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Note for teachers: The pacing below is a general guideline on how much time you need to spend on each unit.. Feel free to adjust according to your students needs. We chose to start with review units: Equations and Linear Functions and then move to Trig. since it is a new and interesting topic that will capture student interest and attention at the start of the school year. However, you may choose to move the units around as it serves you best. Make sure you refer to the Performance Indicators as you go along. The primary text is Algebra 2 by Pearson.Refer to http://www.jmap.org and http://emathinstruction.com for additional practice
Pacing Unit/Essential Questions
Essential Knowledge- Content/Performance Indicators
(What students must learn)
Essential Skills(What students will be able to do)
Vocabulary Resources
Pearson Algebra 2
Sept 4-Sept 13
Unit 1: Equations and Inequalities
How do you solve absolute value equation/inequality and plot on the number line?
A2.A.1 Solve absolute value equations and inequalities involving linear expressions in one variable
Review of Algebra TopicsStudent will be able to
- simplify expressions- write and evaluate algebraic
expressions- represent mathematical phrases and
real world quantities using algebraic expressions
- solve multi step equations and check
- distinguish between solution, no solution and identity
- solve literal equations- solve multi step inequalities and
graph them- write inequality from a sentence
using key word at least, at most, fewer, less, more …
Algebra 2 and Trig. TopicsStudents will be able to
- solve absolute value equations and check
- solve absolute value inequalities and check for extraneous solution
- distinguish between an “and” problem and an “or” problem and accordingly write the solution
Term Constant
term Like terms Coefficient Expression Equation Literal
Equation Inequality Absolute
Value Extraneous
solution
1-3: Algebraic Expressions
1-4: Solving equations.Supplement with additional worksheets on equations with fractional coefficients
1-5: Solving Inequalities
1-6 Absolute Value Equations and inequalities
CURRICULUM MAP: ALGEBRA 2 and TRIG.RCSD- Department of Mathematics
2013 - 2014
Sept16-Sept 27
Unit 2: Linear Equations and Functions
How do you distinguish between Direct and Inverse variation?
How do you distinguish between a relation and a function?
How do you find the domain and range of a function?
How do you transformation with functions?
A2.A.5 Use direct and inverse variation to solve for unknown values
A2.A.37 Define a relation and function
A2.A.38 Determine when a relation is a function
A2.A.39 Determine the domain and range of a function from its equation
A2.A.40 Write functions in functional notation
A2.A.41 Use functional notation to evaluate functions for given values in the domain
A2.A.46 Perform transformations with functions and relations:f(x + a) , f(x) + a, f(−x), − f(x), af(x)
A2.A.52 Identify relations and functions, using graphs
A2.S.8 Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship
Review of Algebra TopicsStudent will be able to
- Determine if a function is linear- Graph a linear function
with/without a calculator.- Find the Slope of a linear function
given an equation, graph or 2 points
- Find the equation for a linear function given two points or a point and a graph.
- Draw a scatter plot and find the line of best fit
Algebra 2 and Trig. TopicsStudent will be able to
- Distinguish between a relation and a function.
- Determine if a relation is a function given a set of ordered pair, mapping diagram, graph or table of values
- Distinguish between direct and indirect variation
- Determine if a given function is direct given a function rule, graph or table of values
- Solve word problems related to direct and indirect variation (ref. to regents questions from jmap.org)
- Distinguish between parallel and perpendicular lines.
- Do linear regression using a graphing calculator
- Determine the correlation between the data sets by viewing or plotting a scatter-plot.
- Perform vertical and horizontal translations
- Graph absolute value equations and perform related translations
Relation Function Vertical line
test Function Rule Function
notation Domain Range Direct
Variation Constant of
Variation Linear
function Linear
equation x-intercept y-intercept Slope Standard
form of linear function
Slope intercept form of linear function
Point slope form of linear function
Line of best fit
Scatter plot Correlation Correlation
coefficient Regression Absolute
value
Overview of Chapter 2 with special emphasis on transformation.
2-1 Relations and Functions2-2 Direct Variation (Review) Inverse Variation will be covered later
2-5 Using Linear Models (emphasize use of graphing calculator to get regression line)
2-6 Families of Functions(transformations of functions)
Sep 30– Oct 11
Unit 3: Intro to Trig
What are the six trigonometric ratios in relation to right triangles?
