∑ Old Books, New Math

First Course in Algebra · 1910

Algebra 1

In 1910 three teachers wrote one of the clearest beginning algebra books of its day. This course keeps their explanations and their problems, more than a century of students' worth, and adds instant answer checking, hints, and progress tracking.

By Herbert E. Hawkes, William A. Luby & Frank C. Touton. Read the original scan.

Start: Symbols

Chapter 1 Introduction to Algebra

Chapter challenge
  1. Symbols §1, 2 · 0/28 solved
  2. The Usefulness of Symbols §3 · 0/20 solved
  3. Factors, Exponents, and Coefficients §4, 5, 6, 7, 8 · 0/17 solved
  4. Order of Operations §9 · 0/14 solved
  5. Evaluating Expressions §10 · 0/50 solved

Chapter 2 Positive and Negative Numbers

Chapter challenge
  1. The Number Line §11 · 0/12 solved
  2. Signed Numbers in Real Life §12 · 0/8 solved
  3. Adding Signed Numbers §13 · 0/32 solved
  4. Subtracting Signed Numbers §14 · 0/51 solved
  5. Multiplying Signed Numbers §15 · 0/20 solved
  6. Dividing Signed Numbers §16 · 0/18 solved
  7. Putting It Together §16 · 0/87 solved

Chapter 3 Addition

Chapter challenge
  1. Adding Monomials §17 · 0/34 solved
  2. Adding Polynomials §18 · 0/31 solved

Chapter 4 Simple Equations

Chapter challenge
  1. Solving Simple Equations §19 · 0/20 solved
  2. Turning Words into Algebra §19 · 0/26 solved
  3. Word Problems §19 · 0/21 solved

Chapter 5 Subtraction

Chapter challenge
  1. Subtracting Monomials §20 · 0/18 solved
  2. Subtracting Polynomials §21 · 0/43 solved

Chapter 6 Identities and Equations of Condition

Chapter challenge
  1. Identities and Transposition §22 · 0/23 solved
  2. Representing Numbers §22 · 0/39 solved
  3. Solving Problems §23 · 0/42 solved

Chapter 7 Parentheses

Chapter challenge
  1. Removing Parentheses §24 · 0/24 solved
  2. Putting Terms in Parentheses §25 · 0/8 solved

Chapter 8 Multiplication

Chapter challenge
  1. Multiplying Monomials §26, 27 · 0/30 solved
  2. Polynomial Times Monomial §28 · 0/20 solved
  3. Multiplying Polynomials §29, 30, 31, 32, 33, 34 · 0/42 solved

Chapter 9 Parentheses in Equations

Chapter challenge
  1. Equations with Parentheses §35 · 0/23 solved
  2. Binomials as Quantities §35 · 0/15 solved
  3. Problems with Two or More Unknowns §36 · 0/35 solved

Chapter 10 Division

Chapter challenge
  1. Dividing Monomials §37 · 0/28 solved
  2. Dividing a Polynomial by a Monomial §38 · 0/23 solved
  3. Long Division of Polynomials §39 · 0/43 solved

Chapter 11 Equations and Problems

Chapter challenge
  1. Equations with Letter Coefficients §40 · 0/20 solved
  2. Uniform Motion §41 · 0/38 solved
  3. Review: Chapters 1 to 11 §Review · 0/66 solved

Chapter 12 Important Special Products

Chapter challenge
  1. The Square of a Binomial §42 · 0/71 solved
  2. Sum Times Difference §43 · 0/80 solved
  3. Binomials with a Common Term §44 · 0/63 solved
  4. Squares of Polynomials, Cubes of Binomials §45, 46 · 0/27 solved

Chapter 13 Factoring

Chapter challenge
  1. Roots of Monomials §47, 48 · 0/42 solved
  2. Common Monomial Factors §49 · 0/24 solved
  3. Factoring by Grouping §50 · 0/43 solved
  4. Perfect Square Trinomials §51 · 0/39 solved
  5. Trinomials $x^2 + bx + c$ §52 · 0/50 solved
  6. Trinomials $ax^2 + bx + c$ §53 · 0/52 solved
  7. The Difference of Two Squares §54 · 0/99 solved
  8. Sums and Differences of Cubes §55 · 0/54 solved
  9. Factoring: Putting It All Together §56 · 0/54 solved

