Engineering

Essentials of College Mathematics, 2e

Cheryl Cleaves and Margie Hobbs

Chapter 1  Review of Basic Concepts

1-1       Basic Operations with Whole Numbers and Decimals

            1.  Compare whole numbers.

            2.  Write fractions with power-of-10 denominators as decimal numbers.

            3.  Compare decimal numbers.

            4.  Round a whole number or a decimal number to a place value.

            5.  Add and subtract whole numbers and decimals.

            6.  Multiply and divide whole numbers and decimals.

1-2       Powers, Roots, and Powers of 10

            1.  Simplify expressions that contain exponents.

            2.  Square numbers and find the square roots of numbers.

            3.  Use powers of 10 to multiply and divide.

1-3       Order of Operations and Problem Solving

            1.  Apply the order of operations to a series of operations.

            2.  Evaluate a formula.

            3.  Solve applied problems using problem-solving strategies.

Chapter 2 Review of Fractions and Percents

2-1       Equivalent Fractions and Decimals

            1.   Write equivalent fractions with different denominators.

            2.   Write improper fractions as whole numbers or mixed numbers.

            3.   Write whole numbers or mixed numbers as improper fractions.

            4.   Change decimals to fractions and fractions to decimals.

            5.   Compare fractions, mixed numbers, and decimals.

2-2       Adding and Subtracting Fractions and Mixed Numbers

            1.   Add fractions and mixed numbers.

            2.   Subtract fractions and mixed numbers.

2-3       Multiplying and Dividing Fractions and Mixed Numbers

            1.   Multiply fractions and mixed numbers.

            2.   Raise a fraction to a power.

            3.   Divide fractions and mixed numbers.

2-4       The U. S. Customary System of Measurement

            1.   Convert from one unit of measure to another using unity ratios.

            2.   Convert from one unit of measure to another using conversion factors.

            3.   Add and subtract U. S. customary measures.

            4.   Multiply and divide U. S. customary measures.

            5.   Change from one U. S. customary rate measure to another.

2-5       Number and Percent Equivalents

            1.   Change any number to it percent equivalent.

            2.   Change any percent to its numerical equivalent.

2-6       Percentage Problems

            1.   Identify the portion, base, and rate in percent problems.

            2    Solve a percentage problems using the percentage formula.

2-7       Increase and Decrease

            1.   Find the amount of increase or decrease.

            2.   Find the new amount in increase or decrease problems.

            3.   Find the rate or base in increase or decrease problems.

Chapter 3 Measurement

3-1       Introduction to the Metric System

            1.   Identify uses of metric measures of length, mass, weight, and capacity.

            2.   Convert from one metric unit of measure to another.

            3.   Make calculations with metric measures.

3-2       Time, Temperature, and Other Measures

            1.   Convert from on unit of time to another

            2.   Make calculations with measures of time.

            3.   Convert Fahrenheit to Celsius temperature.

            4.   Convert Celsius to Fahrenheit temperature.

            5.   Examine other useful measures.

3-3       Metric-U.S. Customary Comparisons

            1.   Convert between U. S. customary measures and metric measures.

3-4       Accuracy, Precision, and Error

            1.   Determine the accuracy and significant digits of a number.

            2.   Find the precision and the greatest possible error of a measurement.

            3.   Find the relative error and the percent error of a measurement.

            4.   Determine an appropriate approximation of measurement calculations.

3-5       Reading Measuring Instruments

Chapter 4 Signed Numbers and Powers of 10

Cumulative Test Chapters 1-4

Chapter 5  Linear Equations

5-1       Variable Notation

            1.   Identify equations, terms, factors, constants, variables, and coefficients.

            2.   Write verbal interpretations of symbolic statements.

            3.   Translate verbal statements into symbolic statements using variables.

            4.   Simplify  variable expressions.

5-2       Solving Basic Linear Equations

            1.   Solve linear equations using the addition axiom.

            2.   Solve linear equations using the multiplication axiom.

            3.   Solve linear equations with like terms on the same side of the equation.

            4    Solve linear equations with like terms on opposite sides of the equation.

5-3       Applying the Distributive Property in Solving Equations

            1.   Solve linear equations that contain parentheses.

5-4       Solving Linear Equations with Fractions by Clearing the Denominators

            1.   Solve fractional equations by clearing the denominators.

