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 specified place value.
5. Add and subtract whole numbers and decimals.
6. Multiply and divide whole numbers and decimals.
1.2 Exponents, 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
2.1 Multiples and Factors
1. Find multiples of a natural number.
2. Find all factor pairs of a natural number.
3. Determine the prime factorization of composite numbers.
4. Find the least common multiple and greatest common factor of two or more numbers.
2.2 Equivalents 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.
2.3 Adding and Subtracting Fractions and Mixed Numbers
1. Add fractions and mixed numbers.
2. Subtract fractions and mixed numbers.
2.4 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.
4. Perform calculations involving fractions with a calculator.
2.5 The U.S. Customary System of Measurement
1. Convert from one unit of measure to another using unit 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.
Chapter 3 Percents
3.1 Percent and Number Equivalents
1. Change any number to its percent equivalent.
2. 2. Change any percent to its numerical equivalent.
3.2 Percentage Problems
1. Identify the portion, base, and rate in percent problems.
2. Solve a percentage problem using the percentage formula.
3. Solve a percentage problem using the percentage proportion.
4. Solve business and consumer problems involving percents.
3.3 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 4 Measurement
4.1 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.
4.2 Time, Temperature, and Other Measures
1. Convert from one unit of time to another.
2. Make calculations with measures of time.
3. Convert between Fahrenheit Temperatures and Celsius temperatures.
4. Examine other useful measures.
4.3 Metric — U.S. Customary Comparisons
1. Convert between U.S. customary measures and metric measures.
4.4 Accuracy, Precision, Error, and Measuring Instruments
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.
5. Read the metric rule.
6. Find the distance and the midpoint of a line segment.
Chapter 5 Signed Numbers and Powers of 10
5.1 Adding Signed Numbers
1. Compare signed numbers.
2. Add signed numbers with like signs.
3. Add signed numbers with unlike signs.
5.2 Subtracting Signed Numbers
1. Subtract signed numbers.
2. Combine addition and subtraction.
5.3 Multiplying and Dividing signed Numbers
1. Multiply signed numbers.
2. Evaluate powers of signed numbers.
3. Divide signed numbers.
5.4 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.
5.5 Powers of 10
1. Multiply and divide powers of 10
2. Raise a power of 10 to a power.
5.6 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.
5. Change among engineering, scientific, and ordinary notations.
Chapter 6 Statistics
6.1 Reading Circle, Bar, and Line Graphs
1. Read circle graphs.
2. Read bar graphs.
3. Read line graphs.
6.2 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.
6.3 Range and Standard Deviation
1. Find the range.
2. Find the standard deviation.
6.4 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.
Chapter 7 Linear Equations
7.1 Variable Notation
1. Identify equations, terms, factors, constants, variables, and coefficients.
2. Write variable interpretations of symbolic statements.
3. Translate verbal statements into symbolic statements using variables.
4. Simplify variable expressions.
7.2 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 sides of the equation.
4. Solve linear equations with like terms on opposite sides of the equation.
7.3 Applying the Distributive Property in Solving Equations
1. Solve linear equations that contain parentheses.
7.4 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 equation by clearing decimals.
7-5 Formulas
1. Evaluate formulas.
2. Rearrange formulas to solve for a specific variable.
Chapter 8 Ratio and Proportion
8-1 Ratio and Proportion
1. Solve fractional equations that are proportions.
8-2 Direct and Joint Variation
1. Solve problems of direct variation using proportions.
2. Solve problems of direct variation using a constant of variation.
3. Solve problems of joint variation using a constant of variation.
8-3 Inverse and Combined Variation
1. Solve problems of inverse variation using proportions.
2. Solve problems of inverse variations using a constant of variation.
3. Solve problems of combined variation using a constant of variation.
Chapter 9 Graphing Linear Equations
9-1 Graphical Representation of Linear Equations and Functions
1. Locate points on a rectangular coordinate system.
2. Represent an equation in two variables as a function.
3. Make a table of solutions for a linear equation or function.
4. Graph a linear equation or function using a table of solutions.
9-2 Graphing Linear Equations in Two Variables Using Alternative Methods
1. Graph linear equations using intercepts.
2. Graph linear equations using slope and y-intercept.
3. Graph linear equations using a graphing calculator.
4. Solve a linear equation in one variable using a graph.
9-3 Slope
1. Calculate the slope of a line, given two points on the line.
2. Determine the slope of a horizontal or vertical line.
9-4 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 equation of a line, given the slope and y-intercept.
