Last updated: 1/27/2014
Niagara Falls City School District
630 66th Street, Niagara Falls, NY 14304


Mathematics - Grades 9-12 - Algebra 2/Trigonometry (Non-Regents) 2005 Edition 10, 20, 30, 40 Weeks

Chapter 1
(2) MST3.A2.N.3 Students perform arithmetic operations with polynomial expressions containing rational coefficients.
Perform arithmetic operations with polynomial expressions containing rational coefficients.

1-3, 1-5

(1) MST3.A2.A.1 Students solve absolute value equations and inequalities involving linear expressions in one variable.
Solve absolute value equations and inequalities involving linear expressions in one variable.

1-4, 3-1

(1) MST3.A2.A.7 Students factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials.
Factor polynomial expressions completely, using any combination of the following techniques:
•  common factor
•  extraction
•  difference of two perfect squares quadratic trinomials

1-6

(1) MST3.A2.A.4 Students solve quadratic inequalities in one and two variables, algebraically and graphically.
Solve quadratic inequalities in one variable, algebraically and graphically

1-8

Chapter 2
(2) MST3.A2.N.3 Students perform arithmetic operations with polynomial expressions containing rational coefficients.
Perform arithmetic operations with polynomial expressions containing rational coefficients

2-2, 2-3, 2-4

(1) MST3.A2.A.16 Students perform arithmetic operations with rational expressions and rename to lowest terms.
Perform arithmetic operations with rational expressions and rename to lowest terms

2-2, 2-3, 2-4

(1) MST3.A2.A.17 Students simplify complex fractional expressions.
Simplify complex fractional expressions

2-6

(1) MST3.A2.A.3 Students solve systems of equations involving one linear equation and one quadratic equation algebraically. Note: This includes rational equations that result in linear equations with extraneous roots.
Solve systems of equations involving one linear equation and one quadratic equation algebraically.  Note:  This includes rational equations that result in linear equations with extraneous roots. 

2-7

(1) MST3.A2.A.23 Students solve rational equations and inequalities.
Solve rational equations and inequalities

2-7, 2-8

Chapter 3
(1) MST3.A2.A.13 Students simplify radical expressions.
Simplify radical expressions

3-3

(1) MST3.A2.N.2 Students perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form.
Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form

3-3, 3-4, 3-5, 3-6

(1) MST3.A2.N.4 Students perform arithmetic operations on irrational expressions.
Perform arithmetic operations on irrational expressions

3-3, 3-4, 3-5, 3-6

(1) MST3.A2.N.5 Students rationalize a denominator containing a radical expression.
Rationalize a denominator containing a radical expression

3-7

(1) MST3.A2.A.15 Students rationalize denominators involving algebraic radical expressions.
Rationalize denominators involving algebraic radical expressions

3-7

(1) MST3.A2.A.22 Students solve radical equations.
Solve radical equations

3-8

Chapter 4
(1) MST3.A2.A.51 Students determine the domain and range of a function from its graph.
Determine the domain and range of a function from its graph

4-1

(1) MST3.A2.A.52 Students identify relations and functions, using graphs.
Identify relations and functions, using graphs

4-1

(1) MST3.A2.A.37 Students define a relation and function.
Define a relation and function

4-1

(1) MST3.A2.A.38 Students determine when a relation is a function.
Determine when a relation is a function

4-1

(1) MST3.A2.A.39 Students determine the domain and range of a function from its equation.
Determine the domain and range of a function from its equation

4-1

(1) MST3.A2.A.43 Students determine if a function is one-to-one, onto, or both.
Determine if a function is one-to-one, onto, or both

4-1, 4-3

(1) MST3.A2.A.40 Students write functions in functional notation.
Write functions in functional notation

4-2

(1) MST3.A2.A.41 Students use functional notation to evaluate functions for given values in the domain.
Use functional notation to evaluate functions for given values in the domain

4-2

(1) MST3.A2.A.5 Students use direct and inverse variation to solve for unknown values.
Use direct and inverse variation to solve for unknown values

4-3, 4-10

(1) MST3.A2.A.42 Students find the composite of functions.
Find the composition of functions

4-7

(1) MST3.A2.A.44 Students define the inverse of a function.
Define the inverse of a function

4-8

(1) MST3.A2.A.45 Students determine the inverse of a function and use composition to justify the result.
Determine the inverse of a function and use composition to justify the result

