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Interesting Mathematical Problems

Non-obvious problems and interesting mathematical challenges for those who want to think outside the box and go beyond the standard curriculum.

Matematyka
Problemy
PDF materials are in English

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What you will learn

Break an unusual problem apart and look for a familiar pattern inside it

Choose a method that fits the problem instead of relying on one memorised recipe

Write a solution that someone else can follow step by step

Check the result and judge whether it makes sense at all

Who this course is for

Students who are bored

These problems go beyond textbook drills and ask for an idea rather than a procedure.

Competition candidates

Good training ground for contests, where the way you think matters more than arithmetic speed.

Teachers looking for material

Ready-made problems with solutions you can put on the board and take apart with a class.

How to use the materials

1

Download a lesson

Every lesson is a short PDF with theory and worked examples. No account required.

2

Work through the examples

Cover the solution, solve it your own way, and only then compare. That is the part that makes it stick.

3

Practise on the board

Open PhiBoard and redo the problem yourself, with formulas, graphs and room to work at hand.

Materials

Open the lesson materials and start learning.

Lesson 1

The square of a difference of roots times the cosine of 120°

Lesson 2

A fraction with powers, a squared logarithm and the sine of 210°

Lesson 3

Powers with logarithmic exponents

Lesson 4

A compound fraction with negative powers and logarithms

Lesson 5

Values of a rational function at irrational arguments

Lesson 6

Determining the domain of a function

Frequently asked questions

Do the problems come with solutions?

Yes. Every problem includes a full step-by-step solution in the same file.

How hard are they?

From strong secondary-school level up to problems that need a genuine idea, of the kind found at university and in competitions.

Are the materials free?

Yes, they are free to download and need no account.

Can I use them in class?

Yes, you may use them with students. We only ask that you keep the attribution.

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Interesting Mathematical Problems | PhiBoard