Course Overview:
Math II covers concepts from geometry, algebra I and II , and probability. Throughout the course students will develop their problems solving skills to analyze applications and data so that they may be more competitive and competent in their future endeavors.

Unit 1: Modeling with Functions, Equations and Systems

Topics include: Direct and inverse variation, solving systems of equations, and solving equations for a given variable.

Unit 2: Families of Functions

Topics include: Function families and parent functions: quadratics, square root, cube root, absolute value, piecewise, greatest integer. Function notation, function transformations, graphing inequalities, graphing systems of inequalities, linear programming.

Unit 3: Operations with Exponents and Polynomials

Topics include:Properties of exponents, radicals, rational exponents, solving radical equations, operations with polynomials.

Unit 4: Modeling with Nonlinear Functions and Equations (Quadratics)

Topics include:Quadratic equations: graphing, factoring, and solving. Common logarithms and exponential equations

Unit 5: Modeling with Transformations

Topics include:Rigid and non-rigid transformations: translations, reflections, rotations, and dilations; rotational symmetry.

Unit 6: Modeling with Geometric Form and Its Function

Topics include:Discover and apply combinations of side and angle conditions that are sufficient to prove two triangles congruent; develop and use equations of circles, solve systems of circles/lines/parabolas; constructions of inscribed polygons, triangle properties including Midpoint Connector Theorem and sum of the measures of the angles of a triangle.

Unit 7: Modeling with Trigonometric Functions

Topics include:Sine, cosine, and tangent ratios; graphing sine, cosine, and tangent functions in degrees from 0 to 180; indirect measurement; Law of Sines; Law of Cosines; Area Formula of Triangles using Trigonometry.

Unit 8: Modeling with Applications of Probability

Topics include: Sets, subsets, Venn diagrams, probability of independent and dependent events, conditional probability, Addition Rule, Multiplication Rule, mutually exclusive events, permutations and combinations.

|| End of Year ||

Math II NC Final Exam - June 2016

2015-2016

Math II Syllabus

Unit 1 - Quadratic Functions

Students will be able to solve quadratics equations in on variable (graphically, taking square roots, factoring, quadratic formula) recognize when the formula generates non-zero roots, solving systems of equations involving quadratic and linear equations, interpret the structure of expressions, perform arithmetic operations on polynomial, multiplication of 3 linear polynomials, understand the relationship between zeros and factors of quadratics. Calculate vertex and discriminant. They will be able to identify: Vertex (max/min), Zeros/Roots/Solutions and X and Y intercepts.

Unit 2 - Equations and Inequalities

Students will be able to create equations and inequalities of one variable and use them to solve problems, explain each step is solving a simple equation, give examples showing how extraneous solutions may arise, use common logs to solve exponential equations, create equations in two or more variables and graph to represent relationships between quantities, represent constraints by equations or inequalities, and systems of equations, rearrange formulas to highlight a quantity of interest, solve equations graphically , the properties of exponents to rational exponents, simplify and multiply radicals (include cubic), introduce proofs, basic common logarithms.

Unit 3 - Functions

Students will be able to evaluate functions for inputs in their domain, even & odd functions, interpret key features of graphs, analyze functions using different representations, parent functions: equations, graphs, and tables, shifts/translations, build a function that models a relationship between two quantities, build new functions from existing functions, graph square root, cube root, piecewise, absolute value and step functions, compare properties of two functions each represented in a different way, using interval notations, focus on power functions and inverse functions. Determine an explicit expression or a recursive process allow informal recursive notation)

Unit 4 - Transformations

Students will be able to understand translations, reflections, rotations, dilations (w/center of (0, 0) and w/o center at (0, 0) and congruence transformations, composition of transformations, figures map onto themselves and onto other figures, and distance & midpoint.

Students will be able to understand congruence in terms of rigid motions, prove geometric theorems, make geometric constructions, and include CPCTC, midsegment theorems, types of angles, angle relationships, triangle sum, triangle congruence theorems.

Unit 6 - Similar Triangles & Trigonometry

Students will be able to understand similarity in terms of side ratios, define trigonometric ratios and solve problems involving right triangles, apply trigonometry to general triangles, graph trig functions by hand and interpret key features of the graph. Students will be able to define amplitude & period, identify Relative Max/Min, identify X and Y intercepts and define amplitude & period of the graphs of sin and cosine. They will be able to use the Law of sine & cosine. They will be able to derive and use formula A = ½ absin(C) to find the area of non-right triangles.

Students will be able to review area and volume, translate between the geometric description and the equations of conic sections, graph and determine equations of circles visualize relationships between two-dimensional and three-dimensional objects, apply geometric concepts in modeling situations.

Unit 8 - Probability

Students will be able to understand and evaluate random processes underlying statistical experiments, evaluate reports based on data, understand independence and conditional probability (include the use of two-way frequency tables) and use them to interpret data, use the rules of probability to compute probabilities of compound events. Use Permutations and combinations to solve probabilities.