4. Find the equation of a line parallel to a given line when at least one point on the parallel line is known.
5. Find the equation of a line perpendicular to a given line when at least one point on the perpendicular line is known.
Chapter 10 Systems of Linear Equations
10-1 Solving Systems of Equations Graphically
1. Solve a system of linear equations by graphing.
10-2 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.
10-3 Solving Systems of Equations Using the Substitution Method
1. Use the substitution method to solve a system of linear equations.
10-4 Problem Solving Using Systems of Equations
1. Use a system of linear equations to solve application problems.
Chapter 11 Powers and Polynomials
11-1 Laws of Exponents
1. Multiply powers with like bases.
2. Divide powers with like bases.
3. Find a power of a power.
11-2 Polynomials
1. Identify polynomials, monomials, binomials, and trinomials.
2. Identify the degree of terms and polynomials.
3. Arrange polynomials in descending order.
11-3 Basic Operations with Polynomials
1. Add and subtract polynomials.
2. Multiply polynomials.
3. Use the FOIL method to multiply two binomials.
4. Multiply polynomials that result in special products.
5. Divide polynomials.
Chapter 12 Roots and Radicals
12-1 Irrational Numbers and Real Number
1. Write roots using radical and exponential notation.
2. Approximate an irrational number.
3. Write powers and roots using rational exponents and radical notation.
12-2 Simplifying Irrational Expressions
1. Find the square root of variables.
2. Simplify square — root radicals using rational exponents and the laws of exponents.
3. Simplify square-root radical expressions containing perfect-square factors.
12-3 Basic Operations with Square-Root Radicals
1. Add and subtract square-root radicals.
2. Multiply and divide square-root radicals.
12-4 Complex and Imaginary Numbers
1. Write imaginary numbers using the letter i.
2. Raise imaginary numbers to powers.
3. Write real and imaginary numbers in complex form, a+bi.
4. Combine complex numbers.
5. Multiply complex numbers.
Chapter 13 Factoring
13-1 The Distributive Property and Common Factors
1. Factor an expression containing a common factor.
13-2 Factoring Special Products
1. Recognize and factor the difference of two perfect squares.
2. Recognize and factor a perfect-square trinomial.
3. Recognize and factor a sum or difference of two perfect cubes.
13-3 Factoring General Trinomials
1. Factor general trinomials whose square 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 14 Rational Expressions and Equations
14-1 Simplifying Rational Expressions
1. Simplify or reduce rational expressions.
14-2 Multiplying and Dividing Rational Expressions
1. Multiply and Divide rational expressions.
2. Use Multiplication and conjugates to rationalize a numerator or denominator of a fraction that has a binomial with an irrational term.
14-3 Adding and Subtracting Rational Expressions
1. Add and subtract rational expressions.
2. Use addition and subtraction of rational expressions to simplify complex fractions.
14-4 Solving Equations with Rational Expressions
1. Exclude certain values as solutions of rational equations.
2. Solve rational equations with variable denominators.
Chapter 15 Quadratic and Higher-Degree Equations
15-1 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 (ax2 +c = 0) by the square-root method.
15-2 Solving Quadratic Equations by Factoring
1. Solve incomplete quadratic equations (ax2 + bx = 0) by factoring.
2. Solve complete quadratic equations (ax2 + bx + c = 0) by factoring.
15-3 Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula
1. Solve quadratic equations by completing the square.
2. Solve quadratic equations using the quadratic formula.
15-4 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.
