# Examples for secondary school students - page 13

1. Scouts
The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
2. Box
Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm2 of cardboard we need to cover overlap and joints that are 5% of ar
3. Morse alphabet
Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters.
4. Train
The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake.
5. Q-Exam
If tg α = 0.9, Calculating sin α, cos α, cotg α .
6. EQL triangle
7. Sector
The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
8. Amazing number
An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.
9. Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
10. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
11. Geodesist
Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
12. Euklid4
Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
13. XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
14. Spherical segment
Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
15. Heron backlaw
Calculate missing side in a triangle with sides 17 and 34 and area 275.
16. Coin and die
Flip a coin and then roll a six-sided die. How many possible combinations are there?
17. Slope of the pool
Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
18. Geometric progression
Fill 4 numbers between 4 and -12500 to form geometric progression.
19. Divisibility
Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
20. Shooter
The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?

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