#### Topics in Algebra I covered by …and Math Tutoring

##### Algebraic Expressions

- The four operations and their signs.
- The function of parentheses.
*Terms*versus*factors*.- Powers and exponents.
- The order of operations.
- Evaluating algebraic expressions.

##### Signed Numbers – Positive and Negative

- 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 and Subtracting Signed Numbers

- “Adding” a negative number.
- Naming terms.
- The rule for adding terms.
- Subtracting a negative number.

##### Multiplying and Dividing Signed Numbers

- The Rule of Signs.

##### Reciprocals and Zero

- The definition of reciprocals.
- The definition of division.
- Rules for 0.

##### Some Rules of Algebra

- The rule of symmetry.
- Commutative rules.
- Inverses.
- Two rules for equations.

##### Removing Grouping Symbols

- Parentheses.
- Brackets.
- Braces.
- The relationship of
*a*?*b*to*b*?*a*.

##### Adding Like Terms

##### Linear Equations

- Inverse operations.
- Transposing.
- A logical sequence of statements.

##### Word Problems

##### Inequalities

##### Absolute Value

##### Exponents

- Adding exponents.
- Power of a product.
- Multiplying exponents.

##### Multiplying out (The Distributive Rule)

##### Common Factor

- The definition of a
*polynomial in**x*. - Factoring polynomials.
- Factoring by grouping.
- Equations that require factoring.

##### Multiplying Binomials

- Quadratic trinomials.

##### Factoring Trinomials

- Quadratics in different arguments.

##### The Square of a Binomial

- Perfect square trinomials.
- The square of a trinomial.
- Completing the square.
- Geometrical algebra.

##### The difference of two Squares

- Summary of Multiplying/Factoring.
- Factoring by grouping.
- Factoring
*a*^{n}±*b*^{n}.

##### Algebraic Fractions

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

##### Negative Exponents

- Subtracting exponents.
- Negative exponents.
- Exponent 0.
- Scientific notation.

##### Multiplying and Dividing Algebraic Fractions

- Complex fractions.

##### Adding Algebraic Fractions

- The Lowest Common Multiple (LCM) of a series of terms.

##### Equations with Fractions

- Clearing of fractions.

##### 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.

##### Radicals: Rational and Irrational Numbers

- Square roots.
- Equations
*x*² =*a*, and the principal square root. - Rationalizing a denominator.
- Real numbers.

##### Simplifying Radicals

- Similar Radical Forms.
- Fractional radicand.

##### Multiplying and Dividing Radicals

- Conjugate pairs.

##### Rational Exponents

- The index of a radical. Fractional exponent.

##### Complex and Imaginary Numbers

- The real and imaginary components.
- Conjugate pairs.

##### Rectangular coordinates

- Actual versus potential infinities.

##### The Pythagorean Distance Formula

- The distance of a point from the origin.
- The distance between any two points.

##### The Equation of a Straight Line

- The equation of the first degree and its graph.
- Vertical and horizontal lines.

##### 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.

##### Simultaneous Linear Equations

- The method of addition.
- The method of substitution.
- Cramer’s Rule: The method of determinants.
- Three equations in three unknowns.

##### Word Problems that Lead to Simultaneous Equations

- Investment problems.
- Mixture problems.
- Upstream-downstream problems.

##### Quadratic Equations

- The
*roots*of a quadratic. - Solution by factoring.
- Completing the square.
- The quadratic formula.
- The graph of a quadratic: A parabola.

##### Logarithms

- Definition.
- The three laws of logarithms.
- Common logarithms.

##### Variation

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

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