# Examples for secondary school students - page 30

- Scouts

Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together? - Similarity

Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity. - Church roof

The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required? - Pool 2

The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later? - Sheep

Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman? - Flowerbed

Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex? - Cylinder surface, volume

The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of cylinder. - Bomber

The aircraft flies at an altitude of 4100 m above the ground at speed 777 km/h. At what horizontal distance from the point B should be release any body from the aircraft body to fall into point B? (g = 9.81 m/s^{2}) - Vinegar

What percentage vinegar we get if we mix 1 if dm³ eight percent vinegar with 1.5 dm³ six percent vinegar? - Digits A, B, C

For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product). - Bevel

I have bevel in the ratio 1:6. What is the angle and how do I calculate it? - Simple interest 4

Find the simple interest if 5243 USD at 4.3% for 261 days. Assume a 361-day year. - Ball

Ball was fired at an angle of 35° at initial velocity 437 m/s. Determine the length of the litter. (g = 9.81 m/s^{2}). - Three-digit numbers

How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)? - Parallelogram

Parallelogram has sides lengths in the ratio 3: 4 and perimeter 2.8 meters. Determine the lengths of the sides. - Slope

What is the slope of the line defined by the equation -2x +3y = -1 ? - Radioactivity

After 548 hours decreases the activity of a radioactive substance to 1/9 of the initial value. What is the half-life of the substance? - Comparing powers

How many times is number 5^{6}larger than number 4^{6}? - BW-BS balls

Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of. - Secret number

Determine the secret number n, which reversed decrease by 16.4 if the number increase by 16.4.

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