Tasks for extracurricular activities in mathematics

These tasks can be used to conduct extracurricular activities in mathematics for high school students, students of the 1st year of SPO institutions.

1. Blitz - questions

For 1 team:
1. More.аor2a? (depends on the sign)а)
2. Is it true that the sum of two odd numbers is odd?
3. How many times a kilometer is more than a millimeter?
4. Who said the phrase: “Mathematics must then be taught, that it puts the mind in order”? (M.V. Lomonosov)
5. Is the bisector a ray or a segment? (in a triangle - a segment, in a charcoal - a ray)
6. What sign must be placed between 0 and 1, to get a number greater than 0 and less than 1?
7. Name the three great mathematicians of antiquity. (Archimedes, Pythagoras, Euclid)
8. What are the angles of a diamond when one diagonal is equal to the side? (120o, 60o, 120o, 60o)
9. How many cubic centimeters in one cubic meter? (million)
10. What number is divided by all numbers without a remainder?
11. What city did Archimedes live in? (Syracuse)
12. What fraction can not be reduced? (if this fraction is the number of the house)
13. In what letter do you need to write a number to increase it by 1?
14. On the way two boys were walking and found 2 rubles. Four more are coming. How many will they find?
15. The rooster, standing on one leg, weighs 3 kg. How much does a rooster weigh on two legs? (3kg)
16. The wheel has 10 spokes. Think about how many gaps there are between them. (10)
17. Which is heavier than 1 kg of fluff or 1 kg of steel?

For 2 teams:
1. What is the number π? (the ratio of circumference to diameter)
2. Who was Pythagoras and where did he live? – Ancient Greek mathematician
3. In which triangle do heights intersect at the top?
4. What is an axiom? (a statement accepted without proof)
5. How many facets does an unfinished pencil have? (8)
6. What is more expensive than 1 kg of ruble coins or 1 kg of two rubles?
7. Is it true that the square of an even number is divided by 4?
8. Fifty divided into half. How much did you get? (100)
9. Which number is 0: even or odd? (neither even nor odd)
10. Which table is more stable: on 3 legs or on 4? (3)
11. How many diagonals is there in a regular heptagon? (14)
12. Who proved that (see figure in appendix)? (Archimedes)
13. Can it rain continuously for two days?
14. A pair of horses ran 10km. How many miles did each horse run? (10 km)
15. A flock of ducks flew. Hunter killed one. How many ducks are left?
16. Two hands have 10 fingers. How many fingers are there in 10 hands? (50)
17. 52 = 25, 62 = 36, the angle in the square is ... (90o)

2. quiz

1. What letter was the number 50 written in ancient Rome? (L)
2. Unit of speed measurement at sea. (knot)
3. Unit of mass of precious stones. (carat)
4. Author of The Beginnings. (Euclid)
5. Specific unit of measurement of oil volume. (barrel)
6. What is an astrolabe? (an instrument for measuring angles on the ground)
7. What is an abacus?
8. Could Omar Khayyam have been a disciple of Euclid?
9. Why do you need to build parallel lines?
10. What does the word algebra mean? (the science of algebraic systems)
11. What is an eker? (a device for determining right angles on the ground)
12. What is the length of the Egyptian triangle? (3, 4 and 5)
13. What's a degree? (1/180 part corner)
14. Which European city has the streets of Pythagoras, Archimedes, Newton and Copernicus? (Amsterdam)

3. Mathematical terms

Name mathematical terms, if you know that they all begin with the letter "C":
1. The surface of the ball.
2. The ratio of the opposite side of the right triangle to the hypotenuse.
3. Units of length.
4. Two straight lines, not lying in the same plane.
5. The segment of a triangle connecting the middle of its sides.
(Answers: sphere, sinus, centimeter, interbreeding, middle line)

T:
1. A statement that needs to be proven.
2. Instrument for measuring angles on a plane.
3. The ratio of the opposite side of a right triangle to the adjacent side.
4. Figure formed by broken, consisting of three links.
5. A quadrangle in which two opposite sides are parallel and the other two are not parallel.
(Answers: theorem, transporter, tangent, triangle, trapezoid)

4. Mathematical terms

(Answers:
Ball, vector, sector, scalar, diameter, cylinder, perimeter, tetrahedron, orthocenter, semiperimeter.

(Answers:
Cube, circle, cone, square, cosine, cotangent, tangent, coefficient, collinearity, complanarity.

5. Tasks in verse
1)
The bear from the bazaar was carrying buns,
But at the edge of the forest.
He ate half the buns.
And half a bucket.
Shel, walked, sat down to rest.
And under the cuckoo
I ate half of the buns again.
And half a bucket.
Darkened, he accelerated the step, but on the porch of the hut
He ate half the rest again.
And half a bucket.
With an empty wallet, alas!
He entered the house despondently...
I want you to tell me,
How many buns were there?
(7 buns)

2)
- I'm two years older than a lion.
Said the wise owl.
- And I'm twice your age.
The porcupine answered.
The lion looked at him proudly.
He said, slightly wrinkled,
- I'm four years older,
Than you, venerable needlefish.
How old are they all together?
Check your answer twice.
(28 years)

6. Rebuses(rebus1, rebus2).

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7. Old challenges

1) When asked how many pupils he had, the ancient Greek mathematician Pythagoras said: Half of my pupils study mathematics, a fourth study nature, a seventh spend time in silent reflection, the rest are three virgins. How many pupils did Pythagoras have? (28 students)

2) One person will drink cadhi drink in 14 days, and with his wife will drink the same cadhi in 10 days, and clearly eat, in how many days his wife will especially drink the same cad. (Arithmetic, author L.F. Magnitsky, early 18th century) (in 35 days)

Literature:
1. Klymenchenko D.V. Problems in mathematics for the curious. Education, 1992.
2.Nagibin F.F., Kanin E.S. Mathematical box. Education, 1988.
3. Materials from Quantum magazine.