What is the unit circle and how is it used in trigonometry?
How do we find the values of the six trigonometric functions?
What is radian measure and how do we convert between radians and degrees?
A2.A.55 Express and apply the six trigonometric functions as ratios of the sides of a right triangle
A2.A.56 Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
A2.A.57 Sketch and use the reference angle for angles in standard position
A2.A.58 Know and apply the co-function and reciprocal relationships between trigonometric ratios
A2.A.59 Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
A2.A.60 Sketch the unit circle and represent angles in standard position
A2.A.61 Determine the length of an arc of a circle, given its radius and the measure of its central angle
A2.A.62 Find the value of trigonometric functions, if given a point on the terminal side of angle θ
A2.A.64 Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent
A2.A.66 Determine the trigonometric functions of any angle, using technology
A2.M.1 Define radian measure
A2.M.2 Convert between radian and degree measures
Students will be able to
- Find missing angle using inverse trig functions
- Understand the concept of the unit circle and its relation to trigonometry
- Sketch a given angle on the unit circle
- Find both negative and positive coterminal angles
- Find the sine and cosine of an angle on the unit circle
- Distinguish between exact and approximate values of trig. functions
- Find the exact value of a sine/cosine function
- Convert between radians and degrees
- Find the length of the intercepted arc
- Find the value of trig. function given a point on the unit circle
- Find the terminal point on the unit circle given a trig. angle.
Trig. Ratios Inverse
Trig functions
Unit Circle Standard
side Initial side Terminal
side Coterminal
angle Exact value Central
angle Intercepted
arc Radian
14-3 Right triangles and Trig Ratios
13-2 Angles and Unit Circle
13-3 Radian measure
Oct15-Nov 1
Unit 4 Trig Functions and Graphing
What are the characteristics of the graphs of the trigonometric functions?
How do you write a trigonometric equation represented by a graph?
How do you sketch the graphs of the six trigonometric functions?
A2.A.63 Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function
A2.A.65 Sketch the graph of the inverses of the sine, cosine, and tangent functions
A2.A.69 Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function
A2.A.70 Sketch and recognize one cycle of a function of theform y = Asin Bx or y = Acos Bx
A2.A.71 Sketch and recognize the graphs of the functions y = sec(x) , y = csc(x), y = tan(x), and y = cot(x)
A2.A.72 Write the trigonometric function that is represented by a given periodic graph
Students will be able to
- Find the amplitude, frequency, period and phase shift of a sine curve given its equation or graph
- Find the amplitude, frequency, period and phase shift of a cosine curve given its equation or graph
- Graph a sine or cosine curve given its equation
- Write the trig. Function given its graph
- Recognize and sketch the inverse trig. Functions (know its domain and range).
- Recognize and sketch the reciprocal trig. Functions (know its domain and range)
- Graph all trig function with a graphing calculator
- Solve trig. functions graphically using a graphing calculator by finding the points of intersection
Periodic function
Cycle Period Amplitude Frequency Phase shift Domain Range Sine curve Cosine
curve
13-1 Exploring Periodic Functions
13-4 The Sine Function
13-5 The Cosine Function
13-6 the Tangent Function
13-7 Translating Sine and cosine Function
13-8 Reciprocal Trigonometric Functions
Nov 4 –Nov 26
Unit 5: Quadratic Equations and functions
How do you perform transformations of functions?
How do you factor completely all types of quadratic expressions?
How do you use the calculator to find appropriate regression formulas?
How do you use imaginary numbers to find square roots of negative numbers?
How do you solve quadratic equations using a variety of techniques?
How do you determine the kinds of roots a quadratic will have from its equation?
How do you find the solution set for quadratic inequalities?
How do you solve systems of linear and quadratic equations graphically and algebraically?
