ALGEBRA 2 - Pasco School Districtand inequalities. Graph quadratic inequalities in two 5.7 Graphing...

1 Updated: Thursday, December 02, 2010

Mathematics Curricular Guide

ALGEBRA 2

2010-2011 SCHOOL YEAR

Pasco School District Algebra 2 2010 – 2011 School Year


MATHEMATICS SCOPE & SEQUENCE

Unit Title Dates Page 1. Chapter 1 – Equations and Inequalities .................................................................................................................................... 3

2. Chapter 2- Linear Equations and Functions .............................................................................................................................. 5

3. Chapter 5 – Quadratic Functions.............................................................................................................................................. 7

4. Chapter 3 – Systems of Linear Equations and Inequalities ..................................................................................................... 10

5. Chapter 6 – Polynomials and Polynomial Functions ............................................................................................................... 12

6. Chapter 12 – Probability and Statistics................................................................................................................................... 14

7. Chapter 7 – Powers, Roots, and Radicals ............................................................................................................................... 17

8. Chapter 8 – Exponential and Logarithmic Functions .............................................................................................................. 19

9. Chapter 9 – Rational Equations and Functions ....................................................................................................................... 21

10. Chapter 11 – Sequences and Series ....................................................................................................................................... 22

11. Chapter 13 – Trigonometric Ratios and Functions ................................................................................................................. 23



Unit Name: Chapter 1 Equations and Inequalities

[Starting Date] [Ending Date]

Standard Lesson & objective Days Formative Assessments/

Assignments Alignment Notes

A2.2.A Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved.

1.1 Real Numbers and Number Operations

Identify properties of and use operations with real numbers.

Recognize and explain the relationship amongst different number systems.

2 This standard is briefly mentioned, but a typical student would not be able to achieve mastery with the available content. A relationship between number systems if not identified. Locate materials to use for instruction and reinforcement.

A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents.

1.2 Algebraic Expressions and Models

Evaluate algebraic expressions.

Simplify algebraic expressions by combining like terms.

2 The laws of rational exponents occur in section 7.2 which will be addressed later in the curriculum.

A2.1.A Select and justify functions and equations to model and solve problems.

1.3 Solving Linear Equations

Solve linear equations.

Use linear equations to model and solve real-life problems.

2 While solving linear equations is not addressed specifically in the PEs, a review of this skill is needed prior to completion of the rest of the curriculum. Refer to 1.3 Practice B and 1.3 Practice C worksheets to find additional application problems.

1.4 Rewriting Equations and Formulas

Rewrite equations with more than one variable.

2 This section is included in anticipation for the unit on solving systems of equations.






1.5 Problem Solving Using Algebraic Models

Use a general problem-solving plan to solve real-life problems.

Have students write a verbal model, assign labels, write an algebraic model, then solve the algebraic model to solve the problem.

2

In anticipation of A2.1.B Solve problems that can be represented by systems of equations and inequalities.

1.6 Solving Linear Inequalities

Solve simple inequalities.

2

3 Add three days for review, reteaching, and assessment.

Process Standards Addressed: A2.8.A Analyze a problem situation and represent it mathematically.

Assessment: Chapter 1 common assessment



Unit Name: Chapter 2 Linear Equations and Functions





2.1 Functions and their graphs

Distinguish between relations and functions.

Graph and evaluate linear functions.

2 Be sure to emphasize the definitions of relation and function. The second objective is included in anticipation of the section on graphing lines which follows.


2.2 Slope and Rate of Change

Use slope to solve real-life problems.

2 A basic review of calculating slope may be necessary before students are ready to solve problems with rate of change. This section is included to address problem solving with rates of change, to meet the PE.

In anticipation of A2.1.B Solve problems that can be represented by systems of equations and inequalities.

2.3 Quick Graphs of Linear Equations

Graph linear equations in slope-intercept form.

2


2.4 Writing Equations of Lines

Model functions by writing linear equations.

2

2.7 Piecewise Functions

Represent piecewise functions.

Use piecewise functions to model real-life situations.

2 Sections 2.7 and 2.8 do not match PEs. They are included so students will be prepared for the Compass test at CBC.

2.8 Absolute Value Functions

Represent absolute value functions.

Use absolute value functions to model real-life situations.

2



Unit Name: Chapter 5 Quadratic Functions [Starting Date] [Ending Date]



A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A2.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

5.1 Graphing Quadratic Functions

Graph quadratic functions.

