1,001 precalculus practice problems for dummies, by Mary Jane Sterling
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 1,001 precalculus practice problems for dummies, by Mary Jane Sterling
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 by Mary Jane Sterling
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 Includes index
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 rdacarrier
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 Contents

 Introduction  pt. I. The questions  1. Getting started with algebra basics  Identifying which system or systems a number belongs to  Recognizing properties of number systems  Simplifying expression with the order of operations  Graphing inequalities  Graphing formulas  2. Solving some equations and inequalities  Using interval and inequality notation  Solving linear inequalities  Solving quadratic inequalities  Solving absolute value inequalities  Working with radicals and fractional notation  Performing operations using fractional exponents  Factoring using fractional notation  Solving radical equations  Rationalizing denominators  3. Function basics  Using function notation to evaluate function values  Determining the domain and range of a function  Recognizing even functions  Identifying odd functions  Ruling out even and odd functions  Recognizing onetoone functions from given relations  Identifying onetoone functions from equations  A function's inverse  Executing operations on functions  Performing function composition  Using the difference quotient  4. Graphing and transforming functions  Functions and their inverses  Sketching quadratic functions from their equations  Writing equations from graphs of parabolas  Graphing radical functions  Absolute value functions  Graphs of polynomial functions  Rational f unctions  Transformation of functions  Transforming selected points using functions  Sketching graphs using basic functions and transformations  5. Polynomials  Using factoring to solve quadratic equations  Solving quadratic equations by using the quadratic formula  Using completing the square to solve quadratic equations  Solving polynomial equations for intercepts  Using factoring by grouping to solve polynomial equations  Descartes's Rule of Signs  Listing possible roots of a polynomial equations  dividing polynomials  Using synthetic division to divide polynomials  Checking for toots of a polynomial by using synthetic division  Writing polynomial expression from given roots  Writing polynomial expressions when given roots and a point  Graphing polynomials  Writing equations from graphs of polynomials  6. Exponential and logarithmic functions  7. Function notation  Graphing exponential functions  Solving exponential equations  Rewriting logarithmic expressions  Rewriting logs of products and quotients as sums and differences  Solving logarithmic equations  Applying function transformations to log functions  Applying logarithms to everyday life  7. Trigonometry basics  Using right triangles to determine trig functions  Solving problems by using right triangles and their functions  Working with special right triangles  Changing radians to degrees  Changing degrees to radians  Finding angle measures in standard position  Identifying reference angles  Determining trig functions by using the unit circle  Calculating trig functions by using other functions and terminal side positions  Using the arc length formula  evaluating inverse functions  Solving trig equations for x in degrees  Calculating trig equations for x in radians  8. Graphing trig functions  Recognizing basic trig graphs  graphing sine and cosine  Applying function transformations to graphs of trig functions  Writing new trig functions using transformations  Graphing tangent and cotangent  Interpreting transformations of trig functions  Graphing secant and cosecant  Interpreting transformations from function rules  9. Getting started with trig identities  Proving basic trig identities  Returning to basic sine and cosine to solve identities  Using multiplication by a conjugate to solve identities  Solving identities after raising a binomial to a power  Solving identities after factoring out a common function  Solving identities after combining fractions  Performing algebraic processes to make identities more solvable
 10. Continuing with trig identities  Using identities that add or subtract angle measures  Doubleangle identities  Using identities that double the size of the angle  Confirming the statements of multipleangle identities  Creating halfangle identities from doubleangle identities  Creating a halfangle for tangent  Using halfangle identities to simplify expressions  Creating products of trig functions from sums and differences  Using producttosum identities to evaluate expressions  Using sumtoproduct identities to evaluate expressions  Applying powerreducing identities  Using identities to determine values of functions at various angles  Working through identities using multiple methods  11. Working with triangles and trigonometry  Applying the Law of Sines to find sides  Utilizing the Law of Sine to find angles  Using the Law of Sines for practical applications  determining all angles and sides of a triangle  Finding side measures by using the Law of Cosines  Using the Law of Cosines to determine an angle  Applying the Law of Cosines to realworld situations  Finding areas of triangles by using the sine  Applying the trig formula for area of a triangle  Using the trig formula for area in various situations  Solving area problems needing additional computations  Finding areas of triangles by using Heron's Formula  Tackling practical applications by using triangular formulas  12. Complex numbers and polar coordinates  Writing powers of i in their simplest form  Adding and subtracting complex numbers  Multiplying complex numbers  Using multiplication to divide complex numbers  Solving quadratic equations with complex solutions  Graphing complex numbers  Identifying points with polar coordinates  Identifying points whose angles have negative measures  Converting polar to rectangular coordinates  Converting rectangular to polar coordinates  Recognizing polar curves  13. Conic sections  Identifying conics from their equations  Rewriting conic equations in standard form  Writing equations for circles  determining foci and axes of symmetry of parabolas  Finding the vertices and directrixes of parabolas  Writing equations of parabolas  Determining centers and foci of ellipses  Writing equations of ellipses  Determining asymptotes of hyperbolas  Writing equations of hyperbolas  Changing equation format from trig functions algebraic  Changing equation format from algebraic to trig  14. Systems of equations and inequalities  Using substitution to solve systems of linear equations with two variables  Using elimination to solve systems of linear equations with two variables  Solving systems of equations involving nonlinear functions  Solving systems of linear equations  Solving systems of linear equations with four variables  Graphing systems of inequalities  Decomposition of fractions  Operating on matrices  Changing matrices to the echelon form  Solving systems of equations using augmented matrices  Solving systems of equations using the inverse of the coefficient matrix  Applying Cramer's Rule to solve systems of equations  15. Sequences and series  Finding terms of sequences  Rules for sequences  Recursively defined sequences  Adding terms in an arithmetic series  Summing terms of a series  Finding rules and summing terms of a series  Calculating the sum of a geometric series  determining formulas and finding sums  Counting items by using combinations  Constructing Pascal's Triangle  Utilizing the binomial theorem  16. Introducing limits and continuity  Determining limits from graphs  Determining onesided limits  Determining limits from function values  Determining limits from function rules  Applying Laws of Limits  Investigating continuity  pt. II. The answers  17. Answers
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 ocn887935824
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 26 cm.
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 x, 533 pages
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 9781118853320
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 2014936392
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 unmediated
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 rdamedia
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 n
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 illustrations
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 (OCoLC)887935824
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