What's a good book for last year of A levels Maths?

[PhysicsLad]

I'm looking for a book to self-study this summer before my last course of Bachillerato (A Levels or High School in other countries).

My performance in Mathematics has only improved and I've just been given the maximum mark this last term (10/10 or A+). This has motivated me a lot to keep studying on my own before attending classes again (in September).

The course content that I need to study is composed by the following:

- Linear Algebra (matrices, determinants, linear equation systems, Cramer's rule)
- Derivatives and Integrals (applications of Calculus, Rolle-Lagrange-Cauchy-l'Hopital, definite and indefinite integrals)
- Geometry (vector space, points planes and lines, positions...)

I'm comfortable at playing with real numbers, doing essential derivative stuff (Chain rule and so on), solving limits. I know basic trigonometry and 2d plane geometry, introductory Statistics and Probability, typical imaginary numbers stuff, binomial theorem, solving basic systems with Gauss method...

The book would ideally be free but I can always access it anyway, if you know what I mean. I will study Physics at uni after this course. If you can point me out some introductory Combinatorics it's a big plus...

 

[verty]

MIT has courses meant for high-schoolers, the "scholar" versions. Search for "MIT Scholar" and you'll find what you need.

PS. I notice what you must learn is not that deep, for example Taylor's theorem is not included. So these scholar courses are probably at the right level for you.

 

[PhysicsLad]

Thank you. I'm taking a look at the Single Variable Calculus lectures.

 

[PhysicsLad]

Anybody?

 

[verty]

You've been helped, young man. And asking for books that you can download anyway is asking for trouble.

 

[PhysicsLad]

Aight, I was just hoping somebody would help with the Geometry and Combinatorics part (I didn't find info about these on MIT).

Where did I mention downloads though? There are plenty of public libraries here (I just prefer open source for readiness and personal preference)