Math 2 Final Review 1 Answers N Rn-2

Secondary Mathematics 2
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Class Introduction

THE FOCUS OF SECONDARY MATHEMATICS Two is on quadratic expressions, equations, and functions and on comparing their characteristics and beliefs to those of linear and exponential relationships from Secondary Mathematics I as organized into six critical areas, or units. The need for extending the set of rational numbers arises, and real and complex numbers are introduced so that all quadratic equations tin be solved. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The report of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. Circles, with their quadratic algebraic representations, circular out the grade. The Mathematical Practise Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject area that makes use of their ability to brand sense of problem situations.

CRITICAL AREA 1: Students extend the laws of exponents to rational exponents and explore distinctions betwixt rational and irrational numbers by considering their decimal representations. Students larn that when quadratic equations do not have real solutions the number system must be extended and then that solutions exist, coordinating to the style in which extending the whole numbers to the negative numbers allows x+1 = 0 to take a solution. Students explore relationships between number systems: whole numbers, integers, rational numbers, real numbers, and complex numbers. The guiding principle is that equations with no solutions in i number system may have solutions in a larger number arrangement.

CRITICAL Surface area 2: Students consider quadratic functions, comparison the key characteristics of quadratic functions to those of linear and exponential functions. They select from amid these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they place the real solutions of a quadratic equation as the zeros of a related quadratic function. When quadratic equations do not have real solutions, students learn that the graph of the related quadratic office does not cantankerous the horizontal centrality. They expand their feel with functions to include more specialized functions�accented value, pace, and those that are piecewise-defined.

CRITICAL Expanse 3: Students begin this unit past focusing on the construction of expressions, rewriting expressions to clarify and reveal aspects of the relationship they represent. They create and solve equations, inequalities, and systems of equations involving exponential and quadratic expressions.

Critical Expanse 4: Edifice on probability concepts that began in the middle grades, students use the languages of set theory to expand their power to compute and interpret theoretical and experimental probabilities for compound events, attending to mutually sectional events, contained events, and conditional probability. Students should brand use of geometric probability models wherever possible. They use probability to make informed decisions.

Disquisitional AREA v: Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They place criteria for similarity of triangles, employ similarity to solve problems, and use similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem. It is in this unit that students develop facility with geometric proof. They utilise what they know about congruence and similarity to prove theorems involving lines, angles, triangles, and other polygons. They explore a variety of formats for writing proofs.

CRITICAL Expanse half dozen: Students bear witness bones theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems nigh chords, secants, and tangents dealing with segment lengths and angle measures. In the Cartesian coordinate system, students use the altitude formula to write the equation of a circle when given the radius and the coordinates of its center, and the equation of a parabola with vertical axis when given an equation of its directrix and the coordinates of its focus. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations to make up one's mind intersections between lines and circles or a parabola and betwixt two circles. Students develop breezy arguments justifying common formulas for circumference, area, and volume of geometric objects, especially those related to circles.

Core Standards of the Course

Strand: MATHEMATICAL PRACTICES (MP)
The Standards for Mathematical Practice in Secondary Mathematics 2 describe mathematical habits of mind that teachers should seek to develop in their students. Students get mathematically skillful in engaging with mathematical content and concepts as they learn, feel, and employ these skills and attitudes (Standards MP.1�eight).

Standard SII.MP.1
Brand sense of problems and persevere in solving them. Explain the meaning of a trouble and wait for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures almost the form and meaning of the solution, plan a solution pathway, and continually monitor progress request, "Does this make sense?" Consider coordinating problems, make connections betwixt multiple representations, identify the correspondence betwixt different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Cheque answers to problems using a different method.

Standard SII.MP.2
Reason abstractly and quantitatively. Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations past contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently besides as the ability to contextualize algebraic representations to make sense of the problem.

