Сборник задач по подготовке учащихся к международным исследованиям timss и pisa



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Task 24. The function and its graph.
Figure 8 shows a plot of the function f (х) ах2 bx c .

Fig. 8

Using the graph of the function, answer the questions.


Question 1. Write down the coordinates of the symmetry of the function graph.
Question 2. Find the coordinates of the minimum point of the function.
Question 3. Record the set of values of the function, if the argument values belong to the interval [-1; 1].


Task 25. The corners.

What is the angle ABC, if the angle РOK = 230 (Fig. 9)?

Fig. 9





Task 26. The corners.

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

Fig. 10



Task 27. The corners.

What is the angle of the CBO, if ВО bisector of the angle, the angle bisector of СВР, ВР angle ABC = 220 and angle of direct AВK
(Fig. 11)?

Fig. 11

2 Collection of problems in preparation for the international research


PISA


    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 evaluated the ability of students, such as thinking, reasoning, problem solving and posing, modeling, the use of different methods of presentation of the results. Thus, training participants of the international competency exam 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.
When performing tasks as a guideline the following instrutsiey.

  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 about what suggestions to simplify facilitate 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 easier reasoning. Remember that good charting - half the success in solving the problem.

  5. In most cases, it is advisable to solve the problem in a general way, all values denoting the corresponding letters and making with them the necessary calculations.

  6. After receiving the decision in general, try to verify its reasonableness, by analyzing dimensions and comparing it with the already solved a 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 job 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 the performance of tasks for scientific literacy. Task 1. It has long been observed that the peeled apples, potatoes, mushrooms and some other fruits and vegetables to darken 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 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 potatoes, you can add finely chopped onions.


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