Chapter 14 Solving Equations by Factoring

Chapter challenge
  1. Solving Equations by Factoring §57 · 0/36 solved
  2. Problems Solved by Factoring §57 · 0/41 solved

Chapter 15 Highest Common Factor and Lowest Common Multiple

Chapter challenge
  1. Highest Common Factor §58 · 0/23 solved
  2. Lowest Common Multiple §59 · 0/28 solved

Chapter 16 Fractions

Chapter challenge
  1. Reducing Fractions to Lowest Terms §60, 61 · 0/25 solved
  2. Changes of Sign in a Fraction §62 · 0/8 solved
  3. Equivalent Fractions and the L.C.D. §63 · 0/18 solved
  4. Adding and Subtracting Fractions §64 · 0/47 solved
  5. Adding Fractions: Watch the Signs §64 · 0/13 solved
  6. Mixed Expressions §65 · 0/14 solved
  7. Multiplying Fractions §66 · 0/25 solved
  8. Dividing Fractions §67 · 0/25 solved
  9. Complex Fractions §68 · 0/30 solved

Chapter 17 Equations Containing Fractions

Chapter challenge
  1. Clearing an Equation of Fractions §69 · 0/24 solved
  2. Problems Leading to Fractional Equations §69 · 0/20 solved
  3. Polynomial Denominators §70 · 0/32 solved
  4. Equations with Decimals §71 · 0/11 solved
  5. Literal Equations §72 · 0/31 solved
  6. Formulas: Primes and Subscripts §73 · 0/22 solved
  7. The Lever §74 · 0/5 solved
  8. Problems: Numbers, Ages, Money, and Areas §74 · 0/26 solved
  9. Problems: Work and Motion §74 · 0/27 solved

Chapter 18 Ratio and Proportion

Chapter challenge
  1. Ratio §75 · 0/15 solved
  2. Dividing in a Given Ratio §75 · 0/10 solved
  3. Proportion §76 · 0/14 solved
  4. Mean, Third, and Fourth Proportionals §76 · 0/18 solved
  5. Products into Proportions; Alternation and Inversion §76 · 0/37 solved
  6. Composition and Division §76 · 0/13 solved
  7. A Series of Equal Ratios §76 · 0/6 solved
  8. Miscellaneous Exercises in Proportion §76 · 0/20 solved

Chapter 19 Graphical Representation

Chapter challenge
  1. Reading a Graph: The Temperature Curve §77 · 0/6 solved
  2. The Falling-Body Curve §78 · 0/2 solved
  3. Coördinates and Plotting Points §79, 80 · 0/6 solved
  4. The Graph of an Equation §80 · 0/7 solved
  5. Graphing Linear Equations §80 · 0/23 solved
  6. Solving Two Equations Graphically §81 · 0/18 solved
  7. Graphs of Statistics §82 · 0/5 solved

Chapter 20 Linear Systems

Chapter challenge
  1. Systems: Solving by Addition or Subtraction §83, 84 · 0/16 solved
  2. Solving by Substitution §85 · 0/12 solved
  3. Systems Containing Fractions §86 · 0/26 solved
  4. Problems in Two Unknowns §86 · 0/24 solved
  5. More Problems in Two Unknowns: Work, Streams, and Trains §86 · 0/22 solved
  6. Literal Equations in Two Variables §87 · 0/20 solved
  7. Problems with Letters §87 · 0/23 solved
  8. More Problems with Letters: Money, Work, and Motion §87 · 0/22 solved
  9. Systems in Three and Four Variables §88 · 0/15 solved
  10. Problems in Three and Four Unknowns §88 · 0/21 solved

