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.

1. In the 5×5 square the numbers 1, 2, 3, 4 and 5 are arranged in such a way that every number occurs precisely once in each column. In the 5×5 square shown, what is the entry in the position marked with * ?

2. The length of the sides of a triangle PQR are PQ=5, QR=3 and RP=4. The bisectors of the angles P and Q meet at the point I. What is the area of the triangle PQI?

3. When 10^2005?2005 is express as a single number, what is the sum of the digits?

4. What is the value of x in the diagram?

5. What is the number of lines of symmetry in the plane of the diagram?

6. A large watermelon weighs 12 kg, with 97% of its weight being water. It is left to stand in the sun, and some of the water evaporates so that now only 90% of its weight is water. What does it now weigh?

7. In Figure, OX=OY=10 are radii of a circular quadrant. A semi-circle is drawn on XY as shown. T, S and C denote the resulting triangles, segment and crescent. What is the area of C ?

8. Five students sit for an exam which has a maximum score of 100. The average of the five scores achieved by the students in the exam was 89. What could the minimum score be gained?

9. N is a positive integer such that N and N + 97 are both perfect squares. What is the positive integer N ?

10. Alan has a stride 75 cm. If he travels by walking 5 steps forward and one step back, what is the least number of steps he needs to reach a spot 24 metres away?

11. If a, b, c and d are positive integers such that

What is the value of a+b+c+d ?

12. A six digit number is represented by abcdef , where a, b, c, d, e and f are its
digits. If this number is multiplied by 6, the result is defabc . What is this six digit number?

13. How many rectangles are there in this grid, where vertices are points of the grid and the edges are lines of the grid?

14. A three-digit number N leaves remainder 3 when divided by 7, remainder 5 when divided by 11 and remainder 8 when divided by 17. What is the number N ?

15. What is the ratio of the shaded square to that of the largest square shown in the diagram?

16. There are 500 unit cubes. As many of these cubes as needed are glued together to form the largest possible cube which looks solid from any point on the outside but is hollow inside. What is the side length of the largest cube?

17. Mr. Sun has a broken calculator. When just turned on, it displays 0. If the + key is pressed, it adds 35. If the x key is pressed, it subtracts 35. If the × key is pressed, it adds 91. If the ÷ key is pressed, it subtracts 91. The other keys do not function. Mr. Sun turns the calculator on. What is the number closest to 2005 that he can get using this calculator?

18. Three man and three children arrive at the river where there is a small boat that will hold one adult or two children. What is the minimum number of trips across the river in either direction to get the family across?

19. A foundation has allocated a certain amount of money for 1st, 2nd and 3rd prizes in a competition. The money is divided in the ratio of 3:2 where the larger amount is for the 1st prize and the smaller amount is divided again in the ratio of 3?2 for the 2nd and 3rd prizes respectively. It becomes known that the 3rd prize is $3300 less than the first prize. How much is the 2nd prize?

]]> http://mathandflash.com/math-olympiad-in-taiwan-imso/feed/ 1 http://mathandflash.com/primary-mathematics-world-contest/ http://mathandflash.com/primary-mathematics-world-contest/#comments Tue, 26 Jul 2011 11:03:04 +0000 admin http://mathandflash.com/?p=712 We have primary mathematics world contest problems for individual contest and may be usefull for your students.

1. There are four kinds of dollar-notes (or dollar-bills) of value $1, $5, $10, and $50 respectively. There is a total of nine dollar-notes, with at least one dollar-note of each kind. If the total value of these dollar-notes is $177, how many $10 dollar-notes are there ?

2. A bus starts from town A to town B and another bus starts from town B to town A on the same road. They run with constant speed to their destinations and back home without stopping. The buses pass by each other for the first time at 700 km (kilometers) from town A and they pass by each other for the second time on the way back at 400 km from town B. How many km is it from town A to town B?

3. A contractor requests 2 men to build brick walls. One man can build a brick wall in 9 hours, while the other man can do the same job in 10 hours. However, when the two men work together, there will be shortfall of a total of 10 bricks per hour, and it takes them exactly 5 hours to complete the brick wall . Find the total number of bricks used on the wall.

4. Clock A is ten seconds faster than standard time every hour. Clock B is twenty seconds slower than the standard time every hour. If we adjust the two clocks to standard time at the same time, then within 24 hours Clock A shows 7:00 while Clock B shows 6:50. What is the standard time at that moment ?

5. How many different isosceles triangles of perimeter 25 units can be formed where each side is a whole number (integer) of units?

6. There are four kinds of dollar-notes (or dollar-bills) of value $1, $5, $10, and $50 respectively. There is a total of nine dollar-notes, with at least one dollar-note of each kind. If the total value of these dollar-notes is $177, how many $10 dollar-notes are there?

7. Peter begins counting up from 100 by 7’s (100, 107, …) and Mary begins counting down from 1000 by 8’s (1000, 992, …) at the same time. If they count at the same rate, what number will they say at the same time?

