From charlesreid1

Review Chapter

Review Chapter section-by-section summary:

  • Real numbers
  • Algebra essentials
  • Geometry essentials
  • Polynomials
  • Factoring polynomials
  • Synthetic division
  • Rational Expressions
  • Radicals, nth roots, and Rational Exponents

Section R1: Real Numbers

Raster notation, sets and set-building

Intersection and union of sets

Complement of set

Number classification (integer, rational, irrational, real)


Value of expression

Commutative property

Associative property

Distributive property

Identity property

Additive inverse


Differences and quotients (definition)

Rules of signs

Zero product property

Add/subtract/multiply/divide quotients (fractions)

Least common multiple for adding fractions

Section R2: Algebra Essentials

Real number line

Positive and negative numbers

Inequality symbols

Absolute value

Distance on a number line

Algebraic expressions

Finding domain of variable

Circumference of circle

Laws of exponents

Negative exponents

Evaluating square roots

Using graphing calculator to do exponents

Scientific to decimal notation

Section R3: Geometry Review

Pythagorean Theorem

Right/isosceles/scalene triangles

Using geometry formulas

Similar triangles

Section R4: Polynomials

Monomials: definition

Polynomials: definition

Addition and subtraction of polynomials

Multiplication of polynomials and distributive properties

Special product formulas

  • Difference of 2 squares x2 - a2
  • Perfect square binomials (x+a)2 or (x-a)2
  • Sum and difference of 2 cubes x3 + a3 = (x+a)(x2 - ax + a2), x3 - a3 = (x-a)(x2 + ax + a2)

Dividing polynomials using long division

Polynomials in 2 variables

Section R5: Factoring

Factor the difference of 2 squares

Factor the sum and difference of 2 cubes

Factor perfect squares

Factor trinomials x2 + bx + c

Factor by grouping

Factor 2nd degree polynomials ax2 + bx + c

Complete the square

Summary: Type of polynomial/method/example

(Skip Section R6: Synthetic Division, already covered in polynomials)

Section R7: Rational Expressions

Reducing rational expressions to lowest terms

Multiplying and dividing rational expressions

Adding and subtracting rational expressions

Using LCM method

Simplifying complex rational expressions

Section R8: Rational Exponents, nth Roots

Working with nth roots, properties of radicals

Simplifying radical expressions

Rationalizing denominators

Simplifying rational exponent expressions