Shaposhnikov and Valtsov's Collection of Algebra Problems, Part II
by N. A. Shaposhnikov & N. K. Valtsov
Translated by Valery Manokhin, PhD
1,531 classical algebra problems with answers, in the first complete English translation. Part II continues the sequence begun in Part I, carrying the student through the advanced topics of the classical Russian algebra course — the problem collection that trained generations of students alongside Kiselev.
· 1531 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 | 9–12 | Algebra 2 → Precalculus |
|---|---|---|
| United Kingdom | Years 10–13 | GCSE Higher (surds are Higher-only) → A-level Pure → Further Maths |
| Canada | Ontario 10–12 | MPM2D → MCR3U → MHF4U |
Not covered in this book
graphs of the trigonometric functions and radian measure · 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 →Work through first
Problems to work alongside it
- Elementary Algebra$69.95
- Kiselev's Algebra II$54.95
Table of contents
50 section headings — the printed contents page in full.
Publisher's Note
Irrational Expressions13 sections
- General Information on Roots. Extraction of a Root from a Monomial
- Bringing a Factor Out from Under the Radical and Introducing a Factor Under the Radical
- Reducing Root Indices and Reducing Radicals to a Common Index
- Reducing Roots to Normal Form
- Similarity of Roots
- Addition and Subtraction of Roots
- Multiplication and Division of Roots
- Raising Roots to a Power and Extracting a Root from Them
- Removing Irrationality in the Denominator of a Fraction
- Square Root of a Binomial of the Form A ± B
- Problems on All Operations with Radicals
- Powers and Roots with Fractional Exponents
- Imaginary Numbers
Functions and Their Graphs
Quadratic Equations4 sections
- Solving Literal Quadratic Equations
- Properties of the Roots of a Quadratic Equation
- Composing Literal Quadratic Equations
- Graph of a Quadratic Function
Equations of Higher Degrees5 sections
- The Biquadratic Equation
- The Binomial Equation
- The Trinomial Equation
- Equations Whose Left-Hand Side Factors
- The Reciprocal, or Symmetric, Equation
Irrational Equations
Systems of Equations of Degree Higher than the First3 sections
- Solving Systems of Equations
- Composing Systems of Equations
- Graphical Solution of Systems of Two Equations of the Second Degree in Two Unknowns
Progressions2 sections
- The Arithmetic, or Difference, Progression
- The Geometric, or Multiple, Progression
Logarithms4 sections
- General Properties of Logarithms
- Decimal Logarithms
- Exponential and Logarithmic Equations
- Compound Interest Problems
Combinatorics
Newton's Binomial
Divisibility of Polynomials
Inequalities
Solving Indeterminate Equations of the First Degree
Continued Fractions
Investigation of Equations3 sections
- Investigation of First-Degree Equations with One Unknown
- Investigation of a System of First-Degree Equations with Two Unknowns
- Investigation of Second-Degree Equations
Limits
Answers16 sections
- Chapter IX. Irrational Expressions
- Chapter X. Functions and Their Graphs
- Chapter XI. Quadratic Equations
- Chapter XII. Equations of Higher Degrees
- Chapter XIII. Irrational Equations
- Chapter XIV. Systems of Equations of Degree Higher than the First
- Chapter XV. Progressions
- Chapter XVI. Logarithms
- Chapter XVII. Combinatorics
- Chapter XVIII. Newton's Binomial
- Chapter XIX. Divisibility of Polynomials
- Chapter XX. Inequalities
- Chapter XXI. Indeterminate Equations of the First Degree
- Chapter XXII. Continued Fractions
- Chapter XXIII. Investigation of Equations
- Chapter XXIV. Limits
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $44.95 | — | Gumroad · Instant download | Buy → | |
| Paperback | $44.95 | 978-1-919012-50-6 | Amazon | Buy → |
| Hardcover | $74.95 | 978-1-919012-51-3 | 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
- 2026-08-24
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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