If she wants to run to school and arrives there at 07:00, at what time must she leave her house?

15. Put the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in the boxes below to make a correct sum. Use each number exactly once.

16. The following are different views of the same cube. What is the letter on the opposite side of the letter H?

17. The graph below shows the revenue from selling products A,B,C, and D. If the revenue from selling the product A is 400, 000 rupiahs and the unit price of the product D is 10, 000 rupiahs, find the number of product D sold.

18. There are three consecutive even numbers. Seven times the smallest number equals five times the largest number. Find the sum of the three numbers.

19. The letter in each square represents a number. The sum of the numbers is shown alongside a row or beneath a column, with the exception of the column with an X. Find the value of X.

20. Find the smallest positive integer X such that the sum of the digits of X and of X + 1 are both divisible by 7.

21. What is the maximum number of different triangles that can be formed by using the points A,B,C,D,E, F, G, and H?

22. Find a number which satisfies the following conditions:
* The number is between 8500 and 8700.
* The sum of its digits is 21.
* The number is divisible by 4.
* The number contains different digits.

23. Four different prime numbers A,B,C,D satisfy expression A × (B × C × D ? 1) = 2000. Find A + B + C + D.

24. The shaded area is bounded by two semi-circles and four quarter circles of radius 1 cm each. Find the area of the shaded figure in cm^2.

Score __________
Name ________________________________

1. There are 5 trucks. Trucks A and B each carry 3 tons. Trucks C and D each carry 4.5 tons. Truck E carries 1 ton more than the average load of all the trucks. How many tons does truck E carry?

2. Let A = 200320032003   2004200420042004 and B = 200420042004  2003200320032003.
Find A – B.

3. There are 5 boxes. Each box contains either green or red marbles only. The numbers of marbles in the boxes are 110, 105, 100, 115 and 130 respectively. If one box is taken away, the number of green marbles in the remaining boxes will be 3 times the number of red marbles. How many marbles are there in the box that is taken away?

4. Find the smallest natural number which when multiplied by 123 will yield a product that ends in 2004.

5. Peter has a weigh balance with two pans. He also has one 200 g weight and one 1000 g weight. He wants to take 600 g of sugar out of a pack containing 2000 g of sugar. What is the minimum number of moves to accomplish this task?

6. It takes 6 minutes to fry each side of a fish in a frying pan.  Only 4 fish can be fried at a time. What is the minimum number of minutes needed to fry 5 fish on both sides?

7. John and Carlson take turns to pick candies from a bag. John picks 1 candy, Carlson 2 candies, John 3, Carlson 4 and so forth. After a while there are too few candies to continue and so the boy whose turn it is, takes all the remaining candies. When all the candies are picked, John has 1012 candies in total. What was the original number of candies in the bag?

8. There are five positive numbers. The sum of the first and the fifth number is 13. The second number is one-third of the sum of these five numbers, the third number is one-fourth of this sum and the fourth number is one-fifth of this sum. What is the value of the largest number?

9. In a class of students, 80% participated in basketball, 85% participated in football, 74% participated in baseball, 68% participated in volleyball. What is the minimum percent of the students who participated in all the four sports events?

10. Three digit numbers such as  986, 852 and 741 have digits in decreasing order. But  342, 551, 622 are not in decreasing order. Each number in the following sequence is composed of three digits:  100, 101, 102, 103, …, 997, 998, 999. How many three digit numbers in the given sequence have digits in decreasing order?

11. In the following figure, the black ball moves one position at a time clockwise. The white ball moves two positions at a time counter–clockwise. In how many moves will they meet again?

12. Compute: 1^2 – 2^2 + 3^2 – 4^2 + ……….. – 2002^2 + 2003^2  – 2004^2 + 2005^2

13. During recess one of the five pupils wrote something nasty on the blackboard. When questioned by the class teacher, they answered in following order:
A: “It was B and C.”
B: “Neither E nor I did it.”
C: “A and B are both lying.”
D: “Either A or B is telling the truth.”
E: “D is not telling the truth.”
The class teacher knows that three of them never lie while the other two may lie. Who wrote it?

14. In the figure below, PQRS is a rectangle.    What is the value of a + b + c?

15. In the following figure, if CA = CE, what is the value of x?

]]> http://mathandflash.com/india-2nd-elementary-mathematics-international-contest-iemic/feed/ 0 http://mathandflash.com/international-youth-mathematics-contest-2007-hemic/ http://mathandflash.com/international-youth-mathematics-contest-2007-hemic/#comments Thu, 29 Sep 2011 16:01:42 +0000 admin http://mathandflash.com/?p=819 Individual Competition

Instructions:

• Write down your name, team name and candidate number on the answer sheet.
• Write down all answers on the answer sheet.
• Answer all 15 problems. Problems are in ascending order of level of difficulty. Only NUMERICAL answers are needed.
• Each problem is worth 6 points and the total is 90 points.
• or problems involving more than one answer, points are given only when ALL answers are correct.
• Take ? = 3.14 if necessary.
• No calculator or calculating device is allowed.
• Answer the problems with pencil, blue or black ball pen.
• All materials will be collected at the end of the competition.

