Math Review - First Quarter (Grade 8)

Vocabulary flashcards covering central tendency concepts and polynomial algebra topics from the lecture notes.

Measure of Central Tendency

Also known as Measures of Central Location; describes a data set and its central position.

Ungrouped data

Raw data that has not been organized.

Outliers

Extreme values that differ from the rest; if present, the median is preferred as a measure of central tendency.

Mean (x̄)

Average; most used measure of central tendency; x̄ = (Σ xᵢ)/N.

Weighted mean

Mean that accounts for frequency: x̄ = (Σ fᵢxᵢ)/N.

Sum notation (Σ)

Symbol for summing all values in a data set.

N (Total Frequency)

Total number of data points in the data set.

Median (x̃)

Middle value when data are ordered; for even N, the mean of the two middle values is used.

Mode (x̂)

Most frequent value in the data set; can be multiple; if all values occur equally, there is no mode.

Polynomial

An expression made up of terms that include variables, coefficients, and exponents separated by addition or subtraction.

Adding polynomials

Process of combining polynomials using addition or subtraction.

Subtracting polynomials

Arrange in descending order, change the sign of the subtrahend, distribute the minus sign, and group like terms.

Horizontal method

Add polynomials by removing parentheses, grouping like terms, and adding coefficients.

Vertical method

Add polynomials by aligning like terms in columns and combining coefficients.

Group like terms

Combine terms that have the same variable and exponent.

Distributive Property

Multiplication distributes over addition/subtraction: a(b ± c) = ab ± ac.

Descending order

Arrange terms from highest to lowest exponent.

Laws of Exponents

Rules for manipulating exponents: Product, Quotient, Power; includes negative and zero exponents.

Product Law

For same base, x^m · x^n = x^{m+n}.

Quotient Law

For same base, x^m / x^n = x^{m−n}.

Power Law

Raising a power to another exponent multiplies exponents: (x^m)^n = x^{mn}.

Power of a power

(xy)^m = x^m y^m; distributing a power over a product.

Quotient raised to a power

(x/y)^m = x^m / y^m.

Negative exponent law

A negative exponent makes the base reciprocal: x^{−n} = 1/x^n.

Zero law

Any nonzero base raised to the 0 power equals 1: x^0 = 1.

Monomial x Monomial

Product of two monomials; multiply numerical coefficients and variables.

Monomial x Polynomial

Multiply a monomial by a polynomial using distributive property.

Polynomial x Polynomial

Product of two polynomials; expanded via distribution or FOIL.

FOIL Method

First, Outer, Inner, Last; method to expand binomials.

Binomial x Binomial

Product of two binomials; typically expanded with FOIL.

Square of a Binomial

If multiplying a binomial by itself, use the square of a binomial rule.

Sum and Difference of two terms

Factoring patterns for sums/differences of two terms.

Difference of Two Squares

A^2 − B^2 factors as (A + B)(A − B).

Dividing Polynomials

Polynomial ÷ Monomial; divide coefficients; apply quotient rules to terms.

Greatest Common Factor (GCF)

Highest common factor of two terms; used to factor polynomials.

Factoring Polynomials

Find a common monomial factor and factor the rest into parentheses.

Perfect Square Trinomial

A trinomial whose first and last terms are perfect squares; factors as a square of a binomial.

Square of Binomial

Expands (a ± b)^2 into a^2 ± 2ab + b^2.

Linear Equations

Equations with highest exponent 1; form ax + b.

Quadratic Trinomials

Polynomials with highest exponent 2; ax^2 + bx + c (often with a ≠ 0).

Inverse Foil Method

Foil-based factoring method for quadratics when a ≠ 1.

AC method (Diamond Method)

Factoring method for quadratics where a ≠ 1; also called the Diamond Method.