Kiselev's Problems and Exercises in Elementary Algebra
by A. P. Kiselev
Translated by Valery Manokhin, PhD
The companion problem collection to Kiselev's Algebra. Hundreds of carefully sequenced problems and exercises that mirror the chapter structure of Algebra Part I and Part II — the same problem set Russian students worked through alongside Kiselev's algebra textbooks for over a century.
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
Not sure this is the right first book? Start here →Full curriculum table — every book by school year →| United States | 7–11 | Algebra 1 → Algebra 2 |
|---|---|---|
| England | Years 8–12 | KS3 → GCSE Higher → AS Pure |
| Canada (Ontario) | Ontario 8–11 | MTH1W → MPM2D → MCR3U |
Not covered in this book
statistics and data handling · probability · graphs of the trigonometric functions and radian measure
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Courses this goes with
- Bugaev's Algebra$64.95
- Davidov's Algebra$59.95
- Barsukov's Algebra$54.95
- Kiselev's Algebra II$54.95
- Kiselev's Algebra I$44.95
More practice in this subject
- Math Circle Problems$44.95
Table of contents
109 section headings — the printed contents page in full.
Translator's Preface
Table of contents109 sections
- Algebraic Notation
- Properties of the First Four Arithmetical Operations
- Addition of Relative Numbers
- Subtraction of Relative Numbers
- Main Properties of Addition and Subtraction
- Multiplication of Relative Numbers
- Division of Relative Numbers
- Some Properties of Multiplication and Division
- Equalities and Their Properties
- Identity. Equation
- The Simplest Problems on Forming Equations
- Polynomial and Monomial
- Subtraction of Polynomials
- Removing Parentheses and Enclosing in Parentheses
- Multiplication of Monomials
- Multiplication of a Polynomial by a Monomial
- Examples of Equations for the Solution of Which Knowledge Of
- Multiplication of a Polynomial by a Monomial Is Required
- Multiplication of Arranged Polynomials
- Some Formulas for the Multiplication of Binomials
- Division of Monomials
- Division of a Polynomial by a Monomial
- Division of a Polynomial by a Polynomial
- Factoring Polynomials
- Reducing the Terms of a Fraction to Integral Form
- Changing the Signs of the Terms of a Fraction
- Reducing Fractions
- Reducing Fractions to a Common Denominator
- Addition and Subtraction of Fractions
- Multiplication and Division of Fractions
- Clearing an Equation of Denominators
- Word Problems Leading to Equations with Fractional Terms
- Properties of Ratios
- Properties of Proportions
- The Geometric Mean and the Arithmetic Mean
- Derived Proportions
- Proportional Dependence (direct and Inverse)
- Graphs of Some Empirical Functions
- Coordinates of a Point
- Graph of a Proportional Dependence
- Graph of a First-degree Binomial
- Construction of a Straight Line from Two Points
- Graphical Solution of an Equation
- Extraneous Roots
- Examples of Equations Having No Roots
- Indeterminate Solution
- Literal Equations
- First-degree Inequalities
- Solution of a System of Two First-degree Equations
- Graphical Solution of a System of Two First-degree Equations
- Problems on Forming Two First-degree Equations
- Solution of a System of Three First-degree Equations
- Special Cases of Systems of Equations
- Problems on Forming Three Equations with Three Unknowns
- Squaring Monomials
- Squaring Polynomials
- Abbreviated Squaring of Whole Numbers
- Graphical Representation of the Functions y=x^2 and y=ax^2
- Proportionality of a Function to the Square of the Independent Variable
- Raising Monomials to the Cube and to Other Powers
- Graphs of the Function y = x^3 and y = ax^3
- The Concept of a Root
- Extraction of a Root from a Product, from a Power, and from a Fraction
- The Simplest Transformations of Radicals
- Extraction of the Greatest Exact Integer Square Root from Whole Numbers
- Extraction of Approximate Square Roots from Whole and Fractional Numbers
- Using the Table of Square Roots
- Extraction of the Square Root from Common Fractions
- Irrational Numbers
- Irrational Values of Radicals
- Approximate Computations
- Some Transformations of Radicals
- Similar Radicals
- Operations on Irrational Monomials
- Operations on Irrational Polynomials
- Removing Radicals from the Denominator of a Fraction
- Solution of Incomplete Quadratic Equations
- Graph of a Second-Degree Binomial
- Solution of Complete Quadratic Equations by Completing the Left-Hand Side to a Perfect Square
- Solution of the Reduced Quadratic Equation by the Formula for its Roots
- Solution of the Quadratic Equation by the General Formula for its Roots
- Problems on Forming a Quadratic Equation
- Properties of the Roots of a Quadratic Equation
- Factorization of a Second-Degree Trinomial into First-Degree Factors
- Graph of a Second-Degree Trinomial
- The Greatest and Least Value of a Trinomial. Its Variation
- Second-Degree Inequalities
- Biquadratic Equations
- Systems of Two Second-Degree Equations
- Miscellaneous Word Problems Leading to Quadratic Equations
- Arithmetic Progression
- Sum of the Squares of the Numbers of the Natural Sequence
- Geometric Progression
- Infinite Progressions
- Negative Exponents
- Fractional Exponents
- Exponential Function
- Definition of the Logarithm and its Notations
- Logarithmic Function
- Logarithming an Algebraic Expression
- Properties of Common Logarithms
- Transformation of a Negative Logarithm
- Finding the Logarithm of a Given Number
- Finding the Number from a Given Logarithm
- Operations on Logarithms with Negative Characteristics
- Replacing Subtracted Logarithms by Added Ones
- Examples of Computation by Means of Logarithms
- Compound Interest, Annuities, and Periodic Payments
- Some Examples of Mathematical Induction (cont.) (after § 301)
Formats and editions
| Format | List price (USD) | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Digital edition | $39.95 | — | Gumroad · Read online | Buy → |
| Kindle | $49.95 | — | Amazon | Buy → |
| Paperback | $44.95 | 978-1-9194658-0-7 | Amazon | Buy → |
| Hardcover | $69.95 | 978-1-919012-00-1 | Amazon | Buy → |
List price: the US publisher list price in USD, shown for reference. Amazon sets its own price in each store — see the current price on Amazon. The Gumroad price is the price charged.
The digital edition is read online in the Gumroad reader. It is not a downloadable file.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- First published
- 2026-06-14
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
More in This Series
Kiselev's Arithmetic
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The foundational arithmetic textbook used in Russian schools for over a century, in complete English translation. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation. Paperback, hardcover and Kindle on Amazon; the digital edition is read online in Gumroad; there is no file to download.
Kiselev's Algebra I
by A. P. Kiselev
US grades 7–9 · UK Years 8–10
6 chapters, 126 sections, 239 exercises. From relative numbers and polynomials through first-degree equations, powers, roots, and quadratics.
Kiselev's Algebra II
by A. P. Kiselev
US grades 9–12 · UK Years 10–13
12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.