1. The product of two three-digit numbers abc and cba is 396396, where a > c. Find the value of abc!

2. In a right-angled triangle ACD, the area of shaded region is 10 cm^2, as shown in the figure below. AD = 5 cm, AB = BC, DE = EC. Find the length of AB!

3. A wooden rectangular block, 4 cm × 5 cm × 6 cm, is painted red and then cut into several 1 cm × 1 cm × 1 cm cubes. What is the ratio of the number of cubes with two red faces to the number of cubes with three red faces?

4. Eve said to her mother, “If I reverse the two-digits of my age, I will get your age.” Her mother said, “Tomorrow is my birthday, and my age will then be twice your age.” It is known that their birthdays are not on the same day. How old is Eve?

5. Find how many three-digit numbers satisfy all the following conditions:
if it is divided by 2, the remainder is 1,
if it is divided by 3, the remainder is 2,
if it is divided by 4, the remainder is 3,
if it is divided by 5, the remainder is 4,
if it is divided by 8, the remainder is 7.

6. A giraffe lives in an area shaped in the form of a right-angled triangle. The base and the height of the triangle are 12 m and 16 m respectively. The area is surrounded by a fence. The giraffe can eat the grass outside the fence at a maximum distance of 2 m. What is the maximum area outside the fence, in which the grass can be eaten by the giraffe?

7. Mary and Peter are running around a circular track of 400 m. Mary’s speed equals 3/5 of Peter’s. They start running at the same point and the same time, but in opposite directions. 200 seconds later, they have met four times. How many metres per second does Peter run faster than Mary?

8. A, B and C are stamp-collectors. A has 18 stamps more than B. The ratio of the number of stamps of B to that of C is 7:5. The ratio of the sum of B’s and C’s stamps to that of A’s is 6:5. How many stamps does C have?

9. What is the smallest amount of numbers in the product 1× 2 × 3× 4 × …× 26 × 27 that should be removed so that the product of the remaining numbers is a perfect square?

10. Evaluate:

11. Train A and Train B travel towards each other from Town A and Town B respectively, at a constant speed. The two towns are 1320 kilometers apart. After the two trains meet, Train A takes 5 hours to reach Town B while Train B takes 7.2 hours to reach Town A. How many kilometers does Train A run per hour?

12. Balls of the same size and weight are placed in a container. There are 8 different colors and 90 balls in each color. What is the minimum number of balls that must be drawn from the container in order to get balls of 4 different colors with at least 9 balls for each color?

13. In a regular hexagon ABCDEF, two diagonals, FC and BD, intersect at G. What is the ratio of the area of ?BCG to that of quadrilateral FEDG?

14. There are three prime numbers. If the sum of their squares is 5070, what is the product of these three numbers?

15. Let ABCDEF be a regular hexagon. O is the centre of the hexagon. M and N are the mid-points of DE and OB respectively. If the sum of areas of ?FNO and ?FME is 3 cm2, find the area of the hexagon.

Below are Mathematics Olympiad questions that ever held in Jakarta, Indonesian in 2006. There are 25 questions with short answers, and hopefully usefull for you to improve your math skill!.

Instructions:
* Write down your name and country on the answer sheet.
* Write your answer on the answer sheet.
* Answer all 25 questions in English.
* You have 60 minutes to work on this test.
* Use pen to write your answer.

1. Three signal lights were set to flash every certain specified time. The first light flashes every 12 seconds, the second flashes every 30 seconds and the third one every 66 seconds. The signal lights flash simultaneously at 8:30 a.m. At what time will the signal lights next flash together?

2. Dina’s money consists of ten-thousand and five-thousand rupiah bills. The number of ten-thousand bills is three more than twice the number of five-thousand bills. If Dina has Rp355, 000, what is the number often-thousand bills that she has?

3. The principal of Makmur Jaya Elementary School is replaced every 4 years. At most how many principals will the school have from 2006 to 2020?

4. The area of the shaded region shown in the figure below is 98cm^2. Find the length of a.

5. The sequence below is arranged by using numbers 1, 2 and 3 only: 1, 2, 2, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, . . . What is the 100th number?

6. Every whole number larger than 7 can always be expressed as a sum of 3’s, 5’s, or both. For example, 9 = 3 + 3 + 3, 10 = 5 + 5 and 19 = 5 + 5 + 3 + 3 + 3. With the rule that 5 always comes before 3, how many ways can we express 444?

7. Consider all possible numbers between 100 and 2006 which are formed by using only the digits 0, 1, 2, 3, 4 with no digit repeated. How many of these are divisible by 6?