A2.A.46 Perform transformations with functions and relations:f (x + a) , f(x)+ a, f (−x), − f (x), af (x)
A2.A.40 Write functions in functional notation
A2.A.39 Determine the domain and range of a function from itsequation
A2.A.7 Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials
A2.S.7 Determine the function for theregression model, using appropriate technology, and use the regression function to interpolate and extrapolate from the data
A2.A.20 Determine the sum and product of the roots of a quadratic equation by examining its coefficients
A2.A.21 Determine the quadraticequation, given the sum and product of its roots
A2.A.13 Simplify radical expressions
A2.A.24 Know and apply thetechnique of completing the square
A2.A.25 Solve quadratic equations, using the quadratic formula
A2.A.2 Use the discriminant to determine the nature of the roots of a quadratic equation
A2.A.4 Solve quadratic inequalities in one and two variables, algebraically and
Students will be able to
- perform horizontal and vertical translations of the graph of y = x2
- graph a quadratic in vertex form: f(x) =a(x - h)2 + k
- identify and label the vertex as ( h , k )
- identify and label the axis of symmetry of a parabola
- graph parabolas in the form of y = a x2 with various values of a
- graph a quadratic in vertex form:- f(x) = ax2+bx+c- find the axis of symmetry
algebraically using the standard form of the equation
- identify the y-intercept as ( 0, c )- find the vertex of a parabola
algebraically using the standard form of the equation
- identify the range of parabolas- sketch a graph of a parabola after
finding the axis of symmetry, the vertex, and the y-intercept
- use the calculator to find a quadratic regression equation
- factor using “FOIL” - finding a GCF- perfect square trinomials- difference of two squares- zero product property- finding the sum and product of
roots- writing equations knowing the
roots or knowing the sum and product of the roots
- solve by taking square roots- solve by completing the square- solve by using the quadratic
formula- use the discriminant to find the
nature of the roots- simplify expressions containing
complex numbers (include rationalizing the denominator)
Parabola Quadratic
function Vertex form Axis of
symmetry Vertex of
the parabola Maximum Minimum Standard
form Domain and
Range Regressions Factoring Greatest
Common Factor
Perfect square trinomial
Difference of two squares
Zero of a function (root)
Discriminant
Imaginary numbers
Complex numbers
Conjugates
4-1 Quadratic functions and transformations
4-2 Standard form of a quadratic function
4-3 Modeling with quadratic functions
4-4 Factoring quadratic expressions
4-5 Quadratic equations
4-6 Completing the square
4-7 Quadratic Formula
4-8 Complex Numbers
Additional resources atwww.emathinstruction.com
Quadratic Inequalities Page 256-257
Powers of complex numbers Page 265
4-9 Quadratic Systems
10-3 Circles
graphically
A2.A.3 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.
A2.N6 Write square roots of negative numbers in terms of i
A2.N7 Simplify powers of i
A2.N8 Determine the conjugate of a complex number
A2.N9 Perform arithmetic operations on complex numbers and write the answer in the form a+bi
A2.A47 Determine the equation of a circle
A2.A48 Write the equation of a circle given a point
A2.A49 Write the equation of a circle from its graph
- solve quadratic inequalities- solve systems of quadratics
algebraically- Determine the equation of a circle
given the center and the radius, a point and the radius, the center and a point
- Determine the equation of a circle in center-radius form by completing the square of the equation in standard form
Dec 2– Dec 20
Unit 6: Polynomials
How do you perform arithmetic operations with polynomial expressions?
How do you factor polynomials?
How do you solve polynomial equation?
How do you expand a polynomial to the nth
Order?
How do you find the nth term of a binomial expansion?
A2.N.3 Perform arithmetic operations with polynomial expressions containing rational coefficients
A2.A.7 Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials
A2.A.26 Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula
A2.A.50 Approximate the solution to polynomial equations of higher degree by inspecting the graph
A2.A.36 Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion
Student will be able to
- combine like terms- subtract polynomial expressions- multiply monomials, binomials and
trinomials- recognize and classify polynomials- factor polynomials using common
factor extraction, difference of two perfect squares and or trinomial factoring.
- Write a polynomial function given its roots.
- Solve polynomial equations /find the roots graphically.
- Divide polynomials by factoring, long division or synthetic division
- Apply the Binomial Theorem to expand a binomial expression
- Find a specific term of a binomial expansion.
Polynomial Monomial Binomial Trinomial Degree Root Solution Zero
Property
5-1 Polynomial Functions
5-2 Polynomials, Linear Factors and Zeros
5-3 Solving Polynomial Equations
5-4 Dividing Polynomials
5-7 The Binomial Theorem
Jan 6– Jan 16
Unit 7: Radical Functions, Rational Exponents, Function Operations
How do you write algebraic expressions in simplest radical form?
How do you simplify by rationalizing the denominator?
How do you express sums and differences of radical expressions in simplest form?
