2. a) The four sides of a quadrilateral are: 1 cm, 1 cm, 2 cm, 2 cm. What special quadrilaterals can you make from these data? Draw sketches and give the name of the quadrilateral.
b) We have a convex polygon. From each vertex maximum 5 diagonals can be drawn. What is the sum of the internal angles of this convex polygon?
3. Let the domain set be the pupils of a secondary school. The following sets are given:
A={brown-haired pupils} B={blue-eyed pupils} C={boys}
What pupils belong to the following sets? Give their properties in a sentence.
a)
b)
c)
d) Using the operations of sets give the following set:
The girls who are brown-haired or blue-eyed.
4. Without using a calculator calculate the exact value of the expression.
5. The graph of the function is given below.
a) With the help of the graph determine the following:
The ordering rule of the function:
The domain set of the function:
The range of the function:
What are the minimum and maximum points of the function? What are the minimum and maximum (turning) values:
b) Solve the following inequality in the domain set of the function.
f(x)≤0
6. a) Can the sum of two prime numbers be 2009? Explain your answer.
Solve the following equation in the set of real numbers.
2. The parallel sides of a symmetrical trapezoid are 6 and 4 cm, the other two sides are 5 cm long. What is the length of the diagonal?
3. The age of a father is the triple of the sum of that of his two children now. 4 years later the age of the father will be the double of the sum of that of his two children. How old is the father now?
4. On three sides of a dice there are one, two and three spots. The other three sides are painted white, red and blue. This dice is thrown 6 times and the 6 scores are recorded. How many different 6-scores are there, if we know that the first score is two and the fifth one is white or blue and in each 6-score all the sides facing upwards are different?
5. The 18 grades of a mathematics test written in a group of 21 pupils are the following:
grade / 1 / 2 / 3 / 4 / 5number of each grade / 1 / 4 / 6 / 4 / 3
3 pupils were absent that is why they wrote this test later. We know that all the three pupils received the same grade. After that the arithmetic mean (average) of the 21 tests has been increased by .
a) What grade did the missing pupils receive?
b) What are the mode and median of the 21 grades?
c) What percentage of the group is below the arithmetic mean (average)?
6. Angle is 66° and angle is 44° in the triangle ABC given below. The centre of the inscribed circle of the triangle is denoted by O. This point O is mirrored on side a of the triangle and its image is denoted by O1.
Determine the internal angles of the quadrilateral COBO1.