Mathematics Survival Kit

 

The Mathematics Survival Kit - Maple Edition 

Version 2 

Jack Weiner 

Table of Contents 

 

Introduction 

Introduction to the Maple Edition 

What's New in This Version? 

Getting Started on Survival 

How to Use This Book - Read This! 

How to Get an "A" in Math 

How to Get Extra Help 

Operation Cooperation and Fraction Traction 

BEDMAS 

Adding and Subtracting Fractions 

Multiplying and Dividing Fractions 

Factoring: A Product of Practice 

Difference of Squares 

Difference of Cubes 

Factoring`+`(`^`(a, n), `-`(`^`(b, n))) and  `+`(`^`(a, n), `^`(b, n)) 

Common Factors 

Factoring Easy Trinomials 

The Remainder and Factor Theorems for Polynomials 

Pliable Polynomials 

Multiplying Polynomials - FOIL 

Adding and Subtracting Polynomial Fractions 

Multiplying and Dividing Polynomial Fractions 

Polynomial Division 

The Straight Goods on Lines and Planes 

Finding the Equation of a Line 

Slope m and y intercept b 

Distance between Two Points and Distance from a  Point to a Line or Plane 

Visually Identifying Slopes of Lines 

Parallel and Perpendicular Lines 

Finding Tangent and Normal Lines to a Curve 

A Few Lines on Linear Algebra 

Solving Two Linear Equations Using Substitution 

Solving Two Linear Equations Using Row Reduction 

Solving Three Linear Equations Using Row Reduction 

Consistent, Inconsistent and Dependent Systems of Linear Equations 

Giving the Third Degree to Second Degree Polynomials: Quadratics! 

Solving Quadratic Equations Using the Quadratic Formula 

Factoring Quadratic Equations Using the Quadratic Formula 

Problems Involving the Sum and Product of the Roots of a Quadratic Equation 

The Graph of y = `+`(`*`(`^`(a(`+`(x, `-`(b))), 2)), c) 

Completing the Square 

Solving Inequalities with Less (<) Difficulty, Greater (>) Ease 

Solving Linear Inequalities 

Solving Quadratic Inequalities 

Solving Inequalities with Two or More Factors 

Solving Rational Inequalities 

Increasing the Magnitude of Your Absolute Value Knowledge 

The Basics of Absolute Value 

Solving Absolute Value Equations 

Solving Easy Absolute Value Inequalities 

Solving Less Easy Absolute Value Inequalities 

Getting to the Root of Square Roots 

The Basics of Square Root and the Reason sqrt(`*`(`^`(x, 2))) = abs(x) 

Solving Equations Involving Square Roots 

Rationalizing Denominators that Have  

Some Basic Graphs and Some Basics about Graphs 

Graphs of Basic Quadratic Relations 

Basic  y = `^`(x, n)  Graphs, where `in`(n, N)  (Even and Odd Functions) 

Basic y = `^`(x, `+`(`-`(n)))  Graphs, where `in`(n, N) 

Basic  y = `^`(x, `/`(1, `*`(n))) Graphs, where  `in`(n, N) 

Shifting or Rescaling a Given Graph 

Tests for Symmetry 

Graphing Polynomials without Calculus 

Vertical and Horizontal Asymptotes 

Slant Asymptotes 

Intersection of Two Curves 

The Greatest Integer (or Floor) Function 

Graphs with the Greatest Integer Function 

The Survival Kit Logs Powerful Time with Exponents and Logarithms 

Properties of Exponents 

Properties of Logarithms 

Basic Exponential Graphs 

Basic Logarithmic Graphs 

Inverse Formulas for Exponents and Logarithms 

Solving Exponential Equations 

Solving Logarithmic Equations 

The Derivative ofexp(x) and  `^`(a, x) 

The Derivative of  ln(x) and  log[a](x) 

Log Differentiation Part I 

Log Differentiation Part II: The derivative of y = `^`(f(x), g(x)) 

Integrals Yielding ln: int(`/`(`*`(du, `*`(u)), `*`(dx)), x) = `+`(ln(abs(u)), C) 

Drawing Your Attention to Some Basic Geometry 

A Degree of Knowledge About Angles 

The Pythagorean Theorem 

Similar Triangles 

Radian Measure of an Angle 

Angling Right in on Trigonometry 

Angles in Standard Position 

Related Angles in Standard Position 

Trig Ratios for the (`^`(30, o), `^`(60, o), `^`(90, o)) Triangle 

Trig Ratios for the (`^`(45, o), `^`(45, o), `^`(90, o)) Triangle 

Trig Ratios for  `^`(30, o), `^`(45, o), `^`(60, o), `^`(90, o), `^`(120, o), and More - A Table! Trig Ratios for `^`(30, o), `^`(45, o), `^`(60, o), `^`(90, o), `^`(120, o), and More - A (Fabulous) Picture!! 

