Toughest elementary mathematics and physics problem book?!!?

by **aldric13** » Sat Jul 14, 2012 10:49 pm

I am a student of class 10 and I am a physics and mathematics enthusiast. But I find the problems given in my textbook very very easy. On asking, my teacher recommended me the Pearson IIT Foundation Course saying that it has some really tough questions. But again, while all my classmates struggled through it, it was a cakewalk for me. I love tough problems, the more tough the more is the FUN provided that the questions are not much out of the scope of my syllabus. So ARE THERE ANY TEXTBOOKS HAVING MIND-BOGGLING QUESTIONS (NUMERICAL PROBLEMS)?
The scope of my syllabus is:
PHYSICS:
1. Motion in one dimension
2. Force
3. Simple Machines (Including block and tackle pulley system)
4. Refraction of light at Plane surfaces
5. Refraction through a lens
6. Spectrum
7. Sound (Including Forced vibrations and resonance)
8. Current Electricity (not including Kirchoff's law)
9. Electrical power and House hold circuits
10. Electro-magnetism
11. Heat and principle of calorimetry
12. Thermionic emissions and radioactivity
MATHEMATICS:
Algebra:
1. Linear inequalities in one variable
2. Quadratic Equations
3. Factorization (including Factor and Remainder theorem)
4. HCF and LCM of Polynomials by factorization
5. Ratio and proportion
6. Matrices
7. Logarithms
Coordinate geometry:
1. Refection (Reflection of a point about a line and reflection of a point about origin)
2. Distance and Section Formula
3. Equation of a straight line
Geometry:
1. Symmetry
2. Triangles (including inequalities)
3. Similarity
4. Loci
5. Circle
6. Properties of arcs and chords
7. Cyclic properties of a circle
8. Properties of tangents
9. Construction
Mensuration:
1. Area and perimeter of a circle
2. Three-Dimensional Solids
Trigonometry:
1. Trigonometry Identities
2. Trigonometric Ratios of Complementary angles
3. Heights and Distances
Statistics and Probability:
1. Graphical Representation
2. Measures of Central Tendency
3. Probability

by **beacher** » Sat Jul 14, 2012 11:03 pm

I am a student of class 10 and I am a physics and mathematics enthusiast. But I find the problems given in my textbook very very easy. On asking, my teacher recommended me the Pearson IIT Foundation Course saying that it has some really tough questions. But again, while all my classmates struggled through it, it was a cakewalk for me. I love tough problems, the more tough the more is the FUN provided that the questions are not much out of the scope of my syllabus. So ARE THERE ANY TEXTBOOKS HAVING MIND-BOGGLING QUESTIONS (NUMERICAL PROBLEMS)?
The scope of my syllabus is:
PHYSICS:
1. Motion in one dimension
2. Force
3. Simple Machines (Including block and tackle pulley system)
4. Refraction of light at Plane surfaces
5. Refraction through a lens
6. Spectrum
7. Sound (Including Forced vibrations and resonance)
8. Current Electricity (not including Kirchoff's law)
9. Electrical power and House hold circuits
10. Electro-magnetism
11. Heat and principle of calorimetry
12. Thermionic emissions and radioactivity
MATHEMATICS:
Algebra:
1. Linear inequalities in one variable
2. Quadratic Equations
3. Factorization (including Factor and Remainder theorem)
4. HCF and LCM of Polynomials by factorization
5. Ratio and proportion
6. Matrices
7. Logarithms
Coordinate geometry:
1. Refection (Reflection of a point about a line and reflection of a point about origin)
2. Distance and Section Formula
3. Equation of a straight line
Geometry:
1. Symmetry
2. Triangles (including inequalities)
3. Similarity
4. Loci
5. Circle
6. Properties of arcs and chords
7. Cyclic properties of a circle
8. Properties of tangents
9. Construction
Mensuration:
1. Area and perimeter of a circle
2. Three-Dimensional Solids
Trigonometry:
1. Trigonometry Identities
2. Trigonometric Ratios of Complementary angles
3. Heights and Distances
Statistics and Probability:
1. Graphical Representation
2. Measures of Central Tendency
3. Probability

You want mind-boggling problems?

Try the Millennium prize problems.
You would even get a Million Dollars for solving them.

Now I know it's not a textbook, but I'd say those problems are hard enough, eh?

Try the Collatz Conjecture.
It's not a featured millennium prize problem, but you would still get a million dollars.

by **ruddy** » Sat Jul 14, 2012 11:15 pm

For physics, you can try to solve problems of
"Problems in General Physics" by I.E.Irodov
For mathematics, I suggest you to buy some book which gives problems asked in IMO (International Math Olympiad) and try to solve them.

Edit:
Let me add that I am, myself, not able to solve a large number of IMO problems and in case, you also failed to do so, you should not get discouraged. Possibly some solutions may be available in the market or on the net which can help you to master the subject. Since you are interested in mathematics and are reasonably good at it, you should be able to achieve your goal.

by **barraq** » Sat Jul 14, 2012 11:22 pm

When you have reached a certain level of mastery in a unit of study, then rather than drill deeper into that same subject matter, it's better to move into the next unit.

If you have all the standard coursework in the syllabus you've outlined well in hand, then it's time you were introduced to analysis/pre-calculus. If those are similarly easy for you, then move on into calculus.

I don't know how your school system is structured, but often there will be administrative resistance to such a program, because "it's too great a burden on the system." My feeling is that if a system can't be bothered with supporting exceptional students, then it will only ever churn out mediocre ones, and it's time to change the system. But if this is the case, it isn't your fight -- you need an adult advocate, i.e., a teacher or parent. I hope it doesn't come to that.

One of my sisters and I had similar experiences. In my case, I was already in an advanced-placement math track, when my teacher in my sophomore year (10th grade) decided I was already on top of the material in the course he was giving. I was lucky he was such an energetic, pro-active teacher, and he saw to it that I got put into the class with the seniors (12th grade), and for the following two years, he got me into night courses in the local community college.

In my sister's case, she was reading two grade levels ahead of the rest of the class, when the teacher called on my parents to meet with her for "a problem" with this student. In her case, her luck was to have our Dad for a father, because when he found out that the problem was that she was so far ahead of the rest of the class that the teacher was having trouble keeping her occupied, he just about had a cow! He saw to it that she got put into a more challenging class, with a more dedicated teacher, and she's been exceptional in letters ever since.

I hope that a similarly positive fate awaits you, but if your school system is too rigid, then just get all the material you can lay a hand on to challenge your ability, and you'll do exceptionally well, as you're obviously cut out to do!

Best of luck, either way!

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