Standard SII.MP.iii
Construct viable arguments and critique the reasoning of others. Sympathise and use stated assumptions, definitions, and previously established results in amalgam arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Answer to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

Standard SII.MP.four
Model with mathematics. Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying of import quantities to construct a mathematical model. Routinely translate mathematical results in the context of the state of affairs and reflect on whether the results make sense, possibly improving the model if information technology has non served its purpose.

Standard SII.MP.5
Use appropriate tools strategically. Consider the available tools and be sufficiently familiar with them to make audio decisions about when each tool might be helpful, recognizing both the insight to be gained too as the limitations. Identify relevant external mathematical resource and use them to pose or solve problems. Use tools to explore and deepen their agreement of concepts.

Standard SII.MP.6
Attend to precision. Communicate precisely to others. Apply explicit definitions in discussion with others and in their own reasoning. They state the pregnant of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the trouble context.

Standard SII.MP.seven
Look for and make employ of structure. Expect closely at mathematical relationships to place the underlying construction by recognizing a simple structure inside a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being equanimous of several objects. For example, see 5 � three(10 � y)² as 5 minus a positive number times a foursquare and employ that to realize that its value cannot be more than 5 for whatsoever real numbers 10 and y.

Standard SII.MP.8
Look for and limited regularity in repeated reasoning. Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results past maintaining oversight of the process while attending to the details.

Strand: NUMBER AND QUANTITY - The Existent Number Organisation (Northward.RN)
Extend the properties of exponents to rational exponents (Standards N.RN.1�2). Use backdrop of rational and irrational numbers (Standard N.RN. 3).

Standard N.RN.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, nosotros ascertain 5^1/3 to be the cube root of 5 because nosotros desire (5^ane/three)³ = 5^(1/3)³ to hold, and then (v^1/iii)ⁱⁱⁱ must equal 5.

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

Standard Northward.RN.3
Explain why sums and products of rational numbers are rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational. Connect to physical situations (e.g., finding the perimeter of a square of area 2).

Strand: NUMBER AND QUANTITY - The Complex Number Organization (N.CN)
Perform arithmetics operations with complex numbers (Standards N.CN.i�2). Utilise complex numbers in polynomial identities and equations (Standards N.CN.vii�9).

Standard N.CN.one
Know there is a complex number i such that i ² = –i, and every complex number has the course a + bi with a and b real.

Standard N.CN.2
Use the relation i ^two = –1 and the commutative, associative, and distributive properties to add, decrease, and multiply complex numbers. Limit to multiplications that involve i ² every bit the highest power of i.

Standard N.CN.7
Solve quadratic equations with real coefficients that take complex solutions.

Standard N.CN.8
Extend polynomial identities to the circuitous numbers. Limit to quadratics with real coefficients. For case, rewrite x² + four equally (x + 2i)(ten – 2i).

Standard N.CN.9
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Strand: ALGEBRA - Seeing Structure in Expression (A.SSE)
Translate the structure of expressions (Standards A.SSE.1�2). Write expressions in equivalent forms to solve problems, balancing conceptual understanding and procedural fluency in piece of work with equivalent expressions (Standard A.SSE.3).

Standard A.SSE.1
Translate quadratic and exponential expressions that represent a quantity in terms of its context.^★

1. Interpret parts of an expression, such as terms, factors, and coefficients.
   
2. Interpret increasingly more complex expressions by viewing one or more of their parts as a single entity. Exponents are extended from the integer exponents to rational exponents focusing on those that represent square or cube roots.
   

Standard A.SSE.2
Utilize the construction of an expression to place ways to rewrite it. For case, come across 10⁴ – y^four equally (xⁱⁱ)ⁱⁱ – (y²)², thus recognizing information technology as a divergence of squares that can exist factored equally (xⁱⁱ – y²)(x^two + y²).

