What is the angle ABC, if  the triangle is equilateral triangle  КВР (Fig. 10)?

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2 Collection of problems in preparation for the international research 
PISA 
 
2.1 Instructions for the implementation of tasks 
 
The priorities of evaluation of functional literacy PISA project students are three 
areas - reading competence, mathematical and scientific literacy. In the PISA study 
the ability of students, such as thinking, reasoning, problem solving and posing, 
modeling, the use of different methods of presentation of the results are evaluated. 
Thus, training competency of the participants of the international exam is determined 
by three educational and informative activities - playing, application and reasoning. 
Each group of tasks PISA examines the personal, social or global context and 
expects different levels of diagnostic sciences and mathematical literacy of students. 
The following instruction is offered
at performing tasks as a guideline . 
1. Read the case studies and extract key information. 
2. Pay attention to the drawings, diagrams, graphs and tables to the tasks of 
facilitating the understanding of the physical process 
3. Think what expressions simplify the solution of the problem. For example, 
when calculating the dynamics of power in them is usually considered permanent. 
4. Try to make a schematic drawing or a picture, it is always make easier 
reasoning. Remember that good charting is a half of the success in solving the 
problem. 
5. In most cases, it is advisable to solve the problem in a general way, denoting 
all values with the corresponding letters and making with them the necessary 
calculations. 
6. After receiving the solution in general, try to verify its reasonableness, by 
analyzing dimensions and comparing it with the solved similar problem. 
In the international PISA study all questions and learning activities for scientific 
literacy are divided into three general groups: "How do you know?" - This is the task 
to use methods of cognition. "Try to explain" - the task to explain phenomena and 
facts. "Draw conclusions" - the task to identify the skills to draw conclusions from 
the data. 
Consider 
doing the tasks for the 
scientific literacy. 
Task 1.
It has long been observed that the peeled apples, potatoes, mushrooms and 
some other fruits and vegetables become darker in the air. 
Question 1. Do you know why this is happening? 
Answer.
The composition of fruits, vegetables and fungi include various organic 
substances cyclic structure, which in the presence of biological catalysts, enzymes are 
oxidized in the air to form a colored compound in dark colors. 
Question 2: How can we prevent this process? 
Answer.
Oxidation processes are slowed down in the presence of organic acids, 
such as citric acid. Therefore, to keep fresh cut apple, you need to cut moisten with 
lemon juice or citric acid. The peeled potatoescfn can be added by finely chopped 
onions. 

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Task 2.
In Kazakhstan, there are areas suitable for the development of 
alternative energy industries. What are these areas and give possible justification. 
Question 1
. 
What are the alternative energy industry?
Question 2:
What are these areas? 
Question 3.
Why is it important to develop these industries? 
Question 4:
What are the requirements for service to the development and 
maintenance of these industries? 
Answer. 
Wind power, energy use of the earth's interior, the use of solar energy; 
the center and south of Kazakhstan is for wind and solar energy, east is foe wind 
energy, west is for solar energy; they prevent contamination of land, air basin, water, 
waste-free, they are convenient to operate, require less labor force at a higher quality 
requirements, special education, in the field of ecology knowledge, general 
knowledge; allow the use of inexhaustible types of natural resources, which is rich in 
Kazakhstan due to its geographical location and the size of the territory. 
Task 3. 
Consider the picture of artist V. Vasnetsov "Magic Carpet" (Figure 1) 
and approximately determine the direction in which part of the light fabulous flying 
machine
is directed . 
A. To the north. 
B. In the north - east. 
C. In the south - east. 
D. South. 
Figure 1 
 
Answer. 
Approximately to the north-east. It is identified by the moon. Pay 
attention to the aging "Moon on the left side of the picture. This can be seen with just 
the morning hours just before sunrise. Now it is about to the east, at the right hand of 
the hero (the picture shows the summer and the summer moon in this phase goes back 
a bit to the north of the east). Consequently, a magic carpet is flying ito the north-
east. 
In international studies PISA mathematics tasks are distributed over six levels: 
1)tasks, where all relevant information is given, and the question is clearly 
asked. Students can identify information and carry out conventional methods, 
according to the certain situations; 
2) tasks, for which students can apply basic algorithms, formulas, methods and 
techniques; 
3) tasks that require sequential execution; 
4) tasks that are specific models for specific situations; 
5) tasks for which you need to define, compare, evaluate, create a specific 

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strategy to address the problems; 
6) tasks which include situations did not exist previously; develop new methods. 
Tasks for mathematical literacy considers assignments with one story, but the 
student is offered a few questions of different levels of complexity, from simple to 
calculate, to the questions of the 5th and 6th levels of difficulty, under which it is 
necessary to use the knowledge of several branches of mathematics, or subjects of 
natural science cycle and requires creativity and logical reasoning. The international 
studies PISA tasks includes structured questions, i.e.
the content of questions content 
is selected in such a way that in the course of their consistent implementation next 
question has to do with the answers to the previous questions, as well as important is 
the ability of students to analyze the information provided in the form of tables, 
charts, graphs. 
Tasks in mathematical literacy. 

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