Math Review

a QuickStudy Laminated Reference Guide

,

• Publisher: QuickStudy Reference Guides
• Year: 2018
• Print ISBN: 9781423218715
• eBook ISBN: 9781423240686
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Best-selling guide for over 20 years, filled with essential elements of mathematics from properties of real numbers to beginning algebra in just 6 laminated pages. Studying with this broad overview that includes the details of what makes the math possible will melt away math phobia, strengthen skills, and boost grades. A strong foundation in math is critical to tackle higher levels of math that reach into so many subjects that are the gateway to interesting and high paying careers. Don't pass up this inexpensive tool with the power to support the core areas of math students struggle with. There is a lot to remember and this reference will give you core answers at your fingertips.
6 page laminated guide includes:

• Set Theory
• Properties of Real Numbers
• Sets of Numbers
• Operations of Real Numbers
• Decimals
• Integers
• Fractions
• Percent, Ratio & Proportion
• Probability
• Mixed Numbers & Improper Fractions
• Geometric Formulas with Diagrams
• Measurement
• Percent Applications
• Statistics & Data
• Algebra

Algebra

VOCABULARY

• Variables are letters or symbols used to represent unknown numbers
• Constants are specific numbers that are not multiplied by any variables
• Coefficients are numbers that are multiplied by one or more variables EX: –4xy has a coefficient of –4; 9m³ has a coefficient of 9; x has an implied coefficient of 1
• Terms are constants or variable expressions EX: 3a, –5c⁴d, 25mp³r⁵, and 7 are all terms
• Like or similar terms are terms that have the same variables to the same degree or exponent value; coefficients may or may not be equal EX: 3m² and 7m² are like terms because they both have the same variable to the same power or exponent value; –15a⁶b and 6a⁶b are like terms; 2x⁴ and 6x³ are not like terms because, although they have the same variable (x), it is to the power of 4 in one term and to the power of 3 in the other
• Algebraic expressions are terms that are connected by either addition or subtraction EX: 2s + 4a² – 5 is an algebraic expression with three terms: 2s, 4a², and –5
• Algebraic equations are statements of equality between at least two terms EX: 4z = 28 is an algebraic equation; 3(a – 4) + 6a = 10 – a is also an algebraic equation; note that both statements have equal signs in them
• Algebraic inequalities are statements that have either > or < between at least two terms EX: 50 < –2x is an algebraic inequality; 3(2n + 7) > –10 is an algebraic inequality

COMBINING LIKE TERMS

• You can add or subtract coefficients of like terms to simplify an algebraic expression; when doing so, the value of the exponent does not change EX: 3a + 7a = 10a; 9d² – 6d² = 3d² EX: 4xy³ and –7y³x are like terms, even though the x and y³ are not in the same order, and may be combined in this manner: 4xy³ + –7y³x = –3xy³; –15a2bc and 3bca⁵ are not like terms because the exponents of the a are not the same in both terms, so the coefficients may not be added or subtracted

MULTIPLYING & DIVIDING TERMS

• Product rule for exponents: (a^m)(aⁿ) = a^{m + n}; that is, when multiplying terms with the same base (a in this case), add the exponents Note: Any terms may be multiplied, not just like terms EX: (n⁸)(n⁵) = n¹³
• When terms include coefficients, multiply the coefficients and follow the product rule for exponents EX: (4a⁴c)(–12a²b³c) = –48a⁶b³c²; note that 4 times –12 became –48, a⁴ times a² became a⁶, c times c became c², and the b³ was written to indicate multiplication by b, but the exponent did not change on the b because there was only one b in the expression
• Power rule for exponents: (a^m)ⁿ = a^{m × n}; that is, when raising a term to a power (a in this case), multiply the exponents EX: (c³)⁴ = c¹²
• When terms include coefficients, raise the coefficients to the power and follow the power rule for exponents EX: (2a²b⁵c)⁵ = 32a¹⁰b²⁵c⁵
• Quotient rule for exponents:

  a^m

  a^n

  = a^m−n ; that is, when dividing a term to a power by a term to a power with the same base (a in this case), subtract the exponents EX:

  p^8

  p^2

  = p⁶
• When terms include coefficients, divide the coefficients and follow the quotient rule for exponents EX:

  −27a^6b

  9a^5

  = −3ab
• Rule for zero exponents: a⁰ = 1; that is, any nonzero base to a 0 power (a in this case) equals 1 EX: x⁰ = 1
• Rule for negative exponents: a⁻ⁿ =

  1

  a^n

  ; t...

Table of contents

• Set Theory
• Properties Of Real Numbers
• Sets Of Numbers
• Operations Of Real Numbers
• Decimals
• Integers
• Fractions
• Percent, Ratio & Proportion
• Probability
• Mixed Numbers & Improper Fractions
• Measurement
• Geometric Formulas
• Percent Applications
• Statistics & Data
• Algebra