8. A bus starts from town A to town B and another bus starts from town B to town A on the same road. They run with constant speed to their destinations and back home without stopping. The buses pass by each other for the first time at 700 km (kilometers) from town A and they pass by each other for the second time on the way back at 400 km from town B. How many km is it from town A to town B?

9. In the figure, MN is a straight line.  The angles a, b and c satisfy the relations, b:a = 2:1 and c:b = 3:1.  Find angle b.

10. A square floor is tiled with congruent square tiles. The tiles on the two diagonals of the floor are black. The rest of the tiles are white. If there are 101 black tiles, what is the total number of white tiles?

11. In trapezoid ABCD, segments AB and CD are both perpendicular to BC. Diagonals AC and BD intersect at E. If AB = 9, BC = 12 and CD = 16, what is the area of triangle BEC?

12.  Refer to the diagram below. In rectangle ABCD, F is the midpoint of AB, BC = 3BE, AD = 4HD. If the area of rectangle ABCD is 300 square-units, how many square-units is the area of the shaded region?

13. I, II, and III are three semi-circles of different sizes. If the ratio of the diameters of I , II and III is 3:4:5, and the area of III is 24cm2, how many cm2 is the sum of the areas of I and II?

14.  Find the value of:

15. Find the fraction with the smallest denominator between 97/36 and 96/35 !

Learning Math should be done regularly and not just in time for the race course. The following I will show you the questions Mathematical Olympiad
international level, held in Hong Kong in 2007. Hopefully helpful!
Download Team Competition

Download Individual Competition

This problem consist of two sections, section A and section B. Section A consist of 12 questions. Each correct answer is worth 5 points. Then, section B, 3 question. Each answer is worth 20 points.

Let’s download this file !

Download International Mathematics Competition 2008

Answer:

x^o+ y^o

= 70 + 50 = 120

(Hint: Use your algebra skills to factor the expression.)

Answer ?
Answer: 1/3

1. A population of squirrels triples each year. If there are 50 squirrels now, how many will there be 5 years from now?

2. Alannah puts $0.01 into a bank account which will double her money each day. She needs $20.00 to buy a toy. How many days will it take until she has enough money?

3. Britney Gallivan was the rst person to fold a piece of paper in half 12 times,
something which had previously been believed to be impossible. How many layers of paper would be in that stack?

4. Ramone dumped a large bucket of water onto his driveway to rinse it o. The water from the bucket covered twice as much area every 2 seconds after it initially hit the ground. After 20 seconds, the whole driveway was covered.
How long did it take the water to cover half of the driveway?

5. Below we see the first couple stages of Sierpinski’s Triangle. In each stage a
triangle 1/4 of the size of each existing black triangle is cut out from the centre of the black triangle. If the original large black triangle has an area of 100 cm², what is the area of the each triangle removed in the 6th stage? How many black triangles are there after the 6th stage?

Answer:

1. 12150 squirrels
2. 11 days
3. 4096
4. 18 seconds

2. Diamond Savings Bank is Rp 200.000,00. After one year, the amount of savings to be Rp 224.000,00. On average each month relationship is …%.

3. A train traveled 720 km with an average speed of 60 km/ hour. Train travel time is … hours.

4. The price of a chicken USD 25000.00. Price a goat Rp650.000, 00. To be able to buy 2 goats must sell as much cock … tail.

5. Gilang marbles 3/5 times the marbles Saiful. The number of marbles Saiful 35 point. The difference is … point their marbles.

6. Broad base of a kerosene drum 45 dm ^ 2, 12o cm high. 1 liter kerosene price of Rp 900,00. Price 1  1 2 drums of kerosene is … rupiah.

7. Price Rp75.000 pair of shoes, 15% discount price. Cash price for those shoes are .. rupiah.

8. Dad dug clay length of 2 m, width 1.5 m and a depth of 5 m. If
whole soil excavation was made brick-shaped beam with a length of 20 cm, 10 cm width, and height 5 cm, then the blocks that can be made of … sheets.

9. If the father installing ceramic floor tile measures 20 cm x 20 cm above the floor of the living room, rectangular house with the 8 m, then the ceramic tiles that needed a lot of … sheets.

10. Dad called from Wartel to his friend outside the city, starting at 21:06 until 21:11. If the price of 1 pulse phone Rp 250,00 per 30 seconds, then the father must pay phone fees that amounted to … rupiah.

Short answer:

1. V = 56 km / h
2. Average interest rates in 1 month is 12%: 12 = 1%
3. Train travel time is 12 hours.
4. The number of chickens sold = 52 tail
5. Saiful and Gilang Difference marbles = 14 points
6. Price 1 1 / 2 drums of kerosene = Rp 729.000.00
7. Cash price = RP 63.750,00 shoes
8. Many blocks = 15.000 bricks
9. Many ceramic pieces = 1600
10. The amount of money to be paid = Rp 2.500.00

Note:
1$ USD = Rp 10.000,00

HoodaMath.Com also good for parents in the process of assisting their children. The site was founded by Middle Math school teacher provides plenty of interesting games, and educates with flash tools. Please visit HoodaMath.Com to study and play.

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