How do you write radicals with fractional exponents?
How do you change an expression with a fractional exponent into a radical expression?
How do you solve radical equations?
How do you add, subtract, multiply, and divide functions?
How do you perform composition of functions?
How do you find the inverse of a function?
How do you determine if a
A2.N.1 Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers
A2.N.2 Perform arithmetic operations with expressions containing irrational numbers in radical form
A2.N.4 Perform arithmetic operations on irrational expressions
A2.A.8 Use rules of exponents to simplify expressions involving negative and/or rational exponents
A2.A.9 Rewrite expressions that contain negative exponents using only positive exponents
A2.A.10 Rewrite algebraic expressions with fractional exponents as radical expressions
A2.A.11 Rewrite radical expressions as algebraic expressions with fractional exponents
A2.A.12 Evaluate exponential expressions
A2.A.13 Simplify radical expressions
A2.A.14 Perform basic operations on radical expressions
A2.N.5 Rationalize a denominator containing a radical expression
A2.A.15 Rationalize denominators of algebraic radical expressions
A2.A.22 Solve radical equations
A2.A.40 Write functions using function notation
Review of Algebra TopicsStudent will be able to
- Use rules of positive and negative exponents in algebraic computations
- Use squares and cubes of numbers- Know square roots of perfect
squares from 1-15
Algebra 2 and Trig TopicsStudents will be able to
- Simplify radical expressions- Multiply and divide radical
expressions- Add and subtract radical
expressions- Use rational exponents - Solve radical equations and check
for extraneous roots- Add, subtract, multiply, and divide
functions- Find composition of functions- Find inverses of functions- Determine if a function is one to
one or onto or both
Exponents Conjugates Radicals Rationalize
the denominator
Extraneous roots
f- 1(x) inverse of a
function one to one onto
Page 360 Properties of exponents
6-1 Simplify radical expressions
6-2 Multiply and divide radical expressions
6-3 Binomial Radical Expressions
6-4 Rational Exponents
6-5 Solve radical equations
6-6 Function operations
6-7 Inverse relations and functions
(the text does not cover “onto” so this will have to be supplemented with Ch 4-1 of AMSCO)
function is 1 to 1 or onto? A2.A.41 Use function notation to
evaluate functions for given values in the domain
A2.A.42 Find the composition of functions
A2.A.43 Determine if a function is 1 to 1, onto, or both
A2.A.44 Define the inverse of a function
A2.A.45 Determine the inverse of a function and use composition to justify the result
Jan 21th – Jan 24th MIDTERM REVIEW
Feb 3 - Feb14
Unit 8:Exponential and Logarithmic Functions
How do you model a quantity that changes regularly over time by the same percentage?
How are exponents and logarithms related?
How are exponential functions and logarithmic functions related?
Which type of function models the data best?
A2.A.6 Solve an application with results in an exponential function.
A2.A.12 Evaluate exponential expressions, including those with base e. A2.A.53 Graph exponential functions of the form. for positive values of b, including b = e.
A2.A.18 Evaluate logarithmic expressions in any base
A2.A.54 Graph logarithmic functions, using the inverse of the related exponential function.
A2.A.51 Determine the domain and range of a function from its graph.
A2.A.19 Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms.
A2.A. 27 Solve exponential equations with and without common bases.
A2.A. 28 Solve a logarithmic equations by rewriting as an exponential equation.
A2.S.6 Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate.
Students will be able to:
- model exponential growth and decay
- explore the properties of functions of the form
- graph exponential functions that have base e
- write and evaluate logarithmic expressions
- graph logarithmic functions- derive and use the properties of
logarithms to simplify and expand logarithms.
- solve exponential and logarithmic equations
- evaluate and simplify natural logarithmic expressions
- solve equations using natural logarithms
asymptote change of
base formula
common logarithm
exponential equation
exponential function
exponential decay
exponential growth
logarithm logarithmic
equation logarithmic
function natural
logarithmic function
7 -1 Exploring Exponential Models
7 - 2 Properties of Exponential functions
7 – 3 Logarithmic Functions as Inverses
- Fitting Curves to Data Page 459
7 - 4 Properties of Logarithms
7 - 5 Exponential and Logarithmic Equations
7 - 6 Natural Logarithms
NOTE- the text only does problems compounding interest continuously. You will need to supplement to do problems that compound quarterly, monthly, etc.)Ch 7-7 AMSCO
Feb 24 – March 7
Unit 9: Rational Expressions and Functions
How do we perform arithmetic operations on rational expressions?
