# Examples for secondary school students

1. PIN code
PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second
2. Integer
Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
3. Eq with reciprocal
Solve given equation with reciprocal member: a-6/a+10=4/8
4. Imagine
Imagine that a unit of air at a temperature of 25°C rises up a mountain range that is 3,000 meters high on the windward side and which descends to 1,200 meters on the leeward side, assuming that the air will remain dry what will its temperature when it cr
5. Nineteenth member
Find the nineteenth member of the arithmetic sequence: a1=33 d=5 find a19
6. A perineum
A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term?
7. Diofant equation
250x + 120y = 5640
8. Air thermal
Imagine that a unit of air rises at 3000 meters high, if temperature decreases 6 degrees celcius for every 1000 meter, what will be its temperature at 1400 meters, 2000 meters, 2500 meters and when it reaches the 3000 meter elevation. Starting temperature
9. Mumbai
A job placement agency in Mumbai had to send ten students to five companies two to each. Two of the companies are in Mumbai and others are outside. Two of the students prefer to work in Mumbai while three prefer to work outside. In how many ways assignmen
10. GP members
The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
11. Peroxide
How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?
12. Deviation of the lines
Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
13. Cuboid walls
If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
14. Inverse matrix
Find out inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3]
15. Isosceles triangle
The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
16. Boys to girls
The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?
17. Flowers 2
Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there?
18. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
19. Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
20. Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m

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