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
  • “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  ab to  ba.
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 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.
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 x² = 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.