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Skill


ALGEBRA

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.

Absolute value equations.
Absolute value inequalities.

Powers of a number.
Rules of exponents: When to add, when to multiply.

The definition of a polynomial inx.
Factoring polynomials.
Factoring by grouping.
Equations in which the unknown is a common factor.

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 .

Rational expressions. The principle of equivalent fractions. Reducing to lowest terms.

Subtracting exponents. Exponent 0. Scientific notation.

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.

Square roots.
Equations x = a. and the principal square root.
Rationalizing a denominator.
Real numbers.

Roots of numbers. The index of a radical.
Fractional exponents.
Negative exponents.

The square root of a negative number.
The real and imaginary components.
Conjugate pairs.

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 discriminant.
The graph of a quadratic: A parabola.

Definition. The three laws of logarithms.
Common logarithms.

Direct variation. The constant of proportionality.
Varies as the square. Varies inversely. Varies as the inverse square.

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Copyright 2017 Lawrence Spector

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