# Algebra I

#### 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
• 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  ab to  ba.
##### Linear Equations
• Inverse operations.
• Transposing.
• A logical sequence of statements.
##### Exponents
• Power of a product.
• Multiplying exponents.
##### Common Factor
• The definition of a polynomial in x.
• Factoring polynomials.
• Factoring by grouping.
• Equations that require factoring.
##### 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 an ± bn.
##### 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.
• 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 x² = a, and the principal square root.
• Rationalizing a denominator.
• Real numbers.
• 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 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.
• The roots of a quadratic.
• Solution by factoring.
• Completing the square.