Please read carefully and then take your paper and pencil to do this math problems.

1. Lily plans to spend all of her $31 to buy different types of pens that cost $2, $3 and $4 respectively. If she wants to buy at least 1 pen of each type, what is the maximum number of pens that she can buy?

Answer: 14

2. a, b and c are two-digit numbers. The unit digit of a is 7, the unit digit of b is 5 and the tens digit of c is 1. If a x b + c = 2006,  find the value of a + b + c .

3. A class of students bought and equally distributed a certain number of notebooks. If the notebooks are distributed to girls only, each girl will receive 15 notebooks. If the notebooks are distributed to boys only, each boy will receive 10 notebooks. If the notebooks are equally distributed to everyone in the class, how many notebooks will each student receive?

4. The lengths of two sides of a triangle are 2006 and 6002 units respectively. If the length, in the same units, of the third side of this triangle is an integer, how many different triangles can exist?

5. We have four cards numbered 1, 2, 3 and 4 respectively. Three of the four cards are placed into the boxes as shown in the equation below.

How many different values of n can be obtained?

6. Solly wants to unlock his friend Koos’s combination lock. The lock consists of 4 reels, each reel displays the digits from 1 to 9. Koos tells Solly that the first digit from left to right is a multiple of 3, the second digit is a prime, the third digit is a multiple of 2 and the whole number is divisible by 4. For example,

By following Koos’ clues, what is the maximum possible number of different ways that Solly can unlock it?

7. There are over 50 children sitting in a circle. They count clockwise around the circle starting from 1. If the same child has counted 2 and 2006, what is the least number of children in the circle?

8. If the number

is divisible by 11, what is the minimum value of n?

9. As shown in the figure below, the big rectangle consists of four smaller rectangles with their areas 12 cm^2, 24 cm^2, 36 cm^2 and 48 cm^2 respectively. If all the lengths, in cm, of the rectangles are integers, what is the area of the shaded region?

10. N is a natural number such that when divided by 10 it leaves the remainder 9, when divided by 9 it leaves the remainder 8, when divided by 8 it leaves the remainder 7, …, when divided by 2 it leaves the remainder 1. Find the smallest value of N.

11. ABCD is a parallelogram that is made up of 12 identical triangles as shown. The lines in the figure are parallel to either AB, AD or BE. How many different parallelograms are there which include the shaded triangle?

12. Find the unit digit of the sum:

13. On a true / false test of 100 items, every item number that is a multiple of 4 is true, and all others are false. If a student marks every item that is a multiple of 3 false and all others true, how many of the 100 items will be correctly answered?

14. The figure shown is formed by seven line segments. What is the total number of triangles in the figure?

15. In the following figure, AMOQ, MBNO, ONCP, QOPD and ABCD are rectangles. If the area of QOPD is 51 square units, the area of ONCP is 17 square units and the area of MBNO is 29 square units, find the area of the quadrilateral MNPQ.

In this posting, I will share IMSO (International Mathematics and Science Olympiad) that be held in 2006. Do this math problem seriously!

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 of ten-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 98cm2. 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.

]]> http://mathandflash.com/imso-2006-short-answer/feed/ 1 http://mathandflash.com/math-question/ http://mathandflash.com/math-question/#comments Mon, 04 Apr 2011 10:36:09 +0000 admin http://mathandflash.com/?p=632 Below is one of math question in Math Olympiad For Primary School.

Amanda and Cindy share a sum of money. If Amanda gives 1/3 of her share
to Cindy, Cindy will have $48 more than Amanda. If Amanda gives 1/6 of her share to Cindy, Cindy will have $30 more than Amanda. What is the ratio of Amanda’s share to Cindy’s share?

Solution:

At the end, Cindy will have $30 more than Amanda.
So,
3u + $48 – 5u = $30
2u = $18
1u = $9
Initial amount of:
Amanda = 6u = 6 × 9 = $54
Cindy = 2u + $48 = 2 × 9 + 48 = $66

Ratio of Amanda : Cindy = $54 ? $66 = 9 ? 11

A. 20^o

B. 60^o

C. 80^o

D. 100^o

E. 120^o

Answer ?

B. 60^o

Problem 2:
The prime numbers between 10 and 20 are added together to form the number Q. What is the largest prime divisor of Q?
A. 2
B. 3
C. 5
E. 7

Do you want to know the answer ?
Answer:
Problem 1: C. 120
Problem 2: C. 5

Although such materials has ever been given in junior high, sometimes when repeated again in high school (grade 10), still many who forget, or do not remember at all, but the problems associated with these materials is also in the UN. Whose fault is it?

Maybe you’ve had an interesting experience while teaching the material? Or the difficulties in explaining to the students? Write your comment below. Your comments will be useful for teachers in other schools in Indonesia.

Well, this time I will make a link to download the module mathematics: quadratic equations, quadratic functions and quadratic inequalities.

Click here to download

Regards,
Istiyanto-2010

b. Is the sequence arithmetic, geometric, or neither ?
Answer:
Neither

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

Click here to download math problems other Indonesian language. Or click here to download the questions in English. For those who have not become a member, please list first through the right side column of this blog. Or if you want to be a Premium member, please click here.

1. One of home completed within 5 months, 3 weeks 5 days. How many days a house is completed?

2. I walk 12 steps forward. Having reached the goal, I’m back again with the same number of steps. If the steps are written in mundurku integers, what is it?

3. My mother go to the market to buy 3 ½ pounds of sugar, 4 ¼ kg of rice, and 2 ¾ kg of salt. At home, kg rice 2 ½ tanak. How much do students groceries Mother?

4.In a map distance of the town A to town B is 2 cm, the city B to city C 4 cm, and the city C to city D 3 cm. Scale on the map 1: 523,000! Find the distance from city A to city D through B and C of the truth!

5. My mother age :  my Sister = 11: 1. When Mom picked brother, both weight is 60 kg. How many pounds brother?

6. A Bookstore has a profit 18% of the initial capital USD 165,000,000.00. How much capital gains plus the bookstore?

7. A temperature in a refrigerator minus 10 degree in Celcius. How many degrees of temperature when measured with a thermometer Reamur? If the Fahrenheit thermometer is measured by whether the result is also a minus?

8. Phone cost in New York is USD $ 70,000.00 per minute. If the brother called his friend in New York for 4 minutes 40 seconds, what is the cost?

9.Bahri set sail to fish at 23:00. When returning to land at the time showed 03.30. How long Bahri sailing fishing?

10. The comparison age between my uncle and Andi is 5: 3.  And Uncle: Sholeh = 4: 3. Number of 82-year age three. What is the age Uncle?

Regards
Istiyanto