Basic Trigonometric Graphs 

The Circle Definition of Sine and Cosine 

Solving the Trig Equation  sin(x) = c 

Solving the Trig Equation  cos(x) = c 

The Sine Law 

The Cosine Law 

Commonly Used Trigonometric Formulas Including Derivatives and Integrals 

A Straightforward Approach to Limits 

Easy Limits: "No Problem" Problems 

"0/0" Limits 

One-sided Limits 

Limits which Approach  

Limits at Infinity 

AnLimit:  

Variations on 

Continuity (There's a Hole in the Function, Dear Liza, Dear Liza) 

Domain (Food for a Function!) 

Continuity and Discontinuity at a Point 

Continuous Functions (Intervals of Continuity) 

Continuity and Branch Functions 

Essential versus Removable Discontinuities 

Derivatives or Going on a Tangent about Slopes 

Finding the Derivative from the Definition 

Differentiable Functions (Intervals of Differentiability) 

Differentiability and Branch Functions 

Critical Numbers 

Min and Max Points from the First Derivative 

Graphing and Interpreting  y versus  diff(y(x), x) versus  diff(y(x), x, x) 

Graph Sketching with Calculus 

Graph Sketching with Calculus: Vertical Tangent! 

Estimating Using the Differential 

Rolle's Theorem 

The Mean Value Theorem 

Derivative Rules Rule 

Derivatives: The Product Rule 

Derivatives: The Chain Rule 

Derivatives: The Quotient Rule 

Derivatives: Implicit Differentiation 

Derivatives: Implicit Differentiation Second Derivative 

Integrating Your Knowledge about the Anti-Derivative 

Easy Integrals/Anti-Derivatives 

Easy Integrals that Need a Little Tweaking 

The Chain Rule In Reverse (CRIR): No Adjustments Needed! 

CRIR: Adjustments Needed BUT Don't Use Substitution! 

CRIR: Adjustments Needed and Using Substitution 

Substitution when the CRIR Won't Work 

Integration by Parts: The Basic Examples 

Integration by Parts: Circular Integration By Parts 

Integration by Parts: The Tan-Sec Connection 

The Derivative of an Integral 

Inverse Functions: Now that's a Switch! 

Finding the Inverse of a Function 

Derivatives of Inverse Functions 

Warming Up to Polar Coordinates 

Polar Coordinates 

Polar to Rectangular Coordinates; Rectangular to Polar Equations 

Rectangular to Polar Coordinates; Polar to Rectangular Equations 

Going to Any Lengths to Give You New Direction with Vectors 

(Very) Basic Vectors 

The Dot or Scalar or Inner Product of Two Vectors 

The Vector or Cross Product of Two Vectors 

The Vector Equation of a Line 

The Vector Equation of a Plane 

The Scalar Equation of a Plane: Ax + By + Cz = D 

Intersection of Two Lines in `*`(`^`(real, 3)): Parallel/Coincident Case 

Intersection of Two Lines in `*`(`^`(real, 3)): Non-Parallel/Non-Coincident Case 

Intersection of Two Planes 

Intersection of Three Planes: Parallel/Coincident Case 

Intersection of Three Planes: Non-Parallel/Non-Coincident Case 

A Few Terms in Sequences and Series and a Sampling of Statistics 

Summation Notation and Common SUM=  Formulas 

Arithmetic and Geometric Sequences and Series 

Combinations and Permutations: Choosing and Arranging 

Mean, Median, Mode and Standard Deviation 

The Binomial Theorem 

End Game 

Feedback Form 

About the Author 

Index 

 

Content from the original print version of The Mathematics Survival Kit, Second Edition is © 2009, 2004, Nelson Education Ltd. All other content is © Maplesoft, a division of Waterloo Maple Inc., 2010. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation. 'Nelson' and 'Nelson Education', and the Nelson and Nelson Education logos are registered trademarks of Nelson Education Ltd. 'Maplesoft' and the Maplesoft logo are registered trademarks of Waterloo Maple Inc. 


ISBN 1-897310-99-4