8. Two runners run in opposite directions from the same starting line. They run around a field which has 300 m perimeter. If the first runner runs at 150 m/minute and the second one runs at 125 m/minute, how many times will the two runners pass each other in the first 20 minutes?

9. The ratio of the number of students in Class A to Class B is 1:2. The ratio of the respective average test scores is 8:9. If the average score of class A is 72, find the average score of all the students.

10. In the following figures, the area of the biggest equilateral triangle is 16cm2. A new triangle is formed by connecting the midpoints of the sides of the previous triangle. If the pattern continues, find the area of the smallest triangle in Figure 5.

11. Each vertex of a regular pentagon is connected to the other vertices as shown in the figure below so that the pentagon is divided into 11 non-overlapping regions. How many non-overlapping regions can be obtained if we do the same procedure to a regular hexagon?

12. A 20cm×40cm×80cm wooden block is sliced into four small identical blocks. Find the largest possible sum of the surface areas of the small blocks.

13. The perimeters of a square and an equilateral triangle are equal. If the length of the side of the equilateral triangle is 8 cm, find the area of the square.

14. The faces of a cube are to be painted so that two faces with a common edge are painted with different colours. Find the minimum number of colours needed to do this.

15. How many non-congruent triangles with perimeter 11 have integer side lengths?

16. The following magic square is to be filled with numbers 17, 18, …, 24 so that the sums of numbers in every column, every row and the two diagonals are equal. Which number should be in the cell with the star (*)?

17. The faces of a dice are marked with dots from 1 to 6. The total number of dots on two opposite faces (top-bottom, left-right, front-back) is 7. Four dices are arranged as shown below. The faces of two dices that touch each other have the same number of dots. What is the total number of dots on the faces that touch each other?

18. Every edge of a cube is colored either red or green. In order to have at least one red edge on every face of the cube, find the minimum number of edges that must be colored red.

19. Let A,B,C represent three different digits such that:

Find the largest possible value of the 3-digit number ABC.

20. When 31513 and 34369 are each divided by a certain 3-digit number,
the remainders are equal. Find this remainder.

21. What is the volume of the concrete foot bridge shown below? (use phi = 22/7)

22. The sides of a trapezoid touch the circle of radius 10 as shown in the figure below. The non parallel sides are of lengths 23 and 27 cm respectively. Find the area of trapezoid.

23. Each of the letters A,D,E,K, S,W and Y represents a different one of the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such that

Which digit does E represent?

24. Dogol writes a sequence of five non-negative 1-digit numbers on the blackboard. He then erases two consecutive numbers and replaces them with their difference. He obtains the sequence 5, 0, 3, 5 on the board.
How many possible sequences can he start with?

25. If you read the picture on the left below, it says there are 3 ones, 1 two and 1 four, which is correct. Fill in the four boxes in the picture on the right to make it correct too. Write down the four digits from left to right as a 4-digit number.

[swfobj src="http://mathandflash.com/wp-content/uploads/2011/04/find-volume.swf" width="400" height="300" allowfullscreen="true"]

1. If a = 15 and b = -9, what is the value of a² + 2ab + b² ?
2. A circular wind power generator turns at a rate of 30 complete revolutions per
minute. Through how many degrees does it turn in one second ?

Solution ?

Solution 1
If a = 15 and b = -9, then a² + 2ab + b² = (a + b)² = (15 + (-9))²= 6² = 36.

Solution 2
Since there are 60 seconds in a minute, the wind power generator turns
30/60=1/2 of a revolution each second.
Since a full revolution is 360^o, then the generator turns 1
2(360^o) = 180^o each second.
(Alternatively, the generator turns through 30×360^o in one minute, so through 30×360^o÷60 =180^o in one second)

2.    The prime numbers between 10 and 20 are needed together to form the number Q. What was the larges prime number divisor of Q ?
A.    2
B.    3
C.    5
D.    7

3. The tenth of our planet, earth is covered with land and rest is covered within water. Ninety-seven percent of water is salt water and the rest is fresh water. What is percentage of earth is covered in fresh water ?
A.    20.1%
B.    79.9%
C.    32.1%
D.    2.1%

Given that the distance of a place A to place B is 10 km and the C right in the middle of the line AB. Determine how the difference in distance traveled by the first choice and the distance traveled by the second option !

Click read more to know the answer

Answer:
The difference is 0 (zero)

If each row, column and diagonal on the square at the top should be filled by all the numbers 1, 2, 3 and 4 the value of K + N is ….

A. 3
B. 4
C. 5
E. 6

Click read more to know the answer.
Answer:
A.3

Answer:
$84

Order the following from least to greates:
1/2, 0.25, 1/6, -0.5, 0.3, -2

Answer:
-2, -0.5, 1/6, 0.25, 0.3, 1/2