4-8

(1) MST3.A2.A.47 Students determine the center-radius form for the equation of a circle in standard form.
Determine the center-radius form for the equation of a circle in standard form

4-9

(1) MST3.A2.A.48 Students write the equation of a circle, given its center and a point on the circle.
Write the equation of a circle, given its center and a point on the circle

4-9

(1) MST3.A2.A.49 Students write the equation of a circle from its graph.
Write the equation of a circle from its graph

4-9

Chapter 5
(1) MST3.A2.A.24 Students know and apply the technique of completing the square.
Know and apply the technique of completing the square

5-1

(1) MST3.A2.A.25 Students solve quadratic equations, using the quadratic formula.
Solve quadratic equations, using the quadratic formula

5-2

(1) MST3.A2.A.2 Students use the discriminant to determine the nature of the roots of a quadratic equation.
Use the discriminant to determine the nature of the roots of a quadratic equation

5-3

(1) MST3.A2.N.6 Students write square roots of negative numbers in terms of i.
Write square roots of negative numbers in terms of i.

5-4

(1) MST3.A2.N.7 Students simplify powers of i.
Simplify powers of i.

5-4 

(1) MST3.A2.N.9 Students perform arithmetic operations on complex numbers and write the answer in the form of a + bi. Note: This includes simplifying expressions with complex denominators.
Perform arithmetic operations on complex numbers and write the answer in the form a + bi
Note:  This includes simplifying expressions with complex denominators.

5-4, 5-5

(1) MST3.A2.N.8 Students determine the conjugate of a complex number.
Determine the conjugate of a complex number

5-5

(1) MST3.A2.A.20 Students determine the sum and product of the roots of a quadratic equation by examining its coefficients.
Determine the sum and product of the roots of a quadratic equation by examining its coefficients

5-7

(1) MST3.A2.A.21 Students determine the quadratic equation, given the sum and product of its roots.
Determine the quadratic equation, given the sum and product of its roots

5-7

Chapter 6
(1) MST3.A2.N.10 Students know and apply sigma notation.
Know and apply sigma notation

6-3

(1) MST3.A2.A.34 Students represent the sum of a series, using sigma notation.
Represent the sum of a series, using sigma notation

6-3

Chapter 7
(1) MST3.A2.A.12 Students evaluate exponential expressions, including those with base e.
Evaluate exponential expressions, including those with base e

7-1, 7-2, 7-3, 7-4, 7-7

(1) MST3.A2.A.9 Students rewrite algebraic expressions that contain negative exponents using only positive exponents.
Rewrite algebraic expressions that contain negative exponents using only positive exponents

7-2

(1) MST3.A2.A.8 Students apply the rules of exponents to simplify expressions involving negative and/or fractional exponents.
Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents

7-2, 7-3

(1) MST3.A2.N.1 Students evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers).
Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers)

7-2, 7-3

(1) MST3.A2.A.10 Students rewrite algebraic expressions with fractional exponents as radical expressions.
Rewrite algebraic expressions with fractional exponents as radical expressions

7-3

(1) MST3.A2.A.11 Students rewrite algebraic expressions in radical form as expressions with fractional exponents.
Rewrite algebraic expressions in radical form as expressions with fractional

7-3

(1) MST3.A2.A.53 Students graph exponential functions of the form y = bx for positive values of b, including b=e.
Graph exponential functions of the form y bx for positive values of b, including b = e 

7-4

(1) MST3.A2.A.27 Students solve exponential equations with and without common bases.
Solve exponential equations with and without common bases

7-6

(1) MST3.A2.A.6 Students solve an application which results in an exponential function.
Solve an application which results in an exponential function

7-7

Chapter 8
(1) MST3.A2.A.28 Students solve a logarithmic equation by rewriting as an exponential equation.
Solve a logarithmic equation by rewriting as an exponential equation

8-2, 8-7

(1) MST3.A2.A.19 Students apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms.
Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms

8-3

(1) MST3.A2.A.18 Students evaluate logarithmic expressions in any base.
Evaluate logarithmic expressions in any base

8-3, 8-4, 8-6

Chapter 9
(1) MST3.A2.A.55 Students express and apply the six trigonometric functions as ratios of the sides of a right triangle.
Express and apply the six trigonometric functions as ratios of the sides of a right triangle

9-1, 9-5

(1) MST3.A2.A.56 Students know the exact and approximate values of the sine, cosine, and tangent of 0°, 30°, 45°, 60°, 90°, 180°, and 270° angles.
Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º,  45º, 60º, 90º, 180º, and 270º angles 

