Skill
in
ALGEBRA
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The four operations and their signs.
The function of parentheses.
Terms versus factors.
Powers and exponents.
The order of operations.
Evaluating algebraic expressions.
12. Signed numbers: Positive and negative
The absolute value and the algebraic sign. Subtracting a larger number from a smaller. The number line.
What are the integers? 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 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.
19. Linear equations
Inverse operations. Transposing. A logical sequence of statements.
10. Word problems
11. Inequalities
12. Absolute value
13. Exponents
Adding exponents. Power of a product. Multiplying exponents.
14. Multiplying out: The distributive rule
15. Common factor
The definition of a polynomial in x.
Factoring polynomials.
Factoring by grouping. Equations that require factoring.
Quadratic trinomials.
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.
Factoring an ± bn.
Rational expressions. The principle of equivalent fractions. Reducing to lowest terms.
Subtracting exponents. Negative exponents. Exponent 0. Scientific notation.
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.
The index of a radical. Fractional exponent.
30. Complex, or imaginary, numbers
The real and imaginary components. Conjugate pairs.
Actual versus potential infinities.
32. The Pythagorean distance formula
The distance of a point from the origin. The distance between any two points.
33. The equation 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 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.
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