Assignments for extracurricular activities in mathematics

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

1, Blitz - Questions

For 1 team:
1, What's bigger a or 2a? (depends on the sign a)
2 Is it true that the sum of two odd numbers is odd? (no)
3 - How many times is a kilometer larger than a millimeter? (a million times)
4. Who said the phrase: "Mathematics must then be taught, that it puts the mind in order"? (M.V. Lomonosov)
5, Is a bisector a ray or a line segment? (in triangle - line segment, in angle - beam)
6 - What sign should be placed between 0 and 1 to make a number greater than 0 and less than 1? (comma)
7 Name the three great mathematicians of antiquity. (Archimedes, Pythagoras, Euclid)
8. What are the corners of the diamond equal to if 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 divisible by all numbers without remainder? (zero)
11 - In which city did Archimedes live? (Syracuse)
12, What fraction cannot be reduced? (if this fraction is house number)
13 - Which letter must a number be inscribed in to increase by 1? (in - O - seven)
14. On the way, two boys walked and found 2 rubles. Four more follow them. How much will they find? (nothing)
15. The rooster, standing on one leg, weighs 3 kg. How much does the rooster weigh when standing on two legs? (3 kg)
16, There are 10 spokes in the wheel Estimate in your mind how many spaces there are between them. (10)
17 - Which is heavier than 1 kg of down or 1 kg of steel? (equal)

For 2 teams:
1. What does the number π mean? (the ratio of the circumference to the diameter)
2 - Who is Pythagoras and where did he live? (ancient Greek mathematician)
3, In which triangle do the heights intersect at the apex? (in a rectangular)
4 What is an axiom? (a statement accepted without proof)
5 - How many faces does an uncorrected pencil have? (8)
6 - What is more expensive than 1 kg of ruble coins or 1 kg of two-ruble coins? (same)
7 Is it true that the square of an even number is divisible by 4? (yes)
8 Fifty divided by half How much did it turn out? (100)
9 - What is the number 0: even or odd? (neither even nor odd)
10 Which table is more stable: on 3 legs or on 4? (on 3)
11 - How many diagonals are there in a regular heptagon? (14)
12 Who proved that (fig. see annex)? (Archimedes)
13 - Can it rain continuously for two days? (no, as night exists)
14. A pair of horses ran 10 km. How many kilometers did each horse run? (10 km)
15 A pack of ducks flew The hunter killed one. How many ducks are left? (one)
16, There are 10 fingers on two hands How many fingers are there on 10 hands? (50)
17. 52=25, 62=36, the angle squared is... (90o)

2, Quiz

1 - What letter was the number 50 written in ancient Rome? (L)
2, Unit of measurement of speed at sea. (node)
3, Unit of mass of gemstones. (karat)
4, Author of The Beginnings. (Euclid)
5, Specific unit of measurement for the volume of oil. (barrel)
6, What is an astrolabe? (an instrument for measuring angles on the ground)
7, What is an abacus? (counting board)
8 Could Omar Khayyam have been a disciple of Euclid? (no)
9, Why is a reisshina needed? (to build parallel lines)
10 - What does the word algebra mean? (science that studies algebraic systems)
11, What is an ecker? (a device for determining right angles on the ground)
12 - What are the lengths of the sides of the Egyptian triangle equal to? (3, 4 and 5)
13, What is a degree? (1/180 part of the angle)
14 - Which European city has Pythagoras, Archimedes, Newton and Copernicus streets? (in Amsterdam)

3 Mathematical terms

Name mathematical terms if they are known to all start with the letter "C":
1, Ball surface.
2, The ratio of the opposing leg of a right triangle to the hypotenuse.
3, Units of measurement of length.
4, Two straight lines not lying in the same plane.
5, A segment of a triangle connecting the midpoints of its sides.
(Answers: sphere, sine, centimeter, crossing, midline)

"T":
1 - The statement to be proved.
2, Instrument for measuring angles on a plane.
3, The ratio of the opposing leg of a right triangle to the adjacent one.
4 A figure formed by a broken piece comprising three links.
5, A quadrangle in which two opposite sides are parallel and the other two are not parallel.
(Answers: theorem, protractor, 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, coplanarity.)

5, Objectives in verse
1)
The bear was carrying buns from the market,
But on the forest edge
He ate half the buns
And plus half a stick.
He walked, walked, sat down to rest
And to the "ku-ku" of cuckoos
I ate half the buns again
And plus half a stick.
It got dark, he accelerated his pace, but on the porch of the hut
He ate half the leftover again
And plus half a stick.
With an empty wallet - alas!
He entered the house sadly...
I want you to tell me
How many buns were there?
(7 buns)

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

6, Rebuses (rebus1, rebus2).

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7, Antique tasks

(1) When asked how many students he had, the ancient Greek mathematician Pythagoras is said to have answered: Half of my students study mathematics, the fourth part is nature, the seventh part spends time in silent reflection, the rest is three virgins How many students did Pythagoras have? (28 students)

(2) One man shall drink a cad of drink in 14 days, and with his wife shall drink the same cad in 10 days, and eat, for a telling matter, in a number of days his wife shall drink the same cad especially. (Arithmetic, by L. F. Magnitsky, early 18th century) (in 35 days)

Literature:
1. Klimenchenko D.V. Mathematics problems for the inquisitive. - M.: Enlightenment, 1992.
2.Nagibin F.F, Kanin E.S. Mathematical box. - M.: Enlightenment, 1988.
3, Proceedings from Quantum Magazine.