Skill
in
ALGEBRA
The four operations and their signs.
The function of parentheses.
Terms versus factors.
Powers and exponents.
The order of operations.
Values and evaluations.
Evaluating algebraic expressions.
12. Signed numbers: Positive and negative
The integers.
The algebraic sign and the absolute value.
Subtracting a larger number from a smaller.
The number line.
The negative of any number.
13. Adding and subtracting signed numbers
"Adding" a negative number.
Naming terms. The rule for adding terms.
Subtracting a negative number.
14. Multiplying and dividing signed numbers
The Rule of Signs.
The rule of symmetry. Commutative rules. Inverses.
Two rules for equations.
The definition of reciprocals. The definition of division. Rules for 0.
Parentheses. Brackets. Braces.
The relationship of b − a to a − b.
19. Linear equations
The law of inverses.
Transposing.
A logical sequence of statements.
Simple fractional equations.
10. Word problems
11. Inequalities
12. Absolute value
Absolute value equations.
Absolute value inequalities.
13. Exponents I
Powers of a number.
Rules of exponents: When to add, when to multiply.
14. Multiplying out: The distributive rule
Quadratic trinomials.
16. Common factor
The definition of a polynomial in x.
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.
19. The difference of two squares
Summary of Multiplying/Factoring.
Factoring by grouping.
The sum and difference of any two powers: an ± bn.
20. Exponents II
Negative exponents. Exponent 0. Scientific notation.
Rational expressions. The principle of equivalent fractions. Reducing to lowest terms.
22. Multiplying and dividing algebraic fractions
Complex fractions.
23. Adding algebraic fractions
The Lowest Common Multiple (LCM) of a series of terms.
Clearing of fractions.
25. Word problems that lead to equations with fractions
The whole is equal to the sum of the parts.
Same time problem: Upstream-downstream.
Total time problem. Job problem.
26. Radicals: Rational and irrational numbers
Square roots.
Equations x² = a, and the principal square root.
Rationalizing a denominator.
Real numbers.
Fractional radicand.
28. Multiplying and dividing radicals
Conjugate pairs.
Roots of numbers. The index of a radical.
Fractional exponents.
Negative exponents.
30. Complex, or imaginary, numbers
The square root of a negative number.
The real and imaginary components.
Conjugate pairs.
Straight lines.
32. The Pythagorean distance formula
The distance of a point from the origin.
The distance between any two points.
A proof of the Pythagorean theorem.
33. The equation and graph of a straight line
The equation of the first degree and its graph.
Vertical and horizontal lines.
34. The slope of a straight line
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.
35. Simultaneous linear equations
The method of addition. The method of substitution. Cramer's Rule: The method of determinants.
Three equations in three unknowns.
36. Word problems that lead to simultaneous equations
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.
38. Logarithms
Definition. The three laws of logarithms.
Common logarithms.
39. Variation
Direct variation. The constant of proportionality.
Varies as the square. Varies inversely. Varies as the inverse square.