The four operations and their signs.
12. Signed numbers: Positive and negative
13. Adding and subtracting signed numbers
"Adding" a negative number.
14. Multiplying and dividing signed numbers
The Rule of Signs.
The rule of symmetry. Commutative rules. Inverses.
The definition of reciprocals. The definition of division. Rules for 0.
Parentheses. Brackets. Braces.
19. Linear equations
The law of inverses.
10. Word problems
12. Absolute value
Absolute value equations.
13. Exponents I
Powers of a number.
14. Multiplying out: The distributive rule
16. Common factor
The definition of a polynomial in x.
Quadratics in different arguments.
Perfect square trinomials.
19. The difference of two squares
Summary of Multiplying/Factoring.
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
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.
26. Radicals: Rational and irrational numbers
28. Multiplying and dividing radicals
Roots of numbers. The index of a radical.
30. Complex, or imaginary, numbers
The square root of a negative number.
32. The Pythagorean distance formula
The distance of a point from the origin.
33. The equation and graph of a straight line
The equation of the first degree and its graph.
34. The slope of a straight line
The slope intercept form of the equation of a straight line.
The general form.
35. Simultaneous linear equations
The method of addition. The method of substitution. Cramer's Rule: The method of determinants.
36. Word problems that lead to simultaneous equations
Investment problems. Mixture problems.
The roots of a quadratic.
Definition. The three laws of logarithms.
Direct variation. The constant of proportionality.
Copyright © 2021 Lawrence Spector
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