Hopefully this math problems will be helpful for your learning.

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Answer Key

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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.

Time limit: 90 minutes

Instructions:

-Write down your name, team name and candidate number on the answersheet.
-Write down all answers on the answer sheet. Only Arabic NUMERICALanswers are needed
- Answer all 15 problems. Each problem is worth 1 point and the total is 15points.
- For problems involving more than one answer, points are given only when
- ALL answers are corrected.
- 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. Starting from the central circle, move between two tangent circles. What is the number of ways of covering four circles with the numbers 2, 0, 0 and 8 inside, in that order?

2. Each duck weighs the same, and each duckling weighs the same. If the total weight of 3 ducks and 2 ducklings is 32 kilograms, the total weight of 4 ducks and 3 ducklings is 44 kilograms, what is the total weight, in kilograms, of 2 ducks and 1 duckling?

3. If 25% of the people who were sitting stand up, and 25% of the people who werestanding sit down, then 70% of the people are standing. How many percent of the people were standing initially?

4. A sedan of length 3 metres is chasing a truck of length 17 metres. The sedan is
travelling at a constant speed of 110 kilometres per hour, while the truck is travelling at a constant speed of 100 kilometres per hour. From the moment when the front of the sedan is level with the back of the truck to the moment  when the front of the truck is level with the back of the sedan, how many seconds would it take?

5. Consider all six-digit numbers consisting of each of the digits ‘0’, ‘1’, ‘2’, ‘3’, ‘4’ and ‘5’ exactly once in some order. If they are arranged in ascending order, what is the 502^nd number?

6. How many seven-digit numbers are there in which every digit is ‘2’ or ‘3’, and
no two ‘3’s are adjacent?

7. How many five-digit multiples of 3 have at least one of its digits equal to ‘3’?

8. ABCD is a parallelogram. M is a point on AD such that AM=2MD, N is a point on AB such that AN=2NB. The segments BM and DN intersect at O. If the area of
ABCD is 60 cm2, what is the total area of triangles BON and DOM?

9. ABCD is a square of side length 4 cm. E is the midpoint of AD and F is the midpoint of BC. An arc with centre C and radius 4 cm cuts EF at G, and an arc with centre F and radius 2 cm cuts EF at H. The difference between the areas of the region bounded by GH and the arcs BG and BH and the region bounded by EG, DE and the arc DG is of the form m? ?n cm², where m and n are integers. What is the value of m+n?

10.  In a chess tournament, the number of boy participants is double the number of girl participants. Every two participants play exactly one game against each other. At the end of the tournament, no games were drawn. The ratio between the number of wins by the girls and the number of wins by the boys is 7:5. How many boys were there in the tournament?

11. In the puzzle every different symbol stands for a different digit.

What is the answer of this expression which is a five-digit number?

12. In the figure below, the positive numbers are arranged in the grid follow by the arrows’ direction.

For example,
“8”is placed in Row 2, Column 3.
“9” is placed in Row 3, Column 2.

Which Row and which Column that “2008” is placed?

13. As I arrived at home in the afternoon. The 24-hour digital clock shows the time as below (HH:MM:SS). I noticed instantly that the first three digits on the platform clock were the same as the last three, and in the same order. How many times in twenty four hours does this happen?

Note: The clock shows time from 00:00:00 to 23:59:59.

Instructions:

* Write down your name and country on every page.

* Answer all 6 questions.* You have 120 minutes to work on this test.

* Write down your answer on the provided answer sheets.

1. We are given a number of equilateral triangles with lateral length 1 cm. They come in two colors, yellow and blue. Three blue and one yellow triangles can be arranged to make an equilateral triangle of lateral size 2 cm (see 1st Pattern below). Six blue and three yellow triangles are arranged to form an equilateral triangle of lateral size 3 cm (see 2nd Patternbelow).

a. How many blue triangles and yellow triangles are required in the arrangement with lateral length 6 cm?

b. If you would like to make a similar arrangement to form an equilateral triangle of lateral size 10 cm, how many blue triangles and yellow triangles are needed?

c. If you would like to make equilateral triangle of lateral size 20 cm, how many blue triangles and yellow triangles are needed?

2. We define a trapezoid as a quadrilateral, which has a pair of parallel laterals; another pair of laterals are not parallel. In the rectangular arrangement below, there are exactly three noncongruent trapezoids. One of them is BCIG.

a. Find the other two non-congruent trapezoids.

b. Find the other 7 trapezoids which are congruent to BCIG.

c. What is the total number of trapezoids that can be made on the arrangement (both congruent and non-congruent, including BCIG).