            2.   Solve applied problems involving rate, time, and work.

            3.   Solve decimal equations by clearing decimals.

5-5       Formulas

            1.   Evaluate formulas.

            2.   Rearrange formulas to solve for a specific variable.

Chapter 6 Ratio and Proportion

6-1       Ratio and Proportion

            1.   Verify that two ratios are proportional.

            2.   Solve fractional equations that are proportions.

6-2       Direct Variation

            1.   Solve problems with direct variation.

            2.   Solve problems that involve similar triangles.

6-3       Inverse Variation

            1.   Solve problems with inverse variation

Chapter 7 Graphing Linear Equations

7-1       Graphical Representation of Equations

            1.   Locate points on a rectangular coordinate system.

            2.   Graph linear equations using a table of solutions.

7-2       Graphing Linear Equations in Two Variables Using Alternative Methods

            1.   Graph linear equations using intercepts.

            2.   Graph linear equations using the slope and y-intercept.

            3.   Graph linear equations using a graphing calculator.

            4.   Solve a linear equation using a graph.

7-3       Slope

            1.   Calculate the slope of a line, given two points on the line.

            2.   Determine the slope of a horizontal or vertical line.

7-4       Linear Equation of a Line

            1.   Find the equation of a line, given the slope and one point.

            2.   Find the equation of a line, given two points on the line.

            3.   Find the slope and y-intercept of a line, given the equation of the line.

            4.   Find the equation of a line, given the slope and y-intercept.

7-5       Parallel and Perpendicular Lines

            1.   Find the equation of a line parallel to a given line when at least one point on the parallel line is known.

            2.   Find the equation of a line perpendicular to a given line when at least one point on the perpendicular line is known.

Chapter 8 Systems of Linear Equations

8-1       Solving Systems of Equations Graphically

            1.   Solve a system of linear equation by graphing

8-2       Solving Systems of Equations Using the Addition Method

            1.   Use the addition method to solve a system of linear equations that contains opposite variable terms.

            2.   Use the addition method to solve a system of linear equations that does not contain opposite variable terms.

            3.   Apply the addition method to a system of linear equations with no solution or many solutions.

8-3       Solving Systems of Equations Using the Substitution Method

            1.   Use the substitution method to solve a system of linear equations.

8-4       Problem Solving Using Systems of Equations

            1.   Use a system of linear equations to solve application problems.

Cumulative Test Chapters 5 - 8

Chapter 9 Powers and Polynomials

9-1       Laws of Exponents

            1.   Multiply powers with like bases.

            2.   Divide powers with like bases.

            3.   Find a power of a power.

9-2       Polynomials

            1.   Identify polynomials, monomials, binomials, and trinomials.

            2.   Identify the degree of terms and polynomials.

            3.   Arrange polynomials in descending order.

9-3       Basic Operations with Polynomials

            1.   Add or subtract polynomials.

            2.   Multiply polynomials.

            3.   Divide polynomials.

Chapter 10 Products and Factors

10-1     The Distributive Property and Common Factors

            1.   Factor an expression containing a common factor.

10-2     Multiplying and Dividing Polynomials

            1.   Multiply polynomials.

            2.   Use the FOIL method to multiply two binomials.

            3.   Multiply polynomials that result in special products.

            4.   Divide polynomials using long division.

10-3     Factoring Special Products

            1.   Recognize and factor the difference of two perfect squates.

            2.   Recognize and factor a perfect-square trinomial.

10-4     Factoring General Trinomials

            1.   Factor general trinomials whose squared term has a coefficient of 1.

            2.   Remove common factors after grouping an expression.

            3.   Factor a general trinomial by grouping.

            4.   Factor any binomial or trinomial that is not prime.

Chapter 11 Quadratic Equations

11-1     Solving Quadratic Equations by the Square-Root Method

            1.   Write quadratic equations in standard form.

            2.   Identify the coefficients of the quadratic, linear, and constant terms of a quadratic equation.

            3.   Solve pure quadratic equations by the square-root method.

11-2     Solving Quadratic Equations by Factoring

            1.   Solve incomplete quadratic equations by factoring.

            2.   Solve complete quadratic equations by factoring.

            Solve quadratic equations using the quadratic formula.

