Shaposhnikov and Valtsov's Collection of Algebra Problems, Part I
by N. A. Shaposhnikov & N. K. Valtsov
Translated by Valery Manokhin, PhD
2,228 classical algebra exercises with answers, in the first complete English translation. First published 1887–1890 and reissued in more than 50 editions, this is the problem collection that trained generations of Russian students alongside Kiselev. 9 chapters, sequenced from elementary operations through quadratic equations, with an answer key covering more than 1,300 entries.
9 chapters · 2228 exercises
Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | 7–10 | Algebra 1, spilling into Algebra 2 |
|---|---|---|
| United Kingdom | Years 8–11 | KS3 → GCSE Foundation and Higher |
| Canada | Ontario 8–10 | MTH1W · MPM2D |
Not covered in this book
graphs and the function concept · coordinate geometry · statistics and data handling · probability
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Problems to work alongside it
- Elementary Algebra$69.95
- Kiselev's Algebra I$44.95
What comes next
Table of contents
59 section headings — the printed contents page in full.
Publisher's Note
Basic Algebraic Notation9 sections
- § 1. Algebraic Expressions
- § 2. Algebraic Formulas
- § 3. The Coefficient
- § 4. Power
- § 5. The Root
- § 6. Order of Operations. Brackets
- § 7. Substitutions
- § 8. General Formulas for Solving Arithmetic Problems
- § 9. Evaluation of Algebraic Expressions
Operations on Signed Numbers3 sections
- § 1. The Notion of a Signed Number. The Number Line
- § 2. Addition and Subtraction of Signed Numbers
- § 3. Multiplication and Division of Signed Numbers
Operations with Monomials and Polynomials11 sections
- § 1. Reduction of Like Terms of a Polynomial
- § 2. Addition and Subtraction of Monomials and Polynomials
- § 3. Removing and Inserting Brackets
- § 4. Multiplication of Monomials
- § 5. Multiplication of a Polynomial by a Monomial
- § 6. Multiplication of Polynomials
- § 7. Division of Monomials
- § 8. Division of a Polynomial by a Monomial
- § 9. Division of a Polynomial by a Polynomial
- § 10. Abbreviated Multiplication
- § 11. Abbreviated Division
Factoring into Factors8 sections
- § 1. Factoring Out a Common Factor
- § 2. Factoring Out a Polynomial Factor
- § 3. The Grouping Method
- § 4. Applying the Abridged-Multiplication Formulas
- § 5. Applying the Abridged-Division Formulas
- § 6. Applying All the Methods Described Above
- § 7. Greatest Common Divisor
- § 8. Least Common Multiple
Fractions7 sections
- § 1. Reduction of Fractions
- § 2. Reducing Fractions to a Common Denominator
- § 3. Addition and Subtraction of Fractions
- § 4. Multiplication of Fractions
- § 5. Division of Fractions
- § 6. Problems on All Operations with Fractions
- § 7. Negative and Zero Exponents
Raising to a Power
Transformation of Equalities. First-Degree Equations7 sections
- § 1. Proportions
- § 2. The Equation in One Unknown
- § 3. The System of Equations
- System of three equations.
- System of four or more equations.
- § 4. Forming Equations
- Problems on Forming Equations
Square Root2 sections
- Extraction of the Square Root of Numbers
- Finding Approximate Square Roots
Quadratic Equations with Numerical Coefficients3 sections
- Solving Numerical Equations of the Second Degree
- Properties of the Roots of a Quadratic Equation and Factoring a Second-Degree Trinomial
- Forming a Quadratic Equation in One Unknown
Answers9 sections
- Chapter I. Basic Algebraic Notation
- Chapter Ia. Operations on Signed Numbers
- Chapter II. Operations with Monomials and Polynomials
- Chapter III. Factoring into Factors
- Chapter IV. Fractions
- Chapter V. Raising to a Power
- Chapter VI. Transformation of Equalities. First-Degree Equations
- Chapter VII. Square Root
- Chapter VIII. Quadratic Equations with Numerical Coefficients
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $49.95 | — | Gumroad · Instant download | Buy → | |
| Paperback | $44.95 | 978-1-919012-37-7 | Amazon | Buy → |
| Hardcover | $74.95 | 978-1-919012-38-4 | Amazon | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- First published
- 2026-08-11
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
More in This Series
Rachinsky's 1001 Problems
by S. A. Rachinsky
US grades 4–8 · UK Years 5–9
1,001 carefully selected problems from the village schoolteacher whose students were depicted in Bogdanov-Belsky's famous 1895 painting "Mental Arithmetic."
Perelman's Entertaining Arithmetic
by Ya. I. Perelman
US grades 4+ · UK Year 5+
The classic of Russian popular mathematics. Puzzles, riddles, and curiosities that make arithmetic genuinely entertaining.
Markov: Probabilities
by Andrei A. Markov
US grades 12 and university · UK Year 13 and university
The foundational 1900 work on probability theory by the mathematician who gave us Markov chains. A modern annotated English translation.