5. Determine the nature of the roots of a quadratic equation by examining the discriminant.
15-5 Solving Higher-Degree Equations
1. Identify the degree of an equation.
2. Solve higher-degree equations by factoring.
3. Graph higher-degree equations.
4. Distinguish between a function and a relation using the vertical line test.
5. Find the domain and range of a relation from a graph.
Chapter 16 Exponential and Logarithmic Equations
16-1 Exponential Expressions, Equations and Formulas
1. Evaluate formulas with at least one exponential term.
2. Evaluate formulas that contain a power of the natural exponential, e.
3. Solve the exponential equations in the form bx = by, where b > 0 and b ≠ 1
4. Graph an exponential function.
16-2 Logarithmic Expressions, Equations and Formulas
1. Write exponential expressions as equivalent logarithmic expressions.
2. Write logarithmic expressions as equivalent exponential expressions.
3. Evaluate common and natural logarithmic expressions using a calculator.
4. Evaluate logarithms with a base other than 10 and e.
5. Evaluate formulas containing at least one logarithmic term.
6. Graph a logarithmic function.
7. Simplify logarithmic expressions by using the properties of logarithms.
Chapter 17 Inequalities and Absolute Values
17-1 Inequalities and Sets
1. Use set terminology.
2. Show inequalities on a number line and write the inequalities in interval notation.
17-2 Solving Linear Inequalities
1. Solve a linear inequality in one variable.
2. Graph a linear inequality in two variables.
3. Solve a system of linear inequalities by graphing.
17-3 Solving Compound Inequalities
1. Identify subsets of sets and perform set operations.
2. Solve compound inequalities with the conjunction condition.
3. Solve compound inequalities with the disjunction condition.
17-4 Solving Quadratic and Rational Inequalities in One Variable
1. Solve quadratic inequalities in one variable.
2. Graph quadratic inequalities in two variables.
3. Solve rational inequalities in one variable.
17-5 Solving Equations and Inequalities Containing One Absolute-Value Term
1. Solve equations containing one absolute-value term.
2. Solve absolute-value inequalities using the “less than” relationship.
3. Solve absolute-value inequalities using the “greater than” relationship.
Chapter 18 Geometry
18-1 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.
18-2 Polygons
1. Find the perimeter of a polygon using the appropriate formula.
2. Find the area of a polygon using the appropriate formula.
18-3 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.
18-4 Volume and Surface Area
1. Find the volume of three-dimensional objects.
2. Find the surface area of three-dimensional objects.
Chapter 19 Triangles
19-1 Special Triangle Relationships
1. Classify triangles by the relationship of the sides or angles.
2. Determine if two triangles are congruent using inductive and deductive reasoning.
3. Solve problems that involve similar triangles.
19-2 Pythagorean Theorem
1. Use the Pythagorean theorem to find the missing side of a right triangle.
2. Use the properties of a 45e, 45e, and 90e triangles to find missing parts.
3. Use the properties of a 30e, 60e, and 90e triangles to find missing parts.
19-3 Inscribed and Circumscribed Regular Polygons and Circles
1. Find the number of degrees in each angle of a regular polygon.
2. Find the area of a regular polygon.
3. Use properties of inscribed and circumscribed squares to find missing amounts.
4. Use the properties of inscribed and circumscribed equilateral triangles to find missing amounts.
5. Use the properties of inscribed and circumscribed regular hexagons to find missing amounts.
19-4 Distance and Midpoints
1. Find the distance between two points on the rectangular coordinate system.
2. Find the coordinates of the midpoint of a line segment if given the coordinates of the end points.
Chapter 20 Right Triangle Trigonometry
20-1 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.
20-2 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 21 Trigonometry with Any Angle
21-1 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. Convert vectors in standard position between rectangular coordinate notation and polar coordinate notation.
4. Find the sum and dot product of vectors.
21-2 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 degrees.
3. Find the trigonometric values of angles of more than 90 degrees using a calculator.
21-3 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.
21-4 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.
21-5 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.