11-4     Graphing Quadratic Equations

Cumulative Test Chapters 9 — 11

Chapter 12 Geometry

12-1     Lines and Angles

            1.   Use various notations to represent points, lines, line segments, rays, planes, and angles.

            2.   Classify angles according to size.

            3.   Determine the measure of an angle by using relationships among intersecting lines.

            4.   Convert angle measures between decimal degrees and degrees, minutes, and seconds.

12-2     Perimeter and Area

            1.   Find the perimeter of a polygon using the appropriate formula.

            2.   Find the area of a polygon using the appropriate formula.

12-3     Circles and Radians

            1.   Find the circumference or area of a circle using the appropriate formula.

            2.   Convert angle measures between degrees and radians.

            3.   Find the arc length of a sector.

            4.   Find the area of a sector or segment.

12-4     Volume and Surface Area

            1.   Find the volume of three-dimensional objects.

            2.   Find the surface area of three-dimensional objects.

12-5     Special Triangle Relationships

            1.   Classify triangles by the relationship of the sides or angles.

            2.   Find the missing sides of a right triangle using the Pythagorean theorem.

Chapter 13 Right Triangle Trigonometry

13-1     Trigonometric Functions

            1.   Find the sine, cosine, and tangent of angles of right triangles, given the measures of at least two sides.

            2.   Find the trigonometric values of the sine, cosine, and tangent functions using a calculator.

            3.   Find the angle measure, given a trigonometric value.

13-2     Solving Right Triangles Using the Sine, Cosine, and Tangent Functions

            1.   Find the missing parts of a right triangle using the sine function.

            2.   Find the missing parts of a right triangle using the cosine function.

            3.   Find the missing parts of a right triangle using the tangent function.

            4.   Select the most direct method for solving right triangles.

            5.   Solve applied problems using right-triangle trigonometry.

Chapter 14 Trigonometry With Any Angle

14-1     Vectors

            1.   Find the magnitude of a vector in standard position given the coordinates of the end point.

            2.   Find the direction of a vector in standard position given the coordinates of the end point.

            3.   Find the sum of vectors.

14-2     Trigonometric Functions for any Angle

            1.   Find related acute angles for angles or vectors in quadrants II, III, and IV.

            2.   Determine the signs of trigonometric values of angles of more than 90°.

            3.   Find the trigonometric values of angles of more than 90° using a calculator.

14-3     Period and Phase Shift

            1.   Graph a sine or cosine function using a calculator.

            2    Find the period of a sine or cosine function.

            3.   Find the phase shift of a sine or cosine function.

14-4     Law of Sines

            1.   Find the missing parts of an oblique triangle, given two angles and a side.

            2.   Find the missing parts of an oblique triangle, given two sides and an angle opposite one of them.

14-5     Law of Cosines

Cumulative Test Chapters 12 — 14

Chapter 15 Statistics

15-1     Reading Circle, Bar, and Line Graphs

            1.   Read circle graphs.

            2.   Read bar graphs.

            3.   Read line graphs.

15-2     Averages and Frequency Distributions

            1.   Find the arithmetic mean or the arithmetic average.

            2.   Find the median and the mode.

            3.   Make a frequency distribution,

            4.   Find the mean of grouped data.

15-3     Range and Standard Deviation

            1.   Find the range.

            2.   Find the standard deviation.

15-4     Counting Techniques and Simple Probability

            1.   Count the number of ways objects in a set can be arranged.

            2.   Determine the probability of an event occurring if an activity is repeated over and over.