Standard A.SSE.3
Choose and produce an equivalent grade of an expression to reveal and explain properties of the quantity represented by the expression. For example, evolution of skill in factoring and completing the foursquare goes hand in manus with agreement what different forms of a quadratic expression reveal. ^★

1. Factor a quadratic expression to reveal the zeros of the function it defines.
   
2. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
   
3. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.xv^1/12)^12t ≈ 1.012^12t to reveal the guess equivalent monthly interest charge per unit if the annual rate is 15%.
   

Strand: ALGEBRA - Arithmetic With Polynomials and Rational Expressions (A.APR)
Perform arithmetics operations on polynomials. Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of 10 (Standard A.APR.1).

Standard A.APR.i
Sympathise that polynomials form a system analogous to the integers, namely, they are closed nether the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Strand: ALGEBRA - Creating Equations (A.CED)
Create equations that describe numbers or relationships. Extend piece of work on linear and exponential equations to quadratic equations (Standards A.CED.1�ii, iv).

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

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

Standard A.CED.iv
Rearrange formulas to highlight a quantity of involvement, using the aforementioned reasoning as in solving equations; extend to formulas involving squared variables.For example, rearrange the formula for the volume of a cylinder 5 = π rⁱⁱ h.

Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)
Solve equations and inequalities in ane variable (Standard A.REI.iv). Solve systems of equations. Extend the work of systems to include solving systems consisting of one linear and i nonlinear equation (Standard A.REI.seven).

Standard A.REI.4
Solve quadratic equations in one variable.

1. Use the method of completing the square to transform any quadratic equation in x into an equation of the course (ten � p)² = q that has the aforementioned solutions. Derive the quadratic formula from this form.
   
2. Solve quadratic equations by inspection (e.thou., for 10 ² = 49), taking square roots, completing the square, the quadratic formula and factoring, every bit appropriate to the initial form of the equation. Recognize when the quadratic formula gives circuitous solutions and write them equally a ± bi for real numbers a and b.
   

Standard A.REI.seven
Solve a simple arrangement consisting of a linear equation and a quadratic equation in ii variables algebraically and graphically. For case, find the points of intersection between the line y = –3x and the circle x ² + y ² = 3.

Strand: FUNCTIONS - Interpret Functions (F.IF)
Translate quadratic functions that ascend in applications in terms of a context (Standards F.IF.iv�half dozen). Analyze functions using different representations (Standards F.IF.7�9).

Standard F.IF.4
For a function that models a human relationship between ii quantities, interpret fundamental features of graphs and tables in terms of the quantities, and sketch graphs showing fundamental features given a verbal description of the relationship. Central features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

Standard F.IF.v
Relate the domain of a part to its graph and, where applicable, to the quantitative relationship it describes. Focus on quadratic functions; compare with linear and exponential functions. For case, if the office h(n) gives the number of person-hours it takes to gather n engines in a factory, then the positive integers would exist an appropriate domain for the function. ^★

Standard F.IF.6
Calculate and interpret the average rate of modify of a office (presented symbolically or as a tabular array) over a specified interval. Guess the rate of change from a graph.^★

Standard F.IF.7
Graph functions expressed symbolically and show cardinal features of the graph, by hand in simple cases and using technology for more complicated cases.^★

1. Graph linear and quadratic functions and show intercepts, maxima, and minima.
   
2. Graph piecewise-defined functions and accented value functions. Compare and contrast absolute value and piecewise-divers functions with linear, quadratic, and exponential functions. Highlight issues of domain, range, and usefulness when examining piecewise-defined functions.
   

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

1. Utilize the process of factoring and completing the foursquare in a quadratic role to show zeros, farthermost values, and symmetry of the graph, and translate these in terms of a context.
   
2. Use the properties of exponents to translate expressions for exponential functions. For example, identify percentage charge per unit of alter in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y = (1.2)^t/10, and classify them as representing exponential growth or decay.
   

