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MODERN ELEMENTARY
ALGEBRA
BARNETT RICH
CONTENTS
Chapter 1
FROM ARITHMETIC TO ALGEBRA
1. Simple relations among numbers, sets, operations, and variables.
2. Inter​c hanging numbers in addition: commutative law of addition.
3. Interchanging numbers in multiplication: commutative law of multiplication.
4. Symbolizing the operations in algebra.
5. Expressing addition and subtraction algebra​ically.
6. Expressing multiplication and division algebraically.
7. Expressing algebraically expressions involving two or more operations.
8. Associative laws of addition and multiplication.
9. Order in which fundamental operations are performed.
10. The uses of parentheses: changing the order of operations.
11. Multiplying factors in terms: numerical and literal coefficient.
12. Repeated multiplying of a factor: base, exponent, and power,
13. Law of closure.
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Chapter 2
SIMPLE EQUATIONS AND THEIR SOLUTION
1. Understanding simple equations and their solution.
2. Translating in verbal problems to obtain equations.
3. Solving simple equations using inverse operations.
4. Rules for solving equations.
5. Using division to solve an equation.
6. Using multiplication to solve an equation: reciprocals and multiplicative inverses.
7. Using subtraction to solve an equation.
8. Using addition to solve an equation.
9. Using two or more operations to solve an equation.
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Chapter 3
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REAL NUMBERS
Understanding real numbers and the real number line.
Using the real number line.
Adding signed numbers: opposites and additive inverses.
Simplifying the addition of signed numbers.
Subtracting signed num​bers.
Multiplying signed numbers.
Finding powers of signed numbers.
7. Finding powers of signed numbers.
8. Dividing signed numbers.
9. Evaluating expressions having signed numbers.
Chapter 4
MONOMIALS AND POL YNOMIALS
1. Understanding monomials and polynomials.
2. Distributive law.
3. Adding monomials.
4. Arranging and adding polynomials.
5. Subtracting monomials.
6. Subtracting polynomials.
7. Using parentheses and other grouping symbols to add or subtract polynomials.
8. M ultiplying monomials and powers of the same base.
9. Multiplying a monomial by a polynomial.
10. Multiplying poly​nomials.
11. Dividing powers and monomials.
12. Dividing a polynomial by a monomial.
13. Dividing a polynomial by a polynomial.
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Chapter 5
EQUATIONS AND INEQUALITIES OF THE FIRST DEGREE lN ONE VARIABLE
1. Reviewing the solution of first degree equations having positive roots.
2. Solving first degree equations having negative roots.
3. Solving equations by using the rule of transposition.
4. Solving equations containing parentheses.
5. Solving equations containing one fraction or fractions having the same de​nominator.
6. Solving equations containing fractions having different denomi​nators: least common denominator.
7. Solving equations containing decimals.
8. Solving literal equations.
9. Solving inequalities of the first degree in one variable.
10. Rules for solving inequalities.
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Chapter 6
GEOMETRY AND FORMULAS
1. Understanding geom.etry.
2. Formulas for perimeters and circumferences: linear measure.
3. Formulas for areas: square measure.
4. Formulas for vol​umes: cubic measure.
5. Deriving formulas.
6. Transforming formulas.
7. Finding the value of a variable in a formula.
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Chapter 7
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COORDINATE GEOMETRY: GRAPHING LINEAR EQUATIONS AND LINEAR
INEQUALITIES
Understanding coordinate planes.
Graph of an equation in one variable: lines parallel to an axis.
Graphs of an equation in two variables.
Graph​ing linear equations.
Slope of a line.
Deriving a linear equation from a table of values.
Graphing inequalities.
Chapter 8
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SYSTEMS OF LINEAR EQUATIONS AND LINEAR INEQUALITIES lN TWO
VARIABLES
Solving graphically a system of linear equations in two variables.
Solving a system of equations by addition or subtraction.
Solving a system of equa​t ions by substitution.
Compound sentences: union and intersection of sets.