Unit 1: Congruence, Proof and Constructions: January 22 – February 14 Priority: G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G-CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Supporting: G.CO.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch) G.CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G.CO.7: Use the definition of congruence in terms of rigid motion to show that 2 triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

a. dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged

Embedded Objectives: A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expressions, such as terms, factors, and coefficients

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. Ex. Interpret P (1+r) as the product of P and a factor not depending on P.

A-APR.1: Understand the polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A-CED.1: Create Equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales. A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in modeling context. A-REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Unit 2: Connecting Algebra and Geometry Through Coordinates: February 15 - 22 Priority: G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation G.CO.10: Prove theorems about triangles. Thms. Include: 1) measures of interior angles of a triangle sum to 180; 2) base angles of isosceles triangles are congruent; 3) the segment joining midpoints of two sides of a triangle is parallel to the third and half the length 4) the medians of a triangle meet at a point Supporting G.GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Unit 3: Similarity, Right Triangles and Trigonometry: February 25 – March 22 Priority: G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor: a: dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. G-MG.3: Apply geometric methods to solve design problems (e.g., designing an abject or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Supporting G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor: b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.7: Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.9: (+) Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G-SRT.11: (+) Understand and apply the Law of Sines and The Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces) G-MG.1: Apply geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder) G-MG.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot) Embedded Objectives A-SSE.2: Use the structure of an expression to identify ways to rewrite it. A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Ohm’s law V = IR to highlight resistance R) A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may rise. A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales. N-Q.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N-Q.2: Define appropriate quantities for the purpose of descriptive modeling. N-Q.3: Choose a level of accuracy appropriate to limitations on measurements when reporting quantities. F-IF.4: For a function that models a relationship between 2 quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior. (Trig functions: sine, cosine and tangent in standard position – 180 or less) F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (At this level: extend to quadratic functions and k f(x)) N-RN.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents . F-IF.2: Use function notation, evaluate functions for the inputs in their domains, and interpret statements that use function notation in terms of a context. (extend to quadratic, simple power and inverse variation functions)

Unit 4: Extending to Three – Dimensions: April 1 - 5 Priority Standards: G-MG.1: Apply geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder) Supporting Standards: G-GMD.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Embedded Objective: N-RN.2 (for solving volume problems involving cubes): Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Benchmark: April 8 - 10

Unit 5: Quadratics: April 9 - 30 Priority Standards: A-APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A-REI.4: Solve quadratic equations in one variable.

b. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b

A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in modeling context. Supporting Standards: A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales. F-IF.2: Use function notation, evaluate functions for the inputs in their domains, and interpret statements that use function notation in terms of a context. (extend to quadratic, simple power and inverse variation functions) F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the h (n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (At this level: extend to quadratic functions and k f(x)) A-REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) F-IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. A-REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. A-SSE.2: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c: Use theproperties of exponents to transform expressions for exponential functions. A-REI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x² + y² = 3. A-REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A-CED.1: Create Equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c. Use the properties of exponents to transform expressions for exponential functions.

Unit 6: Applications of Probability: May 1 - 23 Priority Standards: S-CP.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. S-CP.9: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. Supporting Standards: S-CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not” ) S-CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. S-CP.3: Understand the conditional probability of A given B as P(A and B)/P(B) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. S-CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. S-CP.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. S-CP.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. S-CP.8: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in the terms of the model.

Review and Exams May 28 – June 6

MATH II Released Final Exam Video Solutions

Someone has posted a series of videos where he works out each of the problems from the released version of the Math II exam. Find the links below.

Course Overview:Math II covers concepts from geometry, algebra I and II , and probability. Throughout the course students will develop their problems solving skills to analyze applications and data so that they may be more competitive and competent in their future endeavors.

Unit 1: Modeling with Functions, Equations and Systems

Unit 2: Families of Functions

Unit 3: Operations with Exponents and Polynomials

Unit 4: Modeling with Nonlinear Functions and Equations (Quadratics)

Unit 5: Modeling with Transformations

Unit 6: Modeling with Geometric Form and Its Function

Unit 7: Modeling with Trigonometric Functions

Unit 8: Modeling with Applications of Probability

|| End of Year ||

2015-2016Math II SyllabusUnit 1 - Quadratic FunctionsUnit 2 - Equations and InequalitiesUnit 3 - FunctionsUnit 4 - TransformationsUnit 5 - Congruent TrianglesUnit 6 - Similar Triangles & TrigonometryUnit 7 - Modeling with GeometryConicsConics - ParabolaUnit 8 - ProbabilityGrades 6 -12 Power Points

Math II ExtrasMath II - Lesson PlansMath II

Math 2

Unit 1: Congruence, Proof and Constructions: January 22 – February 14Priority:

G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Supporting:

G.CO.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

G.CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G.CO.7: Use the definition of congruence in terms of rigid motion to show that 2 triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

- a. dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged

Embedded Objectives:A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

- a. Interpret parts of an expressions, such as terms, factors, and coefficients
- b. Interpret complicated expressions by viewing one or more of their parts as a single entity. Ex. Interpret P (1+r) as the product of P and a factor not depending on P.