Chapter 21 Square Root and Radicals

Chapter challenge
  1. Square Root of Polynomials §89 · 0/21 solved
  2. Square Root of Numbers §90 · 0/12 solved
  3. Square Roots in Right Triangles §90 · 0/19 solved
  4. Radicals and Fractional Exponents §91 · 0/38 solved
  5. Writing Radicals with Fractional Exponents §91 · 0/21 solved
  6. Simplest Form of a Radical §92 · 0/35 solved
  7. More Simplification; Radicals Under One Sign §92 · 0/22 solved
  8. Addition and Subtraction of Radicals §93 · 0/25 solved
  9. Multiplication of Radicals §94 · 0/21 solved
  10. Radicals of Different Orders; Products of Polynomials §94 · 0/25 solved
  11. Powers of Radicals §94 · 0/36 solved
  12. Rationalizing Factors §95 · 0/25 solved
  13. Division of Radicals §95 · 0/32 solved
  14. Binomial Divisors and Approximate Values §95 · 0/24 solved
  15. Problems in Simplest Radical Form §95 · 0/16 solved
  16. Factors Involving Radicals §96 · 0/22 solved

Chapter 22 Graphical Solution of Equations in One Unknown

Chapter challenge
  1. Functions and the Graph of a Linear Function §97 · 0/13 solved
  2. Graph of a Quadratic Function §98 · 0/22 solved
  3. Imaginary Roots and the Graph §99 · 0/4 solved

Chapter 23 Quadratic Equations

Chapter challenge
  1. Solution by Completing the Square §100 · 0/21 solved
  2. Harder Equations; Equations in the Quadratic Form §100 · 0/25 solved
  3. Quadratic Equations with Literal Coefficients §101 · 0/21 solved
  4. Solution by Formula §102 · 0/23 solved
  5. Problems Leading to Quadratics §102 · 0/18 solved
  6. Problems of Rate, Work, and Falling Bodies §102 · 0/14 solved
  7. Geometrical Problems §102 · 0/11 solved

Chapter 24 Graphs of Quadratic Equations in Two Variables

Chapter challenge
  1. Parabola, Hyperbola, Circle, and Ellipse §103 · 0/10 solved
  2. Graphical Solution of a Quadratic System §104 · 0/9 solved

Chapter 25 Systems Solvable by Quadratics

Chapter challenge
  1. One Equation Linear, One Quadratic §105, 106 · 0/12 solved
  2. Special Devices: Squares of Sums and Differences §107 · 0/10 solved
  3. Dividing One Equation by the Other §107 · 0/13 solved
  4. Problems Leading to Quadratic Systems §107 · 0/20 solved
  5. Geometrical Problems §107 · 0/12 solved

Chapter 26 Exponents

Chapter challenge
  1. Zero and Negative Exponents §108, 109, 110 · 0/42 solved
  2. Positive Exponents and Expressions Without Denominators §110 · 0/40 solved
  3. Multiplication with Any Exponents §110 · 0/52 solved
  4. Expanding and Longer Products §110 · 0/19 solved
  5. Division with Any Exponents §110 · 0/23 solved

Chapter 27 Irrational Equations

Chapter challenge
  1. Solving Irrational Equations §111 · 0/33 solved
  2. Radicals in Formulas and Problems §111 · 0/10 solved

Chapter 28 Variation

Chapter challenge
  1. Constants, Variables, and Direct Variation §112, 113 · 0/3 solved
  2. Inverse and Joint Variation §114, 115 · 0/8 solved
  3. Problems in Variation §115 · 0/13 solved

Chapter 29 Imaginaries

Chapter challenge
  1. Imaginary and Complex Numbers §116, 117 · 0/24 solved
  2. Multiplication of Imaginaries §118 · 0/25 solved
  3. Division of Imaginaries §119 · 0/23 solved
  4. Equations with Imaginary Roots §120, 121 · 0/15 solved

Chapter 30 Miscellaneous Problems

Chapter challenge
  1. Clock and Planet Problems § · 0/9 solved
  2. Common Multiples of Fractions § · 0/7 solved
  3. Mixture Problems § · 0/6 solved
  4. Problems from Astronomy and Geometry § · 0/11 solved