Use quadratic functions to solve real-life problems.

2

A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. A2.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

5.2 Solving Quadratic Equation by Factoring

Factor quadratic expressions

Solve quadratic equations by factoring

Find solutions (zeros) of quadratic functions.

2

A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.

5.3 Solving Quadratic Equations by Finding Square Roots

Solve quadratic equations by finding square roots.

Use quadratic equations to solve real-life problems.

2


5.4 Complex Numbers

Solve quadratic equations with complex solutions.

2


5.5 Completing the Square

Solve quadratic equations by completing the square.

2



A2.3.A Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

Use completing the square to write quadratic functions in vertex form.




5.6 The Quadratic Formula and the Discriminant

Solve quadratic equations using the quadratic formula.

Use the quadratic formula in real-life situations.

Use the discriminant to determine the number and type of solutions of a quadratic equation.

2


5.7 Graphing and Solving Quadratic Inequalities

Graph quadratic inequalities in two variables

Solve quadratic inequalities in real-life situations.

2


5.8 Modeling with Quadratic Functions

Write quadratic functions given characteristics of their graphs.

2




Unit Name: Chapter 3 Systems of Linear Equations and Inequalities




A2.1.B Solve problems that can be represented by systems of equations and inequalities.

3.1 Solving Linear Systems by Graphing

Graph and solve systems of linear equations.

Use linear systems to solve real-life problems.

2


3.2 Solve Linear Systems Algebraically

Use algebraic methods to solve linear systems.

Use linear systems to model real-life situations.

2


3.3 Graphing and Solving Systems of Linear Inequalities

Graph a system of linear inequalities to find the solutions of the system.

Use systems of linear inequalities to solve real-life problems

2

A2.7.A Solve systems of three equations with three variables.

3.6 Solving Systems of Linear Equations in Three Variables

Solve systems of linear equations in three variables.

2



Use linear systems in three variables to solve real-life problems.






Unit Name: Chapter 6 Polynomials and Polynomial Functions





6.1 Using Properties of Exponents

Use properties of exponents to evaluate and simplify expressions involving powers.

Use exponents to solve real-life problems.

2

A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. A2.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax3 + d as an example of higher order polynomials and solve related equations.

6.2 Evaluating and Graphing Polynomial Functions

Evaluate a polynomial function.

Graph a polynomial function.

2 In order to meet the PE, be sure to emphasize the description of the graphs.

A2.2.C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.

6.3 Adding, Subtracting and Multiplying Polynomials

Add, subtract, and multiply polynomials.

Use polynomial operations in real-life problems.

2

A2.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax3 + d as an example of higher order polynomials and solve related equations.

6.4 Factoring and Solving Polynomial Equations

Factor polynomial expressions.

Use factoring to solve polynomial equations.

Use polynomial equations to solve real-life problems.

2



Unit Name: Chapter 12 Probability and Statistics




A2.1.F Solve problems involving combinations and permutations.

12.1 The Fundamental Counting Principle and Permutations

Use the fundamental counting principle to count the number of ways an event can happen

Use permutations to count the number of ways an event can happen

12.2 Combinations and the Binomial Theorem

Use combinations to count the number of ways and event can happen.

3

A2.6.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).

12.3 An Introduction to Probability

Find theoretical and experimental probabilities.

12.4 Probability of Compound Events

Find probabilities of unions and intersections of two events.

Use complements to

3



find the probability of an event.



A2.6.B Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B. A2.6.C Compute permutations and combinations, and use the results to calculate probabilities.

12.5 Probability of Independent and Dependent Events

Find the probability of independent events

Find the probability of dependent events.

2

A.2.6.D Apply the binomial theorem to solve problems using probability.

12.6 Binomial Distributions

Find binomial probabilities and analyze binomial distributions.

2

A2.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

7.7 Statistics and Statistical Graphs

Use measures of central tendency and measures of dispersion to describe data sets.

12.7 Normal Distributions

Calculate probabilities using normal distributions.

Use normal distributions to approximate binomial distributions.

2

A2.6.G and A2.7.C Calculate and interpret margin of error and confidence intervals for

***MISSING!



population proportions.






Unit Name: Chapter 7 Powers, Roots, and Radicals





7.2 Properties of Rational Exponents

Use properties of rational exponents to evaluate and simplify expressions.

Use properties of rational exponents to solve real-life problems.

2

A2.5.A Construct new functions using the transformations f(x – h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s). ***The construction of new functions using transformations is missing for this PE.

