# Examples for secondary school students - page 69

1. Diagonals of pentagon Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
2. Progression 12, 60, -300,1500 need next 2 numbers of pattern
3. Mast shadow Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
4. The swimmer The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
5. Barrel with water The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
6. Expressions 3 If k(x+6)= 4x2 + 20, what is k(10)=?
7. Axial cut of a rectangle Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
8. SSA and geometry The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
9. Bridge cards How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
10. Find two Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
11. Rectangle - area, perimeter The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
12. Integer Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
13. Points collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
14. Company and employees There are 370 employees in the company - women are 15% less than men. How many men work in the company?
15. Depth angle From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
16. Reciprocal equation 2 Solve this equation: x + 5/x - 6 = 4/11
17. Resistance A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
18. Pavement Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
19. Practice How many ways can you place 20 pupils in a row when starting on practice?
20. Inverted nine In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.