# Examples for secondary school students - page 27

1. Automaker The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?
2. Tournament Determine how many ways can be chosen two representatives from 34 students to school tournament.
3. Peak Uphill leads 2 paths and 1 lift. a) How many options back and forth are there? b) How many options to get there and back by not same path are there? c) How many options back and forth are there that we go at least once a lift?
4. Disinfecting solution How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
5. Angles of the triangle ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
6. Seating rules In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.
7. Medals In how many ways can be divided gold, silver and bronze medal among 21 contestant?
8. Maple Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
9. Painters The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge?
10. Reflector Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
11. Angle A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
12. Against each other From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them?
13. Words How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
14. Sum-log The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
15. Circles In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
16. Permill How many permill is 978 from 84370?
17. Train 2 The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
18. Triangular pyramid Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
19. The camp At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
20. Pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?

Do you have an interesting mathematical word problem 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 the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...