A-APR.1: Understand the polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.A-CED.1: Create Equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales.

A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in modeling context.

A-REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Unit 2: Connecting Algebra and Geometry Through Coordinates: February 15 - 22Priority:

G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation

G.CO.10: Prove theorems about triangles. Thms. Include:

1) measures of interior angles of a triangle sum to 180;

2) base angles of isosceles triangles are congruent;

3) the segment joining midpoints of two sides of a triangle is parallel to the third and half the length

4) the medians of a triangle meet at a point

Supporting

G.GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Unit 3: Similarity, Right Triangles and Trigonometry: February 25 – March 22Priority:

G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

a: dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged

G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

G-MG.3: Apply geometric methods to solve design problems (e.g., designing an abject or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Supporting

G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT.7: Explain and use the relationship between the sine and cosine of complementary angles.

G-SRT.9: (+) Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

G-SRT.11: (+) Understand and apply the Law of Sines and The Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces)

G-MG.1: Apply geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder)

G-MG.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot)

Embedded Objectives

A-SSE.2: Use the structure of an expression to identify ways to rewrite it.

A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Ohm’s law V = IR to highlight resistance R)

A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may rise.

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales.

N-Q.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

N-Q.2: Define appropriate quantities for the purpose of descriptive modeling.

N-Q.3: Choose a level of accuracy appropriate to limitations on measurements when reporting quantities.

F-IF.4: For a function that models a relationship between 2 quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior. (Trig functions: sine, cosine and tangent in standard position – 180 or less)

F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (At this level: extend to quadratic functions and k f(x))

N-RN.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents .

F-IF.2: Use function notation, evaluate functions for the inputs in their domains, and interpret statements that use function notation in terms of a context. (extend to quadratic, simple power and inverse variation functions)

Unit 4: Extending to Three – Dimensions: April 1 - 5Priority Standards:

G-MG.1: Apply geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder)

Supporting Standards:

G-GMD.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Embedded Objective:

N-RN.2 (for solving volume problems involving cubes): Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Benchmark: April 8 - 10

Unit 5: Quadratics: April 9 - 30Priority Standards:

A-APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

A-REI.4: Solve quadratic equations in one variable.

- b. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b

A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in modeling context.Supporting Standards:

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales.

F-IF.2: Use function notation, evaluate functions for the inputs in their domains, and interpret statements that use function notation in terms of a context. (extend to quadratic, simple power and inverse variation functions)

F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the h (n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (At this level: extend to quadratic functions and k f(x))

A-REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line)

F-IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

A-REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

A-SSE.2: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

c: Use theproperties of exponents to transform expressions for exponential functions.

A-REI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x² + y² = 3.

A-REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A-CED.1: Create Equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions

A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

c. Use the properties of exponents to transform expressions for exponential functions.

Unit 6: Applications of Probability: May 1 - 23Priority Standards:

S-CP.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

S-CP.9: (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

Supporting Standards:

S-CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not” )

S-CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S-CP.3: Understand the conditional probability of A given B as P(A and B)/P(B) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

S-CP.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

S-CP.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

S-CP.8: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in the terms of the model.

Review and Exams

May 28 – June 6

MATH II Released Final Exam Video Solutions

Someone has posted a series of videos where he works out each of the problems from the released version of the Math II exam. Find the links below.

NC Math II Released Final Exam: http://www.ncpublicschools.org/docs/accountability/common-exams/released-forms/highschool/mathematics/math2-common-core/common-exam.pdf

NC Math II Released Final Exam Video links for solutions of questions:

1, 2 & 3 ~ 4, 5, 6 , 7 & 8 ~ 9 , 10 & 11: ~

12 , 13, 14 & 15: ~ 16, 17, 18, 19, 20, & 21 ~ 22, 23, 24 & 25:

P(A)Name:Probability function.Explanation:Used to represent the probability of event A.P(A∩B)Name:Probability of events intersection.Explanation:Used to represent the probability of both event A and event B.P(A∪B)Name:Probability of events union.Explanation:Used to represent the probability of event Aorevent B.P(A|B)Name:Conditional probability function.Explanation:Used to represent the probability of Event A.Probability tutorial 1Probability tutorial 2Probability tutorial 3Ch5-Guided-Notes-for-Reading-Textbook-TPS4e-.pdf

TPS4e_Ch5_5.1.ppt

TPS4e_Ch5_5.2.ppt

TPS4e_Ch5_5.3.ppt

Abraham_KeyConceptsProbability.pptx