Maths tests in Europe

Final test Hungary

Secondary vocational school, May 2000.

1.

Give the real solutions of the following equation. 8 points

2.

Solve the following equation in the set of integers. 12 points

3. Determine the equation of a circle which has centre at the point O (-3; -2) and which touches the straight line 2 x + y = 3. 14 points

4. The length of the sides of a right-angled triangle are the first three terms of a gemetrical progression. Determine the angles of this triangle.

16 points

5. A) Determine the length of the opposite sides of a symmetrical hexagon that one can put in a circle ( r=4).

B) Determine the opposite vertices (vertex) of a symmetrical hexagon that one can put around a circle (r=4). 10 points

6. What do you mean for the absolute value of a vector? How can you determine the absolute value of a vector with the help of its coordinates? 6 points

7. Prove (establish the truth of) that the volume of a frustum of pyramid is:

14 points

80 points

80 – 60 = 5

59 – 47 = 4

46 – 33 = 3

32 – 19 = 2

18 -- = 1