Recommendations for books with solutions, to review wholly high school math?

Question

I am looking for books for the full high school maths curriculum, just to refresh myself (it's been years). it must have questions & solutions.

Answer 1

I think you posted this question earlier today and I had about a three paragraph response with a ton of advice but then you deleted the post (apologies if that wasn't you). So... here is the abbreviated version. Read the following books,

• Practice Makes Perfect: Algebra. [Amazon Link]
• Practice Makes Perfect: Precalculus. [Amazon Link]
• Practice Makes Perfect: Calculus. [Amazon Link]

If you are interested in getting access to higher mathematics afterwards I recommend the following book by Chartrand, Polimeni, and Zhang. It is an incredible introduction to proofs and various areas of mathematics.

"Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang. [Amazon Link]

There is an entire chapter devoted to each of the following:

• Communicating Mathematics
• Naive Set Theory
• Logic
• Direct Proof
• Proof by Contrapositive
• Existence and Proof by Contradiction
• Mathematical Induction (and Strong Induction)
• Equivalence Relations (Equivalence Classes, Congruence Modulo n, Modular arithmetic)
• Functions (Bijective, Inverse, Permutations)
• Set Theory (up to Schroder-Bernstein Theorem and the Continuum Hypothesis)
• Number Theory
• Calculus (Limits, Infinite Series, Continuity, Differentiability)
• Group Theory (up to Isomorphic Groups)

With Three Additional Chapters online covering:

• Ring Theory
• Linear Algebra
• Topology

That should keep you busy for a while, and after reading through Chartrand/Polimeni/Zhang, you will know what area of mathematics you are more interested in or if you still want to learn more!