TV is your assistant when applying to a university

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THE NEXT TIME IS COMING FOR ENTRANCE EXAMINATIONS TO HIGHER EDUCATIONAL INSTITUTIONS OF THE COUNTRY. It is typical that year after year applicants become better prepared to join the ranks of the student body. In this, they are greatly assisted by the teaching staff of the school, part-time and correspondence preparatory courses operating at a large number of colleges, and various lecture halls organized by organizational institutes together with branches of the Knowledge Society… The opportunities for current applicants to strengthen their knowledge are extensive, but, unfortunately, soldiers of the Soviet Army, students in rural areas and some working youth are deprived of some of these opportunities. In such cases, television can come to the rescue.

For several years now, the training program studio of Central Television has been providing assistance to applicants entering universities. At the end of the academic year, television preparatory mathematics courses were created for the first time. They started working in October 1969. The course program consistently covers all the main sections of elementary mathematics within the scope of the requirements for applicants in the entrance exams. Qualified higher education staff are involved in teaching the courses.

The course work is structured as follows. On the one hand, teachers give lectures on each topic, conduct practical classes on solving problems, organize consultations, give out test papers, analyze the test work after a certain period of time, analyzing typical mistakes made by cases when solving a particular problem, answer numerous letters, give out homework, and monitor the current educational work of each service.

On the other hand, course students are absent daily according to the established form (coupons) for attendance at the next television lesson and for completing the corresponding homework, and participate in tests (completed tests are sent to the studio for checking). In their letters to the studio, they ask questions of both organizational and mathematical nature, express various kinds of wishes, recommendations, suggestions on the essence of the material being studied and the organization of classes.

After each regular program, the listener, having completed his homework, responds to the studio with a coupon in which he reports the result of his work. These results are assessed in points according to a specially developed rating scale and are simply added to the listener’s record card. The submitted test work must be checked and evaluated in points, and, in addition to the results of solving problems, self-study in the test work is assessed. The scorecard shows the level of activity of the listener.

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At the end of the school year, a full-time test in mathematics is conducted; A student who successfully passes the test will receive a certificate of completion of television preparatory mathematics courses.

All homework assignments, answers to them, methodological instructions, tests, answers to student letters were regularly published in the Moskovsky Komsomolets newspaper and in the weekly Radio and Television Programs.

Opportunities for admission to television mathematics preparatory courses are unlimited. Anyone can enroll in them. This academic year, 1,000 people are taking courses, and we maintain constant contact with each of them. The experience of television courses, judging by the numerous letters from viewers (for example, 6,000 letters between October and February), indicates their effectiveness and growing popularity.

The final stage of the course is the organization of meetings between television course participants and representatives of subject examination committees of various types. At these meetings, teachers talk about the profile of their institute, introduce them to/watchthet, give examples of written work in mathematics, and talk about the nature of the questions in the oral exam.

Now we want to bring to the attention of readers the tests that were completed by students in the 1969/70 academic year.

Test No. 1

1. Simplify an expression
   $$\frac{|x-1|+|x|+x}{3x^2-4x+1}.$$

2. Calculate
   $$\frac{x-1}{x+x^0.5+2,7^\circ}:\frac{x^{-0,2}+x^{0,3}}{x^{1,3}-x^{-0,2}}+\frac{(0,5)^{-1}}{x^{-0,5}}$$
   at $x=\sqrt{2}-1$.

3. Simplify an expression
   $$\frac{a+\sqrt{2+\sqrt{5}}\cdot\sqrt[12]{(9-4\sqrt{5})^3}}{\sqrt[3]{2-\sqrt{5}}\cdot\sqrt[6]{9+4\sqrt{5}}-\sqrt[3]{a^2}+\sqrt[3]{a}}.$$

4. Simplify an expression
   $$\frac{(4a^2m^{-2}+a^{-2}m^2-4)^{-0,5}}{2ma(m^2-a^2)^{-0,5}}\times\left(2\sqrt{m^4-\frac{a^2}{m^{-2}}}-\frac{2a^2}{\sqrt{1-a^2}m^{-2}}\right).$$

5. The sum of the first three terms of the reactive geometric progression is 91. If we add the correspondence 25, 27, 1 to these numbers, we get three numbers that coincide with the first three terms of the arithmetic progression. Prove that the sum of the first 7 terms of the arithmetic progression is equal to the difference of the fifth and first terms of the geometric progression.

Test No. 2

1. Solve the equation
   $$6x^4-13x^3-27x^2+40x-12=0.$$

2. Solve the equation
   $$(x^2-6x)^2-2(x-3)^2=45.$$

3. Solve a system of equations (limit to real solutions)
   $$\begin{cases} x^2+y^2=34, \\ x+y+xy=23. \end{cases}$$

4. Two skins of valuable fur with a total cost of 225 rubles. were sold at an international auction with approximately 40%. What is the cost of each skin separated, if from the first 25% was obtained approximately, and from the second 50% approximately?

5. Two automatic vehicles left simultaneously from one point in the same direction, one at a speed of 50 km/h, the other at a speed of 40 km/h. Half an hour later, a third car followed him, which overtook the first 1.5 hours later than the second. Find the speed of the third car.

Test No. 3

1. Solve the equation
   $$\sqrt{3x^2-2x+15}+\sqrt{3x^2-2x+8}=7.$$

2. Solve the equation
   $$\sqrt{2x^2+8x+6}+\sqrt{x^2-1}=2x+2.$$

3. Solve the equation
   $$\sqrt[3]{(2-x)^2}+\sqrt[3]{(7+x)^2}-\sqrt[3]{(7+x)(2-x)}=3.$$

4. In an equilateral triangle, the base is 48 in. and the side is 30 in. Determine the radii of the inscribed and circumscribed circle and the distance between the centers of the circles.

5. An equilateral triangle and a square having a common vertex are inscribed in a circle of radius $R$. Calculate the area of ​​the common part of the triangle and the square.

In addition to those indicated, three more tests were carried out: one - on logarithms, logarithmic and exponential equations, the second - a task on stereometry and inequalities, the third - on trigonometry.

In the next academic year, television preparatory mathematics courses will continue to operate. We invite all applicants from 1971 to take part in the courses. Remember: TV is your assistant when preparing in.by!