7.3 Power Functions and Function Operations

Perform operations with functions including power functions.

Use power functions and function operations.

2 ***The construction of new functions using transformations is missing for this PE. While composition of functions is not a PE, this skill is needed for the Compass test at CBC.

In anticipation of A2.4.A Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

7.4 Inverse Functions

Find inverses of linear functions.

Find inverses of non-linear functions.

2

A2.5.B Plot points, sketch, and describe the

graphs of functions of the form f(x) = a (x − c) + d , and solve related equations.

7.5 Graphing Square Root and Cube Root Functions

Graph square root and cube root functions.

Use square root and cube root functions to find real-life quantities.

2





A2.5.B Plot points, sketch, and describe the

graphs of functions of the form f(x) = a (x − c) + d , and solve related equations.

7.6 Solving Radical Equations

Solve equations that contain radicals or rational exponents.

Use radical equations to solve real-life problems.

2

A2.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

7.7 Statistics and Statistical Graphs

Use measures of dispersion to describe data sets.

2






Unit Name: Chapter 8 Exponential and Logarithmic Functions




A2.4.C Solve exponential and logarithmic equations.

8.1 Exponential Growth

Graph exponential growth functions

Use exponential growth functions to model real-life situations

2

A2.4.C Solve exponential and logarithmic equations.

8.2 Exponential Decay

Graph exponential decay functions

Use exponential decay functions to model real-life situations

2

A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.

8.3 Using the Number e

Use the number e as the base of exponential functions.

Use the natural base e in real-life situations.

2


8.4 Logarithmic Functions

Evaluate logarithmic functions.

Graph logarithmic functions.

Use logarithmic functions to model real-life situations.

2


8.5 Properties of Logarithms

Use properties of logarithms.

Use properties of logarithms to solve real-life problems.

2






8.6 Solving Exponential and Logarithmic Equations

Solve exponential equations in real-life situations

Solve logarithmic equations in real-life situations

2


8.7 Modeling with Exponential and Power Functions

Model data with exponential functions.

Model data with power functions.

2






Unit Name: Chapter 9 Rational Equations and Functions




A2.1.E Solve problems that can be represented by inverse variations of the forms f(x) = (a/x) + b, f(x) = (a/x2) + b, and f(x) = a/(bx+c).

9.1 Inverse and Joint Variation

Write and use inverse variation models.

2


9.4 Multiplying and Dividing Rational Expressions

Multiply and divide rational expressions

Use rational expressions to model real-life quantities.

2


9.5 Addition, Subtraction, and Complex Fractions

Add and subtract rational expressions.

2 Complex fractions are not part of the PE.

A2.5.C Plot points, sketch, and describe the graphs of functions of the form f(x) = (a/x) + b, f(x) = (a/x2) + b, and f(x) = a/(bx+c), and solve related equations.

9.6 Solving Rational Equations

Solve rational equations.

Use rational equations to solve real-life problems.

2






Unit Name: Chapter 11 Sequences and Series




A2.7.B Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.

11.1 An Introduction to Sequences and Series

Use and write sequences.

Use summation notation to write series and find sums of series.

11.2 Arithmetic Sequences and Series

Write rules for arithmetic sequences and find sums of arithmetic series.

11.3 Geometric Sequences and Series

Write rules for geometric sequences and find sums of geometric series.

11.4 Infinite Geometric Series

Find sums of geometric series.

8






Unit Name: Trigonometric Ratios and Functions




***NOTE: While this chapter does not meet any State PE’s, the committee felt it needed to be included in preparation for Pre-Calculus.

13.1 Right Triangle Trigonometry

Use trigonometric relationships to evaluate trigonometric functions of acute angles.

Use trigonometric functions to solve real-life problems.

2

13.2 General Angles and Radian Measure

Measure angles in standard position using degree measure and radian measure.

Calculate arc lengths and areas of sectors.

2

13.3 Trigonometric Functions of Any Angle

Evaluate trigonometric functions of any angle.

Use trigonometric functions to solve real-life problems.

2

13.4 Inverse Trigonometric Functions

2



Evaluate inverse trigonometric functions.

Use inverse trigonometric functions to solve real-life problems.

13.5 The Law of Sines

Use the law of sines to find the sides and angles of a triangle.

Find the area of any triangle.

2

13.6 The Law of Cosines

Use the law of cosines to find the sides and angles of a triangle.

Use Heron’s formula to find the area of a triangle.

2


Process Standards Addressed:


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