Exercises of mathematics

Hi. My name is Cristian Barbarosie. This page is about a collection of exercises in mathematics. Chapters published up to 2012.06 are:

Chapter	Number of exercices
1. Adding, subtracting, multiplying	20
2. Fractions	43
3. Powers	75
4. Equations	70
5. Inequations	47
6. Square roots	33
7. Cubic roots	21
8. Inequalities	23
9. Functions	44
10. Functions	38
11. Composition of functions	25

Click here to download the pdf file (version 2012.06). The version of the document is exhbited at the bottom of each page. I am working on expanding and improving this collection of exercises.

What are they good for ?

I have observed that, in these days, students encounter serious difficulties in learning mathematics and applying correctly mathematical knowledge. One reason for this is that each notion or technique, even after having been understood, needs to be "cemented" through practice, by solving many exercises. Students nowadays do not usually train enough the notions they have learned, and this list of exercises gives them the opportunity to train. Another reason for their difficulties in learning mathematics has to do with their habit of working and sudying in groups. Working in a group is great for devolopping the cooperation spirit, but in this way none of the students gets to know exactly what he or she has learned, since his or her knowledge get mixed with the other members of the group. Thus, students cannot self-evaluate and understand exactly what they have learned and how much they still have to study. This is why I these exercises should be solved by each student alone, with no help from the outside.

Are they difficult ?

The exercises are grouped by topic, and have an increasing degree of difficulty. Each exercise uses knowledge aqquired by solving the previous exercises.

At the end of the list, I have included some hints.

How can I know the correct answer to a given exercise ?

The document does not include answers. I am working in order to expand it and also to include some of the answers. In the meanwhile, you may send me your solution and I will gladly return to you my comments and corrections.

How do I send you my solution of an exercise ?

You can send it by e-mail, as a jpg or png file. Perhaps the easiest way to do it is to use a pad, writing directly on the touchscreen. I shall return to you my comments and corrections in the same format. My e-mail address is

Writing a solution to an exercise :

Please be careful when writing your solution to an exercise. Be sure to include the complete statement of the exercise. Then write down your solution, explaining each step you do. Write legibly and correctly, otherwise I might not be able to understand your text. You can use colors like green or blue, but do not use red (my comments will be written in red).

Can I send you an exercise and receive the solution ?

No. I offer solely to correct solutions sent by you.