Essentials of College Mathematics, 2e | | |
Cheryl Cleaves and Margie Hobbs | | |
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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. | | |
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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. | | |
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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 | | |
1. Read the metric rule. | | |
2. Read the slide caliper. | | |
3. Read the micrometer. | | |
4. Read circular, uniform, and nonuniform scales. | | |
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Chapter 4 Signed Numbers and Powers of 10 | | |
4-1 Adding Signed Numbers | | |
1. Compare signed numbers. | | |
2. Add signed numbers with like signs. | | |
3. Add signed number with unlike signs. | | |
4-2 Subtracting Signed Numbers | | |
1. Subtract signed numbers. | | |
2. Combine addition and subtraction . | | |
4-3 Multiplying and Dividing Signed Numbers | | |
1. Multiply signed numbers. | | |
2. Evaluate powers of signed numbers. | | |
3. Divide signed numbers. | | |
4-4 Signed Fractions and Decimals | | |
1. Change a signed fraction to an equivalent signed fraction. | | |
2. Perform basic operations with signed fractions and decimals. | | |
3. Apply the order of operations with signed numbers. | | |
4-5 Powers of 10 | | |
1. Multiply and divide powers of 10. | | |
2. Raise a power of 10 to a power. | | |
4-6 Scientific Notation | | |
1. Change a number from scientific notation to ordinary notation. | | |
2. Change a number from ordinary notation to scientific notation. | | |
3. Multiply and divide numbers in scientific notation. | | |
4. Raise a number in scientific notation to a power. | | |
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Cumulative Test Chapters 1-4 | | |
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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. | | |
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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 | | |
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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. | | |
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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. | | |
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Cumulative Test Chapters 5 - 8 | | |
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Chapter 9 Powers and Polynomials | | |
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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. | | |
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Chapter 10 Products and Factors | | |
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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. | | |
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Chapter 11 Quadratic Equations | | |
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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. | | |
11-3 The Quadratic Formula | | |
Solve quadratic equations using the quadratic formula. | | |
11-4 Graphing Quadratic Equations | | |
1. Graph quadratic equations using the table-of-solutions method. | | |
2. Graph quadratic equations by examining properties. | | |
3. Solve a quadratic equation from a graph. | | |
4. Graph quadratic equations using a graphing calculator. | | |
11-5 Imaginary Numbers | | |
1. Write imaginary numbers using the letter j. | | |
2. Raise imaginary numbers to powers. | | |
3. Determine the nature of the roots of a quadratic equation by examining the discriminant. | | |
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Cumulative Test Chapters 9 — 11 | | |
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Chapter 12 Geometry | | |
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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. | | |
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Chapter 13 Right Triangle Trigonometry | | |
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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. | | |
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Chapter 14 Trigonometry With Any Angle | | |
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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 | | |
1. Find the missing parts of an oblique triangle, given three sides of the triangle. | | |
2. Find the missing parts of an oblique triangle, given two sides and the included angle of the triangle. | | |
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Cumulative Test Chapters 12 — 14 | | |
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Chapter 15 Statistics | | |
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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. | | |
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