Beginning and Intermediate Algebra An Integrated Approach 4th Edition by David Gustafson, Peter Frisk ISBN 978-0534463779 0534463770

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Product details: 

ISBN 10:  0534463770

ISBN 13: 978-0534463779

Author: R. David Gustafson,  Peter D. Frisk

Tried and true, Gustafson and Frisk’s BEGINNING AND INTERMEDIATE ALGEBRA teaches solid mathematical skills while supporting the student with careful pedagogy. This text helps students develop the ability to synthesize and conceptualize material by thoroughly integrating coverage of graphing and problem solving without sacrificing manipulative skills. Each book in this series maintains the authors’ proven style through clear, no-nonsense explanations, as well as the mathematical accuracy and rigor that only Gustafson and Frisk can deliver. The text’s clearly useful applications emphasize problem solving to effectively develop the skills students need for future mathematics courses, such as college algebra, and for real life. BEGINNING AND INTERMEDIATE ALGEBRA is the ideal text for professors who want to eliminate the significant overlap of topics found in separate beginning and intermediate algebra texts. The Seventh Edition of BEGINNING AND INTERMEDIATE ALGEBRA also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes BCA/iLrn Testing and Tutorial, vMentor live online tutoring, the Interactive Video Skillbuilder CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by BCA/iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math.

Table of contents: 

CHAPTER 1 REAL NUMBERS AND THEIR BASIC PROPERTIES

Natural numbers: {1, 2, 3, 4, 5,…)

Whole numbers: (0, 1, 2, 3, 4, 5,…)

Integers: {. ,-3,-2,-1,0, 1, 2, 3, …}

Rational numbers: {All numbers that can be written as a fraction with an integer numerator and a nonzero integer denominator)

Real numbers: {All numbers that are either a rational number or an irrational number}

Prime numbers: {2, 3, 5, 7, 11, 13, 17,…)

Composite numbers: (4, 6, 8, 9, 10, 12, 14, 15,…)

Even integers: (.,6,4,2, 0, 2, 4, 6,…)

Odd integers: (.5,-3,-1,1,3,5,…)

Fractions:

If there are no divisions by 0, then

ac

hx b

bd bd

C bd b be a-b a+b d d d d

ad

b -+ d d

Exponents and order of operations:

If n is a natural number, then

factors of x

To simplify expressions, do all calculations within each pair of grouping symbols, working from the innermost pair to the outermost pair.

1. Find the values of any exponential expressions.

2. Do all multiplications and divisions from left to right.

3. Do all additions and subtractions from left to right.

In a fraction, simplify the numerator and denominator separately and then simplify the fraction, if possible.

Figure

Figure

Volume

Rectangular solid

Cylinder

V-Iwh

V-Br

1 V-3Bh

Pyramid

1 V-Bh 3

Cone

4 3

Sphere

*B is the area of the base.

If a, b, and c are real numbers, then

Closure properties:

a+b is a real number.

b is a real number.

ab is a real number.

1 is a real number (b+0).

b

Commutative properties:

a+b-b+a

ab – ba

Associative properties:

(a+b)+ca+(b+c)

(ab)ca(bc)

Distributive property:

a(b+c) ab + ac

CHAPTER 2 EQUATIONS AND INEQUALITIES

Let a, b, and e be real numbers.

If ab, then a + c b + c.

If ab, then a c-b-c.

If ab. then b (c+0).

If ab, then ca ch.

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Perimeter

Area

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Square

Rectangle

P-45

A-3

Percentage rate base

P-21+2w

A- Yes

1 A–bh 2 bh

Solving inequalities:

Triangle

P-a+b+c

Let a, b, and e be real numbers.

1 A-h(b + d)

Trapezoid

P-a+b+c+d

If a < b. thena-cb-c.

Circle

C – D – 2π

If ab, then a + c < b + c.

If a band c > 0, then ac < bc.

If a band c be.

b If a band > 0, then <

If a < b and c <0, then

CHAPTER 3 GRAPHING AND SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES

de_ad

ba+b

+ b d be d d d

Ax + By C

General form of the equation of a line:

Equation of a vertical line:x-a

Equation of a horizontal line: y-b

CHAPTER 4 POLYNOMIALS

Properties of exponents: If x is a number, m and are in-tegers, and there are no divisions by 0, then

n factors of x I

a_no b

d d d

CHAPTER 5 FACTORING POLYNOMIALS

Factoring the difference of two squares:

a²-b²(a+b)(ab)

Factoring perfect-square trinomials:

a²+2ab+b²= (a+b)²

a²-2ab+b²(ab)²

Factoring the sum and difference of two cubes:

x+y²(x + y)² – xу + y²) xy(xy)(x²+ xy + y²)

Zero-factor property: Let a and b be real numbers.

If ab 0, then a O or b-0.

21 (x2+x)

Equations of a line:

yym(xx) point-slope form

y=mx+b slope-intercept form

Ax + By C general form

y-b a horizontal line (slope is 0)

xa a vertical line (slope is undefined)

Two lines with the same slope are parallel.

If the product of the slopes of two lines is-1, the lines are perpendicular.

Direct variation: y-kx

Inverse variation: y

Joint variation: y kxz

kx Combined variation: y

CHAPTER 6 PROPORTIONS AND RATIONAL EXPRESSIONS

b Ба then ad – bc.

If there are no divisions by 0, then

fr be b 1 0

is undefined

bd bd

CHAPTER 7 MORE EQUATIONS, INEQUALITIES, AND FACTORING

If x ≥ 0, then x I.

If x < 0, then x

Ifk > (0, then

-1 1 – Egypt

xk is equivalent tox-korx-k.

x<k is equivalent to -k < x <k.

xk is equivalent to x k.

CHAPTER 8 WRITING EQUATIONS OF LINES, FUNCTIONS, AND VARIATION

Slope of a nonvertical line: If P(x1, y₁) and Q(x, y₂) are two points on a line, the slope of the line is

Special products:

(x+y)x²+2xy + y²

(xy)²²-2xy + y²

(x+y)(xy)²²

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