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Published:
April 2, 2019

Pre-Calculus Workbook For Dummies

Overview

Get a handle on pre-calculus in a pinch!

If you’re tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you’ll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem. 

In Pre-Calculus Workbook For Dummies, you’ll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you’ll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations. 

  • Get ample review before jumping into a calculus course
  • Supplement your classroom work with easy-to-follow guidance
  • Make complex formulas and concepts more approachable
  • Be prepared to further your mathematics studies

Whether you’re enrolled in a pre-calculus class or you’re looking for a refresher as you prepare for a calculus course, this is the perfect study companion to make it easier.

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About The Author

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Trigonometry For Dummies and Finite Math For Dummies.

Sample Chapters

pre-calculus workbook for dummies

CHEAT SHEET

Pre-calculus uses the information you know from Algebra I and II and ratchets up the difficulty level to prepare you for calculus. This cheat sheet is designed to help you review key formulas and functions on the fly as you study. It includes formulas, the laws of logarithmic functions, trigonometric values of basic angles, conic section equations, and interval notation.

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Articles from
the book

Here are ten pitfalls that normally trip up the pre-calculus student. Make sure that you understand the order of operations, how to properly multiply binomials and monomials with exponents, how to break up and flip fractions, how not to combine terms, and how to keep from disregarding the negative sign. Going out of order (of operations) Operations in an expression or an equation aren’t all meant to be done from left to right.
Once upon a time, mathematicians delved into their imaginations and invented a whole new set of numbers. They needed these numbers so they could finish some math problems — problems in which the square root of a negative number occurred.Fields like engineering, electricity, and quantum physics all use imaginary numbers in their everyday applications.
The fundamentals are important. That’s why they’re called fundamentals. Pre-calculus is the stepping stone for calculus. It’s the final stepping stone after all those years of math: algebra I, geometry, algebra II, and trigonometry. Now all you need is pre-calculus to get to that ultimate goal — calculus. Pre-calculus begins with certain concepts that you need to be successful in any mathematics course.
In pre-calculus, you need to evaluate the six trig functions — sine, cosine, tangent, cosecant, secant, and cotangent — for a single angle on the unit circle. For each angle on the unit circle, three other angles have similar trig function values. The only difference is that the signs of these values are opposite, depending on which quadrant the angle is in.
Depending on how many times you must multiply the same binomial — a value also known as an exponent — the binomial coefficients for that particular exponent are always the same. The binomial coefficients are found by using thecombinations formula. If the exponent is relatively small, you can use a shortcut called Pascal's triangle to find these coefficients.
The fundamental theorem of algebra can help you find imaginary roots. Imaginary roots appear in a quadratic equation when the discriminant of the quadratic equation — the part under the square root sign (b2 – 4ac) — is negative. If this value is negative, you can’t actually take the square root, and the answers are not real.
Sometimes your geometry teacher may spice things up a bit with complicated polar coordinates — points with negative angles and/or radii. The following list shows you how to plot in three situations — when the angle is negative, when the radius is negative, and when both are negative. When the angle is negative: Negative angles move in a clockwise direction.
Knowing whether a function is even or odd helps you to graph it because that information tells you which half of the points you have to graph. These types of functions are symmetrical, so whatever is on one side is exactly the same as the other side.If a function is even, the graph is symmetrical about the y-axis.
Whether an exponential equation contains a variable on one or both sides, the type of equation you’re asked to solve determines the steps you take to solve it.The basic type of exponential equation has a variable on only one side and can be written with the same base for each side. For example, if you’re asked to solve 4x – 2 = 64, you follow these steps: Rewrite both sides of the equation so that the bases match.
In a system of linear equations, where each equation is in the form Ax + By + Cz + . . . = K, you can represent the coefficients of this system in matrix, called the coefficient matrix.If all of the variables line up with one another vertically, then the first column of the coefficient matrix is dedicated to all the coefficients of the first variable, the second row is for the second variable, and so on.
If fundamentals such as the order of operations are the foundation of your pre-calculus house, then the skills you pick up in Algebra I and II are the mortar between your pre-calculus bricks. Review inequalities, radicals, and exponents and work on your interval notation. How to solve inequalities Inequalities are mathematical sentences that indicate that two expressions are something other than just equal.
Pre-calculus uses the information you know from Algebra I and II and ratchets up the difficulty level to prepare you for calculus. This cheat sheet is designed to help you review key formulas and functions on the fly as you study. It includes formulas, the laws of logarithmic functions, trigonometric values of basic angles, conic section equations, and interval notation.
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