Saturday, September 12, 2015

ALGEBRA

Algebra

ALGEBRA

Chapter 1
The four operations and their signs.
The function of parentheses.
Terms versus factors.
Powers and exponents.
The order of operations.
Evaluating algebraic expressions.
The absolute value and the algebraic sign.
Subtracting a larger number from a smaller.
The number line.
What is an integer?
The negative of any number.
"Adding" a negative number.
Naming terms. The rule for adding terms.
Subtracting a negative number.
The Rule of Signs.
The definition of reciprocals. The definition of division. Rules for 0.
The rule of symmetry. Commutative rules. Inverses.
Two rules for equations.
Parentheses. Brackets. Braces.
The relationship of  b − a  to  a − b.
The law of inverses.
Transposing.
A logical sequence of statements.
Simple fractional equations.
11.  Inequalities
Absolute value equations.
Absolute value inequalities.
Chapter 2
13.  Exponents
Powers of a number.
Rules of exponents: When to add, when to multiply.
The definition of a polynomial in x.
Factoring polynomials.
Factoring by grouping.
Equations in which the unknown is a common factor.
Quadratic trinomials.
Quadratics in different arguments.
Perfect square trinomials.
The square of a trinomial.
Completing the square.
Geometrical algebra.
Summary of Multiplying/Factoring.
Factoring by grouping.
The sum and difference of any two powers:  an ± bn.
Chapter 3
Rational expressions. The principle of equivalent fractions. Reducing to lowest terms.
Subtracting exponents. Exponent 0. Scientific notation.
Complex fractions.
The Lowest Common Multiple (LCM) of a series of terms.
Clearing of fractions.
The whole is equal to the sum of the parts.
Same time problem: Upstream-downstream.
Total time problem. Job problem.
Chapter 4
Square roots.
Equations x² = a, and the principal square root.
Rationalizing a denominator.
Real numbers.
grapic
Fractional radicand.
Conjugate pairs.
Roots of numbers. The index of a radical.
Fractional exponents.
Negative exponents.
grapic
The square root of a negative number.
The real and imaginary components.
Conjugate pairs.
Chapter 5
Actual versus potential infinities.
The distance of a point from the origin.
The distance between any two points.
A proof of the Pythagorean theorem.
The equation of the first degree and its graph.
Vertical and horizontal lines.
The slope intercept form of the equation of a straight line. The general form.
Parallel and perpendicular lines.
The point-slope formula. The two-point formula.
The method of addition. The method of substitution. Cramer's Rule: The method of determinants.
Three equations in three unknowns.
Investment problems. Mixture problems.
Upstream-downstream problems.
The roots of a quadratic.
Solution by factoring.
Completing the square.
The quadratic formula.
The graph of a quadratic: A parabola.
Chapter 6
38.  Logarithms
Definition. The three laws of logarithms.
Common logarithms.
Chapter 7
39.  Variation
Direct variation. The constant of proportionality.
Varies as the square. Varies inversely. Varies as the inverse square.


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Copyright © 2015 Lawrence Spector
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