How do we simplify a complex fraction?
How do we solve a rational equation?
A2.A.5 Use direct and inverse variation
A2.A.16 Perform arithmetic operations with rational expressions and rename to lowest terms
A2.A.17 Simplify complex fractional expressions
A2.A.23 Solve rational equations and inequalities
Review of Algebra TopicsAll topics in this unit except complex fractions are taught in Integrated Algebra. In Algebra most problems involve monomials and simple polynomials. In Algebra 2 factoring becomes more complex and may require more than one step to factor completely.
Algebra 2 TopicsStudents will be able to
- Identify from tables, graphs and models direct and inverse variation
- Solve algebraically and graph inverse variation
- Graph rational functions with vertical and horizontal asymptotes
- Simplify a rational expression to lowest terms by factoring and reducing
- State any restrictions on the variable
- Multiply and divide rational expressions
- Add and subtract rational expressions
- Simplify a complex fraction - Solve rational equations - Solve rational inequalities
Inverse Variation
Asymptotes Simplest
form Rational
Expression Common
factors Reciprocal Least
Common Multiple
Lowest Common Denominator
Common factors
Complex Fraction
Rational equation
8-1 Inverse Variation(omit combined and joint variation)
8-2 Reciprocal functions and transformations
8-3 Rational functions and their graphs
8-4 Rational Expressions
8-5 Adding and Subtracting Rational Expressions- includes simplifying complex fractions
8-6 Solving Rational Equations
NOTE: Teachers must supplement for solving rational inequalities(Ch. 2-8 of AMSCO)
March10 - March 28
Unit 10: Solving Trig Equations
How do you verify a trigonometric identity?
How do you solve trigonometric equations?
How do you use the trigonometric angle formulas to find values for trig functions?
A2.A.67 Justify the Pythagorean identities
A2.A.68 Solve trigonometric equations for all values of the variable from 0º to 360º
A2.A.59 Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
A2.A.76 Apply the angle sum and difference formulas for trigonometric functions
A2.A.77 Apply the double-angle and half-angle formulas for trigonometric functions
Students will be able to
- Identify reciprocal identities- Verify trig equations using trig
identities- Verify Pythagorean identities- Simplify trig expressions using
identities- Solve linear and quadratic trig
equations within the given domain- Verify an angle identity- Use the angle sum and difference
formulas to evaluate a trig expression or verify a trig. equation
- Use the angle double angle and half angle formulas to evaluate a trig expression or verify a trig. equation
Trig. Identities
Reciprocal Trig. Function
Pythagorean identities
Negative angle identity
Cofunction identity
Angle sum formula
Angle difference formula
Double angle formula
Half angle formula
14-1 Trigonometric Identities
14-6 Angle Identities
14-7 Double Angle and Half Angle Identities
14-2 Solving Trigonometric Equations
Ma r 31– April 11
Unit 11 Trig Applications (Laws)
How do you use the Law of Sines to find missing parts of oblique triangles?
How do you use the Law of Cosines to find missing parts of oblique triangles?
How do you use the trigonometry to find the area of oblique triangles?How many distinct triangles are possible given certain parts of oblique triangles?
A2.A.73 Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines
A2.A.74 Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle
A2.A.75 Determine the solution(s) from the SSA situation (ambiguous case)
Students will be able to
- Use the Law of Sines to find a missing angle or missing side
- Use the Law of Cosines to find a missing angle or missing side
- Find the area of a triangle or a parallelogram
- Find the possible number of triangles given an angle and two sides
- Apply the Law of Sines and Law of Cosines to word problems
Law of Sine
Law of Cosine
Oblique triangle
14-4 Area and the Law of Sines
14-5 The Law of Cosines
Page 927 The Ambiguous Case
April 21 – May 2
Unit 12: Probability
How do you calculate the probability of an event?
A2.S.9 Differentiate between situations requiring permutations and those requiring combinations
A2.S.10 Calculate the number of possible permutations (nPr) of n items taken r at a time
A2.S.11Calculate the number of possible combinations (nCr) of n items taken r at a time.
