In this lesson, we will use an important result known as the Triangle Inequality:

|x| + |y| ≥ |x + y|

This inequality shows that the sum of the absolute values of two numbers is always greater than or equal to the absolute value of their sum. In geometry, this means the sum of the lengths of two sides of a triangle is always at least as large as the length of the third side.

‍

Problems

Solve the equation |2026 − x| + |x − 2026| = 2025.
Solve the inequality |x + 2025| < |x − 2026|.
Prove that if a + b + c + d > 0, a > c, and b > d, then |a + b| > |c + d|.
Prove that there are no real numbers x, y, t such that all three inequalities hold at the same time: |x| < |y − t|, |y| < |t − x|, |t| < |x − y|.
On the coordinate plane, plot all points whose coordinates satisfy the equation y² − |y| = x² − |x|.
Sophie says that for any three points A, B, and C in the plane, the inequality AB ≥ |AC − BC| holds. Prove that she is correct.
Emily claims that in any triangle, the length of any side does not exceed the semiperimeter. Prove that she is right.
Two rivers (straight lines) — one with fresh water and one with salt water — intersect at an acute angle. Inside this acute angle stands Tom, who wants to collect both fresh and salt water and return to his starting point. How should he do this while travelling the minimum possible distance

‍

Where do you hold your classes?

We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.

What do you need to start learning online?

For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.

When can I take the trial lesson?

You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.

What should I expect from the trial lesson?

The trial lesson is a 30-minute online session designed to get a sense of how your child approaches mathematical thinking and problem solving. (In practice, it often runs a bit longer if the student is engaged!)

We typically explore a range of fun and challenging problems drawn from competitions. We adapt the difficulty based on how the student responds, aiming to make it both accessible and stimulating.

After the session, we’ll have a quick conversation with the parent to share observations and suggest a personalised path forward.

I can't attend class, what should I do?

It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to

I don't have much free time, will I have time to study?

Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.

How long is one lesson?

All classes last 1 hour.

Meet our team

Our teachers will tell you how to prepare for exams, help you cope with difficult tasks and win the Olympiad
‍
They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them

George Ionitsa

Founder &
Maths and Coding Coach

Hear from some of our amazing students who already achieved incredible results with us!

"Olympiad Maths Lessons helped me a lot to get the Gold medal in Junior Maths Challenge"

St. Paul's Student

"Thanks to the 'Data Science' and 'Coding in Python' lessons I got accepted to my dream university."

Data Science Student
Warwick University

"Great courses, which thoroughly explained topics beyond the capability of the GCSE answer sheet. Thanks so much."

Ivan

GCSE Student in Dubai

"Financial Mathematics! Best course to understand Python and Mathematics behind Finance!"

Gleb

VC Investor

"We got silver in PMC! Thanks George!"

Mum of St. Paul's Student

Prepare for the Primary Maths Challenge

"My daughter took a batch of 10 classes with George to understand Python with Turtle. I found George extremely knowledgeable and accessible."

Dad of Latymer School Student

Python with Turtle