Technology Leaders of the Future | Fully-Funded Scholarship Program

Prerequisites

Below, you can find prerequisites based on the selected program:

The oral exam is held individually, and you will need to select a time slot for your participation.
The first part is very similar to the written math exam (see this link).
Unlike the written exam, you’ll have 60 minutes. You don’t need to write out full solutions — just notes to help you explain them orally.
After uploading your notes, you will join a Zoom call. Make sure Zoom is installed beforehand: zoom.us/download.
Once the teacher is available, you’ll be moved to a private breakout room.
You’ll have access to an online board with your problems and notes. You’ll explain your solutions and answer questions.
If time permits, the teacher may give you an additional problem to discuss.

The hardware requirements are the same as for the written exam (see link).
Additionally, you must install Zoom and know how to join a meeting using an ID and password.

Topics for problems are listed below.
Problems will be in English.
You’ll need to explain solutions and answer teacher’s questions.
You may use your handwritten notes during the discussion.
The teacher may assign an additional problem.
You don’t have to solve every problem, but try your best.
Problems may be solved in any order.
You may use pen, pencil, and paper.
Calculators, help from others, AI tools (ChatGPT etc.), and tab switching are prohibited.
If needed, use the chat button ("?") to ask a question or request translation help.

You will first select your exam time via a link we will provide.
Do a test run in advance to make sure everything works correctly.
At the appointed time, start the exam just like in the written version.
You’ll have 60 minutes and may only make supporting notes.
After uploading your notes, join the Zoom call and sign in with your full name in Latin script.
When the teacher is ready, you’ll be transferred to a private room for discussion.
You will have 30 minutes to present your solutions and answer questions.

Number theory
- Divisibility and its properties
- Divisibility tests for 3, 4, 8, 9, 11
- Euclidean division
- Prime and composite numbers
- Fundamental theorem of arithmetic
- Greatest Common Divisor and Least Common Multiple
Algebra
- Percents
- Inequalities and operations with them
- Laws of exponents with integer exponents
- Linear equations and inequalities
- System of equations
- Properties of graphs of linear functions. Parallel and orthogonal lines
- Absolute value and its properties. Triangle inequality
- Rational numbers. Infinite periodic decimals
- Average speed and "joint work" text problems
- "Remarkable identities"
  - \((a+b)^2\), \((a-b)^2\)
  - \(a^2-b^2\)
  - \((a+b)^3\), \((a-b)^3\)
  - \(a^3-b^3\), \(a^3+b^3\)
  - \(a^{2n+1}-b^{2n+1}\), \(a^{2n+1}+b^{2n+1}\)
Combinatorics and Probability theory
- Venn's diagram
- Rule of sum
- Rule of product
- Permutations
- Arrangement with repetition
- Definition of probability
- Average, median, mode
- Quartiles
Geometry
- Congruent triangles. Criteria for congruence
- Angles between parallel lines and a transversal
- Sum of angles of a triangle, quadrilateral, pentagon, \(n\)-gon
- Properties of isosceles triangles. The median, altitude, and angle bisector drawn from the vertex opposite the base coincide.
- Area of a rectangle, right triangle, disc, composite figures
- Circle, radius, diameter. Properties of radius orthogonal to diameter.

In addition to the topics above:

Algebra
- Rational exponent
  - Surds. Definition, properties, rationalisation.
  - Graph of \(\sqrt[n]{x}\)
  - Rational exponent and its properties
- Quadratic function
  - Quadratic equations and equations equivalent to quadratic
  - Completing the square
  - Graph of a quadratic function
  - Quadratic inequalities
Combinatorics and probability theory
- Probability with a finite set of outcomes
Geometry
- Quadrilaterals
  - Parallelogram, rhombus, rectangle. Properties and criteria
  - Trapezium. Properties and criteria
  - Midsegment of a parallelogram, triangle, and trapezium
- Right triangle
  - Trigonometry of right triangle
  - Pythagoras theorem
- Circle
  - Tangent. Properties of a circle inscribed in an angle, incircle of a triangle
  - Parallelogram is inscribed if and only if it is a rectangle
  - Trapezium is inscribed if and only if it is an isosceles trapezium

In addition to the topics above:

Algebra
- Arithmetic progressions and their properties
- Geometric progressions and their properties
- Trigonometric function
  - Definition and basic properties
  - Cofunction identities and periodicity
  - Graph of trigonometric function
  - Angle sum and difference identities
  - Double-angle formulae
Combinatorics and probability theory
- Conditional probability, law of total probability
Geometry
- Law of cosines
- Law of sines
- Similar triangles. Triangle tests. Areas of similar figures.