Here are few elementary algebra problems from a collection of Russian math test problems for school students.

While they may appear rudimentary to math students, keep in mind that those present just an example of algebra test problems that every high school graduate was expected to solve within a short time limit. Compare that to some standard tests of today, like ACT and SAT in the United States. Also, the arrangement of the problems gives an interesting historical perspective. Enjoy.

1. Several years ago there were 10,000 trees in the forest. Now there are 15,600 trees in the forest. Over how many years the growth took place, if each year the number of trees increases by 0.1?

(From a High School Diploma test, 1875).

2. A dirigible first traveled 40 km going against a 30 km/hr wind and then returned, spending 2.5 hours total for the round trip. Find the dirigible’s speed in a still air.

(From a High School Diploma test, 1913)

3. A collective farm worker, set out from his village to the railroad station. Having walked 3 km after one hour, he observed that if he continued at the same speed, he would arrive 40 min late for his train. So he paced up and walked at 4 km/hr for the rest of the trip. Thus he arrived to the station 45 min before his train’s scheduled departure.

Find the distance from the village to the station.

(From Math Olympiads, ~6th grade level, 1950s)

4. A man walked every day along 1 km stretch of the streetcar rail. After 1 month he had counted 45 passing trams that moved in the same direction and 120 trams that moved toward him. Given that the man walked 1 km in 12 min, find the speed of tram.

(From Military School tests, 1947).

5. Two bodies simultaneously departed from point A on the circumference of a circle, moving along the circumference in the opposite directions. When the two bodies met, it turned out the first body had traveled the distance 7 cm greater than the second. After the meeting the bodies continued their motion and the first body arrived to the point A 4 seconds later, whereas the second body arrived to the point A 9 seconds later.

Find the circumference.

(From a university admission test, 1958)

*Note: Each university in Russia had their own admission test.

## Question

## Prime 15

Here are few elementary algebra problems from a collection of Russian math test problems for school students.

While they may appear rudimentary to math students, keep in mind that those present just an example of algebra test problems that every high school graduate was expected to solve within a short time limit. Compare that to some standard tests of today, like ACT and SAT in the United States. Also, the arrangement of the problems gives an interesting historical perspective. Enjoy.

1.Several years ago there were 10,000 trees in the forest. Now there are 15,600 trees in the forest. Over how many years the growth took place, if each year the number of trees increases by 0.1?(From a High School Diploma test, 1875).

2.A dirigible first traveled 40 km going against a 30 km/hr wind and then returned, spending 2.5 hours total for the round trip. Find the dirigible’s speed in a still air.(From a High School Diploma test, 1913)

3.A collective farm worker, set out from his village to the railroad station. Having walked 3 km after one hour, he observed that if he continued at the same speed, he would arrive 40 min late for his train. So he paced up and walked at 4 km/hr for the rest of the trip. Thus he arrived to the station 45 min before his train’s scheduled departure.Find the distance from the village to the station.

(From Math Olympiads, ~6th grade level, 1950s)

4.A man walked every day along 1 km stretch of the streetcar rail. After 1 month he had counted 45 passing trams that moved in the same direction and 120 trams that moved toward him. Given that the man walked 1 km in 12 min, find the speed of tram.(From Military School tests, 1947).

5.Two bodies simultaneously departed from point A on the circumference of a circle, moving along the circumference in the opposite directions. When the two bodies met, it turned out the first body had traveled the distance 7 cm greater than the second. After the meeting the bodies continued their motion and the first body arrived to the point A 4 seconds later, whereas the second body arrived to the point A 9 seconds later.Find the circumference.

(From a university admission test, 1958)

*Note: Each university in Russia had their own admission test.

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