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