Mathematics Olympiad (5th grade)

Assignments for the school round of the Olympiad for students in grades 5 of secondary school. For the school Olympiad, tasks were selected within the framework of the state educational standard, emphasis was placed on interesting, varied tasks of a creative nature that would be both instructive and have practical application. The tasks help to reveal the creative potential of students, broaden their horizons, develop interest in studying the subject and identify gifted, creative-minded schoolchildren and students with non-standard thinking.

Option 1

1. 1. Instead of asterisks, put the numbers so that the addition is done correctly:

73*8
+ **46*
9*36
97125

1. Square is 9 equal squares How many squares are there in total?
   
2. Three identical watermelons should be divided equally between 4 children. How to do this by making the smallest number of cuts?
3. A cyclist left the city for the village, the distance between which is 32 km. at the same time, a pedestrian left the village for the city at a speed of 4 km/h. Which of them will be further from the city in 2 hours?
4. To get 40-year-old Snake Gorynych out of the world, Koschey the Immortal came up with the idea of getting him used to smoking. He calculated that if Snake Gorynych smoked 17 cigarettes every day for a year, he would die in 5 years, and if 16, then in 10 years. How many years will the Snake Gorynych live to see if he doesn’t smoke?

Option 2

1. Write down all natural numbers divisible by 2 lying on the number ray between the numbers 1992 and 2007.
2. Cut the rectangle into 3 triangles so that among the resulting triangles only 1 is rectangular.
3. How to use a 7-liter bucket and a 3-liter jar to pour exactly 5 liters of water into a pan?
4. The older brother walks from home to school 30 minutes, and the younger brother - 40 minutes. In how many minutes will the older brother catch up with the younger one if he came out 5 minutes earlier?
5. From the number 12345678910111213...5657585960 cross out 100 digits so that the remaining number becomes the largest.

Literature used:

1. Farkov A.V. Extracurricular work in mathematics. grades 5-11 - M. Iris-Press 2006.
2. Rusanov V. N. Mathematical Olympiads for junior schoolchildren. - M. "Enlightenment", 1990.
3. Subject weeks at school Mathematics Comp. L.V. Goncharova - Volgograd "Teacher" 2002.
4. Nagibin F. F, Kanin U. S. Mathematical Box - M. Enlightenment 1988.
5. Shevkin A.V. School Olympiad in Mathematics. Tasks and solutions.. - M. "Russian Word" 2004.

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