A2.S.12 Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event)
A2.S.13 Calculate theoretical probabilities, including geometric applications
A2.S.14 Calculate empirical probabilities
A2.S.15 Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most
Students will be able to
- Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event)
- Determine theoretical and experimental probabilities for events, including geometric applications
- Find the probability of the event A and B
- Find the probability of event A or B
- Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most
Permutation Combinatio
n Factorial Counting
Principle Event Outcome Sample
Space Theoretical
probability Experimenta
l Probability Dependent
events Independent
events Mutually
exclusive
11-1 Permutations and Combinations
11-2 Probability
11-3 Probability of Multiple Events
11-8 Binomial Distributions
You may wish to supplement the text using additional resources from www.emathinstruction.com
May 5-May16
Unit 13: Statistics
What methods are there for analyzing data?
A2.S.1 Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment)
A2.S.2 Determine factors which may affect the outcome of a survey
A2.S.3 Calculate measures of central tendency with group frequency distributions
A2.S.4 Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations
A2.S.5 Know and apply the characteristics of the normal distribution
A2.S.16 Use the normal distribution as an approximation for binomial probabilities
Students will be able to
- Calculate measures of central tendency given a frequency table
- Calculate measures of dispersion - (range, quartiles, interquartile
range, standard deviation, variance) for both samples and populations (standard deviation & variance using graphing calculator)
- Calculate probabilities using the normal distribution (use the normal curve given on the Algebra 2 reference sheet)
Survey Experiment Bias Sample Population Standard
deviation Variance Central
tendency Outlier Frequency
distribution Dispersion Quartiles Interquartile
range Binomial
probability Normal
Distribution
11-5 Analyzing Data
11-6 Standard Deviation
11-7 Samples and Surveys
11-9 Normal Distributions
P 741 Approximating a Binomial Distribution
May 19-May 30
Unit 14: Sequences and Series
What is the difference between arithmetic and a geometric sequence?
How do you find an explicit formula?
How do you write a recursive definition for a sequence?
How do you find the common difference and the nth term of an arithmetic sequence?How do you find the common ratio and the nth term of a geometric sequence?
How do you find the sum of a finite series using the formulas?
A2.A.29 Identify an arithmetic or geometric sequence and find the formula for its nth term
A2.A.30 Find the common difference in an arithmetic sequence
A2.A.31 Determine the common ratio of a geometric sequence
A2.A.32 Determine a specified term of an arithmetic or a geometric sequence
A2.A.33 Specify terms of a sequence given its recursive definition
A2.N.10 Know and apply sigma notation
A2.A.34 Represent the sum of a series using sigma notation
A2.A.35 Determine the sum of the first n terms of an arithmetic or a geometric series
Students will be able to
- Use patterns to find subsequent terms of a sequence
- Use explicit formulas to find terms of sequences
- Find a recursive definition for a sequence
- Find an explicit formula to define a sequence
- Tell whether a sequence is arithmetic, geometric, or neither
- Find the common difference of an arithmetic sequence
- Find the nth term of an arithmetic sequence
- Find the common ratio in a geometric sequence
- Find the nth term of a geometric sequence
- Find the sum of a finite arithmetic series
- Write a series using sigma notation- Find the sum of a finite geometric
series
Sequence Arithmetic
sequence Geometric
sequence Explicit
formula Recursive
definition Finite Series Sigma
notation
9-1 Mathematical patterns
9-2 Arithmetic Sequences
9-3 Geometric Sequence
9-4 Arithmetic Series
9-5 Geometric series
June 2nd – June 16th CATCH-UP, REVIEW AND FINALS
Algebra 2 Regents Exam Blueprint
There will be 39 questions on the Regents Examination in Algebra 2/Trigonometry. The percentage of total credits that will be aligned with each content strand.
1) Number Sense and Operations 6—10% 2) Algebra 70—75% 4) Measurement 2—5% 5) Probability and Statistics 13—17%
Question Types The Regents Examination in Algebra 2/Trigonometry will include the following types and numbers of questions:
27 Multiple choice (2 credits each) 8 two-credit open ended 3 four-credit open ended 1 six-credit open ended
Calculators Schools must make a graphing calculator available for the exclusive use of each student while that student takes the Regents Examination in Algebra 2/Trigonometry.
RCSD Post Assessment (if applicable)20 multiple choice questions5 open ended questions