3. There are 96 distinct ways an I-tromino (1 × 3 rectangular tile) can be positioned on squares of an 8 × 8 chessboard, along the lines of the chessboard. There are 48 vertical positions and 48 horizontal positions. (see picture).

a. In how many distinct ways can an V-tromino (see picture) be positioned on squares of the chessboard?

b. In how many distinct ways can a T-tetramino (see picture) be positioned on squares of the chessboard?

c. In how many distinct ways can an L-tetramino (see picture) be positioned on squares of the chessboard?

4.  Right-isosceles triangles are used to make various arrangements, so that the arrangements contain squares, as in the following illustrations:

1st illustration: Using two triangles, we can make an arrangement, which contains one square: ABCD.

2nd illustration: Using four triangles, we can make an arrangement, which contains two squares: ABEF and BCDE.

3rd illustration: Using eight triangles, we have six squares: ABEF,BCDE,EDIH, FEHG,BDHF and ACIG.

a. Using 10 of such triangles, how many squares at most can we find?

b. How about using 12 triangles?

c. How about using 18 triangles?

d. How about using 24 triangles?

5. Popon is to deliver newspapers along the streets in his neighborhood. He is paid by the distance he makes, and thus the farther he makes, the higher the pay is. While he can cross any intersection as many times as he likes, he cannot pass any street more than once ( a street is one segment between 2 adjacent points). For example, in a neighborhood which looks like this, Popon is to start from K and to finish at O. To get the highest payment, he takes the longest possible route. One possibility is indicated by 1-2-3-4-5-6-7-8 in the figure below.

If the neighborhood looks like the following picture, what is the longest possible route from A to B? Trace and indicate the route by writing numbers 1,2,3,… on the streets of the route.

The following figures show a triangular pyramid and some of its nets.

You are given 3 sheets of graph paper to work on ( you may not use them all), and one sheet of pink paper. You are asked to draw the largest cube net on the graph paper, such that the cube net fits the pink paper.

Best Regards!!!

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/indonesia-elementary-mathematics-international-contest-inaemic-2006/ http://mathandflash.com/indonesia-elementary-mathematics-international-contest-inaemic-2006/#comments Mon, 24 Oct 2011 10:15:34 +0000 admin http://mathandflash.com/?p=840

Problems:

1. When Anura was 8 years old his father was 31 years old. Now his father is twice as old as Anura is. How old is Anura now?

2. Nelly correctly measures three sides of a rectangle and gets a total of 88 cm. Her brother Raffy correctly measures three sides of the same rectangle and gets a total of 80 cm. What is the perimeter of the rectangle, in cm?

3. Which number should be removed from: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 so that the average of the remaining numbers is 6.1?

4. The houses in a street are located in such a way that each house is directly opposite another house. The houses are numbered 1, 2, 3, … up one side, continuing down the other side of the street. If number 37 is opposite number 64, how many houses are there in the street altogether?

5. There are 6 basketball players and 14 cheerleaders. The total weight of the 6 basketball players is 540 kg. The average weight of the 14 cheerleaders is 40 kg. What is the average weight of all 20 people?

6. How many natural numbers less than 1000 are there, so that the sum of its first digit and last digit is 13?

7. Two bikers A and B were 370 km apart traveling towards each other at a constant speed. They started at the same time, meeting after 4 hours. If biker B started 1/22 hour later than biker A, they would be 20 km apart 4 hours after A started. At what speed was biker A traveling?

8. In rectangle ABCD, AB = 12 and AD = 5. Points P, Q,R and S are all on diagonal AC, so that AP = PQ = QR = RS = SC. What is the total area of the shaded region?

9. In triangle ABC, AP = AQ and BQ = BR. Determine angle PQR, in degrees.

10. In the equation below, N is a positive whole number.

A numbered card is placed in each box. If three cards numbered 1, 2, 3 are used, we get 2 different answers for N, that is 2 and 4. How many different answers for N can we get if four cards numbered 1, 2, 3, and 5 are used?

11. A mathematics exam consists of 20 problems. A student gets 5 points for a correct answer, a deduction of 1 point for an incorrect answer and no points for a blank answer. Jolie gets 31 points in the exam. What is the most number of problems she could have answered (including correct and incorrect answers)?

12. Joni and Dini work at the same factory. After every nine days of work, Joni gets one day off. After every six days of work, Dini gets one day off. Today is Joni’s day off and tomorrow will be Dini’s day off. At least how many days from today they will have the same day off?

13. In a bank, Bava, Juan and Suren hold a distinct position of director (D), manager (M) and teller (T). The teller, who is the only child in his family, earns the least. Suren, who is married to Bava’s sister, earns more than the manager. What position does Juan hold? Give your answer in terms of D, M or T.

