Preliminary Course for College Applicants of Mathematics

The course is intended for high-school students who have completed 11th grade and are planning to apply to the universities in the end of the academic year 2013/14.

Our primary goal is to offer to the future college applicants a early and timely estimate of the level of their knowledge, compared to the requirements of the entrance exams. These exercises will be of use to students who have already gotten good education in their schools and desire to review and replenish their skills during the Summer break. At the same time, for those who are unsure in their preparedness, this will be invaluable opportunity to catch up on their knowledge and to master the required problem-solving techniques.

The problems are grouped in 10 basic topics:

PART I (25 hours, 1 week)

  • 1. Rational equations and inequalities
  • 2. Irrational equations and inequalities
  • 3. Planimetry 1
  • 4. Combinatorics
  • 5.Trigonometry 1

*The first half of the course is also appropriate for students who have just finished 10th grade.

PART II (25 hours, 1 week)

The second half concerns from 11th grade.

  • 6. Systems of equations
  • 7. Sequences.
  • 8. Trigonometry 2.
  • 9. Planimetry 2. Applications of trigonometry for solving geometric problems.
  • 10. Statistics.

PART III (25 hours, 1 week)

The third part of the course is designed for students from 12th grade. During the academic year 2013/14 we intend to offer this course of lectures to the graduates of the first two parts. Currently we offer an abbreviated version for the college applicants who are still getting ready for entrance exams during the summer of 2013.

  • 15. Exponential and logarithmic functions.
  • 16. Stereometry.
  • 17. Derivatives of functions.
  • 18. Problems given on previous exams.