Solving a system of linear inequalities graphically.
Graphing equations involving absolute values.
Chapter 9
PROBLEM-SOLVING
1. Number problems having one unknown.
2. Number problems having two unknowns.
3. Consecutive integer problems.
4. Age problems.
5. Ratio prob​lems.
6. Angle problems.
7. Perimeter problems.
8. Coin and stamp prob​lems.
9. Cost and mixture problems.
10. Investment or interest problems.
11. Motion problems.
12. Work problems.
13. Combination problems.
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13. Combination problems.
14. Digit problems.
15. Statistics problems.
Chapter 10
SPECIAL PRODUCTS AND FACTORING
1. Understanding factors and products.
2. Factoring a polynomial having a common monomial factor.
3. Squaring a monomial.
4. Finding the square root of a monomial.
5. Finding the product of the sum and ditference of two numbers
6. Factoring the ditference of two squares.
7. Finding the product of two binomials with like terms.
8. Factoring trinomials in form of x 2 + bx + c: coefficient of x 2 is 1.
9. Factoring trinomials in form of x 2 + bx + c: coefficient of x 2 is a, a 0.
10. Squaring a binomial.
11. Factoring a perfect square trinomial. 12. Completely factoring polynomials.
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Chapter 11
FRACTIONS AND RATIONAL EXPRESSIONS
1. Understanding fractions and ration al expressions.
2. Equivalent fractions.
3. Reciprocals and multiplicative inverses.
4. Reducing fractions to lowest terms.
5. Multiplying fractions.
6. Dividing by a fraction.
7. Adding or subtracting fractions having the same denominator.
8. Adding or subtracting fractÏQns having ditferent denominators.
9. Simplifying complex fractions.
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Chapter 12
ROOTS AND RADICALS
1. Understanding roots and radicals.
2. Understanding rational and irrational numbers.
3. Finding the square root of a number by using a table.
4. Com​puting the square root of a number.
5. Simplifying the square root of a prod​uct.
6. Simplifying the square root of a quotient or a fraction.
7. Adding and subtracting square roots of numbers.
8. Multiplying square roots of numbers.
9. Dividing by the square root of a number.
10. Rationalizing the denominator. 11. Solving radical equations.
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Chapter 13
QUADRATIC EQUATIONS lN ONE VARIABLE
1. Understanding quadratic equations in one variable.
2. Solving quadratic equations by factoring.
3. Solving incomplete quadratic equations.
4. Solving a quadratic equation by completing the square.
5. Solving a quadratic equa​t ion by quadratic formula.
6. Solving quadratic equations graphicaIly.
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Chapter 14
INDIRECT MEASUREMENT
1. Indirect measurement: using triangles drawn to scale.
2. D = SN: a formula of indirect measurement for figures drawn to scale on maps, graphs, models, and blueprints.
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Chapter 15
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LAW OF PYTHAGORAS, PROPORTIONS, AND SIMILAR TRIANGLES
1. Law of Pythagoras.
2. Proportions: equal ratios.
3. Similar triangles.
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Chapter 16
TRIGONOMETRY
1. Understanding trigonometric ratios.
2. Solving trigonometry problems.
3. Angles of elevation and depression.
4. Inclination of a line and its slope.
Chapter 17
THE VARIABLE: DIRECT, INVERSE, JOINT AND POWER VARIATION
1. Understanding the variable.
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3.
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6.
Understanding direct variation: y = kx or
Understanding inverse variation: xy = k.
Understanding joint variation: z = kxy.
Understanding power variation.
Using a symbol to simplify variation.
= k.
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6. Using a symbol to simplify variation.
Chapter 18
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FUNCTIONS AND RELATIONS
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Understanding relations.
Understanding functions.
Function nota​t ion.
Cartesian product sets.
Chapter 19
REVIEWING ARITHMETIC
1. Reviewing whole numbers.
2. Reviewing fractions.
3. Reviewing decimals.
4. Reviewing per cents and percentage.
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APPENDIX
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INDEX
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