9-1, 9-2, 9-3, 9-4

(1) MST3.A2.A.60 Students sketch the unit circle and represent angles in standard position.
Sketch the unit circle and represent angles in standard position

9-3, 9-4, 9-5, 9-6, 9-7, 9-8

(1) MST3.A2.A.62 Students find the value of trigonometric functions, if given a point on the terminal side of angle Θ.
Find the value of trigonometric functions, if given a point on the terminal side of angle Θ

9-3, 9-4, 9-5, 9-6

(1) MST3.A2.A.57 Students sketch and use the reference angle for angles in standard position.
Sketch and use the reference angle for angles in standard position

9-4

(1) MST3.A2.A.58 Students know and apply the co-function and reciprocal relationships between trigonometric ratios.
Know and apply the reciprocal relationships between trigonometric ratios

9-5

(1) MST3.A2.A.59 Students use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0°, 30°, 45°, 60°, 90°, 180°, and 270° angles.
Use the reciprocal relationships to find the value of the secant, cosecant, and cotangent of 0°, 30°, 45°, 60°, 90°, 180°, and 270° angles.

9-6

(2) MST3.A2.A.64 Students use inverse functions to find the measure of an angle, given its sine, cosine, or tangent.
Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent

9-7

(2) MST3.A2.A.66 Students determine the trigonometric functions of any angle, using technology.
Determine the trigonometric functions of any angle, using technology

9-7, 9-8

Chapter 10
(1) MST3.A2.A.61 Students determine the length of an arc of a circle, given its radius and the measure of its central angle.
Determine the length of an arc of a circle, given its radius and the measure of its central angle

10-1

(1) MST3.A2.M.2 Students convert between radian and degree measures.
Convert between radian and degree measures

10-1, 10-2

(2) MST3.A2.A.66 Students determine the trigonometric functions of any angle, using technology.
Determine the trigonometric functions of any angle, using technology

10-2

(1) MST3.A2.A.67 Students justify the Pythagorean identities.
Justify the Pythagorean identities

10-3

(2) MST3.A2.A.63 Students restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function.
Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function

10-5

(2) MST3.A2.A.64 Students use inverse functions to find the measure of an angle, given its sine, cosine, or tangent.
Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent

10-5

Chapter 11
(1) MST3.A2.A.70 Students sketch and recognize one cycle of a function of the form y = Asin Bx or y = Acos Bx.
Sketch and recognize one cycle of a function of the form y = A sin Bx or y = A cos Bx

11-1, 11-2, 11-3, 11-4, 11-8

(1) MST3.A2.A.69 Students determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function.
Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function

11-3, 11-4

(1) MST3.A2.A.72 Students write the trigonometric function that is represented by a given periodic graph.
Write the trigonometric function that is represented by a given periodic graph

11-4

(1) MST3.A2.A.65 Students sketch the graph of the inverse of the sine, cosine, and tangent functions.
Sketch the graph of the inverse of the sine, cosine, and tangent functions

11-7

(2) MST3.A2.A.63 Students restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function.
Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function

11-7

Chapter 12
(1) MST3.A2.A.76 Students apply the angle sum and difference formulas for trigonometric functions.
Apply the angle sum and difference formulas for trigonometric functions

12-3, 12-4, 12-5, 12-6

Chapter 13
(1) MST3.A2.A.68 Students solve trigonometric equations for all values of the variable from 0° to 360°.
Solve first degree trigonometric equations for all values of the variable from 0° to 360°

13-1

Chapter 14
(1) MST3.A2.A.73 Students solve for an unknown side or angle, using the Law of Sines or the Law of Cosines.
Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines

    14-2, 14-3,
14-4, 14-5, 14-6

(1) MST3.A2.A.74 Students determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle.
Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle

14-4, 14-5

(1) MST3.A2.A.75 Students determine the solution(s) from the SSA situation (ambiguous case).
Determine the solution(s) from the SSA situation (ambiguous case)

14-6

Chapter 15
(1) MST3.A2.S.3 Students calculate measures of central tendency with group frequency distributions.
Calculate measures of central tendency with group frequency distributions

15-2, 15-3

(1) MST3.A2.S.4 Students calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations.
Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations

15-2, 15-3, 15-4, 15-5

(1) MST3.A2.S.5 Students know and apply the characteristics of the normal distribution.
Know and apply the characteristics of the normal distribution

15-6

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