DC Public Library System

1,001 pre-calculus practice problems for dummies, by Mary Jane Sterling

eng

illustrations

index present

non fiction

1,001 pre-calculus practice problems for dummies

887935824

by Mary Jane Sterling

For Dummies

This handy guide gives you opportunities to gain confidence in your math skills. The pre-calculus problems are ranked from easy to hard, and are accompanied by detailed explanations and step-by-step solutions for each one

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 one-to-one functions from given relations -- Identifying one-to-one 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 solvable10. Continuing with trig identities -- Using identities that add or subtract angle measures -- Double-angle identities -- Using identities that double the size of the angle -- Confirming the statements of multiple-angle identities -- Creating half-angle identities from double-angle identities -- Creating a half-angle for tangent -- Using half-angle identities to simplify expressions -- Creating products of trig functions from sums and differences -- Using product-to-sum identities to evaluate expressions -- Using sum-to-product identities to evaluate expressions -- Applying power-reducing 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 real-world 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 one-sided limits -- Determining limits from function values -- Determining limits from function rules -- Applying Laws of Limits -- Investigating continuity -- pt. II. The answers -- 17. Answers

One thousand and one pre-calculus practice problems for dummiesPre-calculus for dummies