10

ALGEBRA

FIRST COURSE

BY

EDITH LONG

=

DEPARTMENT OF MATHEMATICS, HIGH SCHOOL, LINCOLN, NEBRASKA

TABLE OF CONTENTS

CHAPTER I

INTRODUCTION.

(The numbers refer to articles.)

1. The Operations of Arithmetic. 2. The Whole Numbers, or

integers. 3. Addition. 4. Subtraction. 5. Multiplication.

6. Division. 7. Subject Matter of Algebra. 8. Algebraic Ex-

pressions. Their Forms and Values.

CHAPTER II

MEASUREMENTS LENGTHS, ANGLES, AREAS, VOLUMES..

9. English Units of Length. 10. Metric Units of Length.

11. Comparison of English and Metric Units of Length. 12.

Angles. Definitions and Notations. 13. Classification of An-

gles. 14. Measurement of Angles. 15. The Number T. 16.

Measurement of Areas. 17., Measurement of Volumes. Sum-

mary.

PAGES

1-13

14-27

CHAPTER III

TEMPERATURE, WEIGHT AND

MEASUREMENTS CONTINUED.

DENSITY, FORCE..

18. Measurement of Temperature. 19. English Units of

Weight. 20. Metric Units of Weight. 21. The Beam Balance.

22. The Lever. 23. Density or Specific Gravity. 24. Sum-

mary. 25. Questions and Problems for Review.

28-41

CHAPTER IV

GRAPHIC REPRESENTATION OF QUANTITY...

26. The Amount of any Quantity Represented by the Length

of a Line.

CHAPTER V

POSITIVE AND NEGATIVE NUMBERS..

27. Exercises. 28. Opposite Qualities. 29. Positive and

Negative Numbers. 30. Graphic Representation of Positive
and Negative Numbers. 31. Summary.

42-48

49-54

CHAPTER VI

ADDITION AND SUBTRACTION.

32. Notation. 33. Addition of Directed Line Segments. 34.

Geometric Addition of Numbers. 35. Exercises and Problems.

36. Subtraction. 37. Summary.

PAGES

55-70

CHAPTER VII

MULTIPLICATION AND DIVISION..

71-80

38. Meaning of Multiplication.

39. Geometric Illustra-

tions of Multiplication. 40. Multiplication of General Num-
bers. 41. Division. 42. Summary.

CHAPTER VIII

ADDITION AND SUBTRACTION OF POLYNOMIALS.

43. Definitions. 44. Addition and Subtraction of Poly-

nomials. 45. Rules for Adding and Subtracting Polynomials.

46. Removal of Parentheses. 47. Summary.

CHAPTER IX

MULTIPLICATION AND DIVISION OF POLYNOMIALS.

48. Multiplication of a Polynomial by a Monomial. 49. Dis-

tributive Law. 50. The Commutative Law of Addition. 51.
The Commutative Law of Multiplication. 52. Exponents. 53.
Multiplication of One Polynomial by Another. 54. Division
of Polynomials. 55. Summary.

81-89

90-104

CHAPTER X

PROBLEMS LEADING TO SIMPLE EQUATIONS.

56. Problems. 57. Formation of an Equation. 58. Solu-

tion of the Equation. 59. Summary.

CHAPTER XI

105-126

SIMPLE AREAS AND THEIR ALGEBRAIC EXPRESSIONS. ELEMENTS

OF FACTORING.

60. Rectangles. 61. Geometric Theorems on Factoring. 62.

Parallelograms. 63. Theorem. 64. Triangles. Theorem. 65.
Regular Polygons. 66. Theorem. 67. Trapezoids. Theorem.
68. Circles. 69. Factoring Continued. 70. Summary. Exer-
cises.

127-149

CHAPTER XII

PAGES

FRACTIONS.

71. Reduction of Fractions to Lowest Terms. Cancellation.

72. Multiplication of Fractions. 73. Division of Fractions.
74. Reduction to a Common Denominator. 75. Addition and
Subtraction of Fractions. 76. Complex Fractions. 77. Long
Division. 78. Equation Involving Fractions.

QUADRATIC EQUATIONS.

CHAPTER XIII

79. Definitions. 80. Some Problems Leading to Quadratic

Equations. 81. Square Roots of Numbers. Pythagorean

Theorem. 82. Geometric Construction of Square Roots. 83.

Rational and Irrational Numbers. 84. Factoring of Quadratic

Expressions. 85. Factors of ax2 + bx + c. 86. Algebraic So-

lution of the General Quadratic Equation. 87. Imaginary

Roots. 88. To find the Square Root of a Number. 89. Sum-

mary and Problems.

150-165

166-205

CHAPTER XIV

VARIABLES. CONSTANTS. FUNCTIONS OF VARIABLES. GRAPHIC

REPRESENTATION..

90. Variables. 91. Constants. 92. Functions of Variables.

93. Functions of a Single Variable. 94. The Function Notation.

95. Graphic Representation. Linear Functions. 96. Graph of

of Quadratic Functions. 97. Graphs of Other Functions. 98.

Summary.

USES OF THE GRAPH.

CHAPTER XV

99. Graphic Representation of Measurements of a Variable

Quantity. 100. Graphic Solution of Equations. 101. Nature
of the Roots of a Quadratic Equation. 102. Graphic Solution of
Equations of Higher Degree. 103. Summary.

CHAPTER XVI

LOCI. SIMULTANEOUS EQUATIONS.

104. Meaning of the Word Locus. 105. Coördinates. 106.

Straight Line Loci in General. 107. Simultaneous Equations.

108. Summary and Problems.

206-224

225-240

241-262