NYS Performance Indicators  Objectives  Text Resources  Resources (Suggested Activities)  CrossCurriculum Connections  Assessment Items  


Chapter 1  

Perform arithmetic operations with polynomial expressions containing rational coefficients. 
13, 15 


Solve absolute value equations and inequalities involving linear expressions in one variable. 
14, 31 


Factor polynomial expressions completely, using any combination of the following techniques: • common factor • extraction • difference of two perfect squares quadratic trinomials 
16 


Solve quadratic inequalities in one variable, algebraically and graphically 
18 


Chapter 2  

Perform arithmetic operations with polynomial expressions containing rational coefficients 
22, 23, 24 


Perform arithmetic operations with rational expressions and rename to lowest terms 
22, 23, 24 


Simplify complex fractional expressions 
26 


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. 
27 


Solve rational equations and inequalities 
27, 28 


Chapter 3  

Simplify radical expressions 
33 


Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form 
33, 34, 35, 36 


Perform arithmetic operations on irrational expressions 
33, 34, 35, 36 


Rationalize a denominator containing a radical expression 
37 


Rationalize denominators involving algebraic radical expressions 
37 


Solve radical equations 
38 


Chapter 4  

Determine the domain and range of a function from its graph 
41 


Identify relations and functions, using graphs 
41 


Define a relation and function 
41 


Determine when a relation is a function 
41 


Determine the domain and range of a function from its equation 
41 


Determine if a function is onetoone, onto, or both 
41, 43 


Write functions in functional notation 
42 


Use functional notation to evaluate functions for given values in the domain 
42 


Use direct and inverse variation to solve for unknown values 
43, 410 


Find the composition of functions 
47 


Define the inverse of a function 
48 


Determine the inverse of a function and use composition to justify the result 
48 


Determine the centerradius form for the equation of a circle in standard form 
49 


Write the equation of a circle, given its center and a point on the circle 
49 


Write the equation of a circle from its graph 
49 


Chapter 5  

Know and apply the technique of completing the square 
51 


Solve quadratic equations, using the quadratic formula 
52 


Use the discriminant to determine the nature of the roots of a quadratic equation 
53 


Write square roots of negative numbers in terms of i. 
54 


Simplify powers of i. 
54 


Perform arithmetic operations on complex numbers and write the answer in the form a + bi Note: This includes simplifying expressions with complex denominators. 
54, 55 


Determine the conjugate of a complex number 
55 


Determine the sum and product of the roots of a quadratic equation by examining its coefficients 
57 


Determine the quadratic equation, given the sum and product of its roots 
57 


Chapter 6  

Know and apply sigma notation 
63 


Represent the sum of a series, using sigma notation 
63 


Chapter 7  

Evaluate exponential expressions, including those with base e 
71, 72, 73, 74, 77 


Rewrite algebraic expressions that contain negative exponents using only positive exponents 
72 


Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents 
72, 73 


Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers) 
72, 73 


Rewrite algebraic expressions with fractional exponents as radical expressions 
73 


Rewrite algebraic expressions in radical form as expressions with fractional 
73 


Graph exponential functions of the form y = b^{x} for positive values of b, including b = e 
74 


Solve exponential equations with and without common bases 
76 


Solve an application which results in an exponential function 
77 


Chapter 8  

Solve a logarithmic equation by rewriting as an exponential equation 
82, 87 


Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms 
83 


Evaluate logarithmic expressions in any base 
83, 84, 86 


Chapter 9  

Express and apply the six trigonometric functions as ratios of the sides of a right triangle 
91, 95 


Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles 
91, 92, 93, 94 


Sketch the unit circle and represent angles in standard position 
93, 94, 95, 96, 97, 98 


Find the value of trigonometric functions, if given a point on the terminal side of angle Θ 
93, 94, 95, 96 


Sketch and use the reference angle for angles in standard position 
94 


Know and apply the reciprocal relationships between trigonometric ratios 
95 


Use the reciprocal relationships to find the value of the secant, cosecant, and cotangent of 0°, 30°, 45°, 60°, 90°, 180°, and 270° angles. 
96 


Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent 
97 


Determine the trigonometric functions of any angle, using technology 
97, 98 


Chapter 10  

Determine the length of an arc of a circle, given its radius and the measure of its central angle 
101 


Convert between radian and degree measures 
101, 102 


Determine the trigonometric functions of any angle, using technology 
102 


Justify the Pythagorean identities 
103 


Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function 
105 


Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent 
105 


Chapter 11  

Sketch and recognize one cycle of a function of the form y = A sin Bx or y = A cos Bx 
111, 112, 113, 114, 118 


Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function 
113, 114 


Write the trigonometric function that is represented by a given periodic graph 
114 


Sketch the graph of the inverse of the sine, cosine, and tangent functions 
117 


Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function 
117 


Chapter 12  

Apply the angle sum and difference formulas for trigonometric functions 
123, 124, 125, 126 


Chapter 13  

Solve first degree trigonometric equations for all values of the variable from 0° to 360° 
131 


Chapter 14  

Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines 
142, 143, 


Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle 
144, 145 


Determine the solution(s) from the SSA situation (ambiguous case) 
146 


Chapter 15  

Calculate measures of central tendency with group frequency distributions 
152, 153 


Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations 
152, 153, 154, 155 


Know and apply the characteristics of the normal distribution 
156 