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I'll be doing some tutoring and (to help myself with the presentation of the material) I need to find a rigorous and concise book (or books) about the topics that are commonly taught since primary school until the end of high school (right before starting the "calculus" sequences).

Does such books exist? Can you provide some examples?

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  • $\begingroup$ What are topics you'd like to see covered? I imagine they'd be something like: counting, addition, subtraction, multiplication, division (including long division), rationals, volumes and areas of simple shapes, (squares, circles, spheres, cubes, etc.), negative numbers, integer powers and integer roots, basic properties of polynomials, factoring trinomials, exponents, logarithms, trigonometry (the six major functions and their various identities), $e$, $\pi$, basic probability (over finite sample spaces), geometric and arithmetic series, and absolute value, and basic set theory. $\endgroup$ – Duncan Ramage Oct 30 '17 at 21:34
  • $\begingroup$ As well as what all those represent physically, and the various algorithms surrounding them. $\endgroup$ – Duncan Ramage Oct 30 '17 at 21:34
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It is not quite clear what level of rigor you are actually looking for, but you can try to look at the following books by Gelfand and co-authors:

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