14. The following figures show a sequence of equilateral triangles of 1 square unit. The unshaded triangle in Pattern 2 has its vertices at the midpoint of each side of the larger triangle. If the pattern is continued as indicated by Pattern 3, what is the total area of the shaded triangles in Pattern 5, in square units?

15. There are five circles with 3 different diameters. Some of the circles touch each other as shown in the figure below. If the total area of the unshaded parts is 20 cm2, find the total area of the shaded parts, in cm2.

]]> http://mathandflash.com/indonesia-elementary-mathematics-international-contest-inaemic-2006/feed/ 0 http://mathandflash.com/asean-primary-schools-mathematics-olympias-2003-essays/ http://mathandflash.com/asean-primary-schools-mathematics-olympias-2003-essays/#comments Sat, 08 Oct 2011 17:00:59 +0000 admin http://mathandflash.com/?p=832

Directions
1. Answer all 15 problems.
2. Show all works. Do not give theanswer only.
3. You have 90 minutes to work on this test.

1. Now we are in the year 2003. The ratio of ages of my father, my mother and my youngers brother is 12:9:1. Five years from now, my father will be 41 years old. In what year was my younger brother born?

2. Laila’s saving in a bank is $100. Tina’s saving is $40. Every end of week, Laila withdraw $3 from her savings. At the same time, Tina always deposit $2.40 into her savings. After how many weeks will Laila’s savings be $6 than Tina’s savings?

3. The product of two positive integers is even, but not divisible by 4. Is their sum odd or even?

4. On the table, there are 6 coins each of values $5, $10, and $50. Deni takes $75. The number of coins Deni takes is more than 5, but less than 9. Does Deni take all the three types of coins? If not, which type does he not take?

5. The weight of small box, two medium boxes and large box altogether is 10 kg. The weight of small box, two medium boxes and two large boxes altogether is 15 kg. What is the total weight of two small boxes and four medium boxes?

6. Replace the letter A with an modd digit and the letter B with an even digit, so that 12 is a factor of the number A579B. Find the possible values of A579B.

7. Find the missing digits.

8. Find the total area of the shaded regions in the figure.

9. In the following figure, the three squares have equal areas. Determine wheter the areas of the three shared regions in each square are also equal.

10. If the patters below is continued, what is the percentage of the area of the shaded regions in third picture compared to the are of the largest square?

11. Four wheel A, B, C, D are connected by belts, see figure. The wheels B and C are fastened together. The diamters of wheels A, B, C, and D are 12 cm, 36 cm, 9 cm and 27 cm, respectively. The wheel A tursn at a speed of 450 rotations per minute. At what speed does the wheel D turn?

12. Three circular disks of radius 7 cm each are bound tightly with a belt. see figure. What is the length of the belt?

13. The volume of a small balloon is 2 liters and a larger ballon is 5 liters. The larger ballon  is deacreased at the rate of 0.12 liters per second. After how many seconds will the two balloons have the same volume?

14. A train travels between two stations. The train will be on time if it runs at an average speed of 50 km/hour. What is the distance between two stations?

15. Twice the number of marbles in bag A less than the number of marbles in bag B. The sum of the number of marbles in bags A and C is less than hte number
of marbles in bag B. There are more marbles in bag D than in bag B. There are 6 marbles in bag C and 9 marbles in bag D. How many marbles does bag B contain?

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.

Clues Across
1. A square number
3. A multiple of 11
Clues Down
1. A multiple of 7
2. A cube number

2. Notice that 2^2 + 2^2 = 23 , so two squares can sum to give a cube; however, the two squares here are equal (to 4).
(a) Find two unequal squares whose sum is a cube.
(b) Show that there are infinitely many pairs of unequal squares whose sum is equal to a cube.

Note: ^ means square

3. Is it possible to find a number 11…11 that is divisible by 19?

4. The menu in the school cafeteria never changes. It consists of 10 different dishes. Peter decides to make his school lunch different everyday (at least 1 dish). For each lunch, he may eat any number of dished, but no two are identical.
(a) What is the maximum numbers of days Peter can do so?
(b) What is the total number of dishes Peter has consumed during this period?

5. A sequence of shapes is made as follows.
(1) Shape S1 is a shaded square of side 1 unit.
(2) Shape S2 is made by dividing S1 into 9 equal squares and removing four of these, so that only the central and corner squares remain.
(3) Shape S3 is made by applying the process in (2) to each of the squares of S2.
(4) Shape S4 is made by applying the process in (2) to each of the squares of S3.
And so on.

(a) Find the area and perimeter of shape S3, giving your answers as fractions.
(b) Find the least value of k for which the shape Sk has the area less than 1/30 and also has perimeter greater than 30.