Standard F.IF.9
Compare backdrop of 2 functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factored. For instance, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Strand: FUNCTIONS - Building Functions (F.BF)
Build a function that models a relationship betwixt ii quantities (Standard F.BF.ane). Build new functions from existing functions (Standard F.BF.3).

Standard F.BF.i
Write a quadratic or exponential role that describes a relationship between 2 quantities.^★

1. Determine an explicit expression, a recursive process, or steps for calculation from a context.
   
2. Combine standard function types using arithmetic operations. For instance, build a office that models the temperature of a cooling body by adding a constant function to a decaying exponential, and chronicle these functions to the model.
   

Standard F.BF.3
Identify the effect on the graph of replacing f(x) by f(10) + grand, k f(x), f(kx), and f(x + m) 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 engineering science. Include recognizing fifty-fifty and odd functions from their graphs and algebraic expressions for them.

Strand: FUNCTIONS - Linear, Quadratic, and Exponential Models (F.LE)
Construct and compare linear, quadratic, and exponential models and solve problems (Standard F.LE.3).

Standard F.LE.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more by and large) as a polynomial function.

Strand: FUNCTIONS - Trigonometric Functions (F.TF)
Evidence and utilise trigonometric identities. Limit θ to angles between 0 and ninety degrees. Connect with the Pythagorean Theorem and the altitude formula (Standard F.TF.8).

Standard F.TF.8
Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

Strand: GEOMETRY - Congruence (G.CO)
Evidence geometric theorems. Encourage multiple means of writing proofs, such as narrative paragraphs, flow diagrams, two-column format, and diagrams without words. Focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning (Standards G.CO.9�xi).

Standard G.CO.nine
Show theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment'due south endpoints.

Standard K.CO.10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are coinciding; the segment joining midpoints of ii sides of a triangle is parallel to the tertiary side and half the length; the medians of a triangle meet at a indicate.

Standard G.CO.xi
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, reverse angles are congruent, the diagonals of a parallelogram bifurcate each other, and conversely, rectangles are parallelograms with congruent diagonals.

Strand: GEOMETRY - Similarity, Correct Triangles, and Trigonometry (G.SRT)
Sympathise similarity in terms of similarity transformations (Standards G.SRT.1�3). Prove theorems involving similarity (Standards G.SRT.4�5). Ascertain trigonometric ratios and solve problems involving right triangles (Standards G.SRT.6�8).

Standard G.SRT.1
Verify experimentally the backdrop of dilations given past a eye and a calibration factor.

1. 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.
   
2. The dilation of a line segment is longer or shorter in the ratio given by the scale gene.
   

Standard Thousand.SRT.two
Given two figures, employ the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all respective pairs of angles and the proportionality of all respective pairs of sides.

Standard 1000.SRT.iii
Employ the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Standard Thou.SRT.four
Testify theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other ii proportionally, and conversely; the Pythagorean Theorem (proved using triangle similarity).

Standard G.SRT.v
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Standard 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.

Standard Chiliad.SRT.7
Explain and utilise the human relationship between the sine and cosine of complementary angles.

Standard Yard.SRT.8
Apply trigonometric ratios and the Pythagorean Theorem to solve correct triangles in applied problems.

Strand: GEOMETRY - Circles (Thou.C)
Empathize and use theorems about circles (Standard G.C.1�4). Find arc lengths and areas of sectors of circles. Use this equally a ground for introducing the radian as a unit of measure. It is not intended that it be practical to the development of circular trigonometry in this course (Standard Thousand.C.5).

Standard Chiliad.C.1
Prove that all circles are like.

Standard Grand.C.2
Identify and describe relationships among inscribed angles, radii, and chords. Relationships include the human relationship between central, inscribed, and confining angles; inscribed angles on a bore are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Standard G.C.3
Construct the inscribed and circumscribed circles of a triangle, and show backdrop of angles for a quadrilateral inscribed in a circle.

Standard G.C.four
Construct a tangent line from a bespeak exterior a given circumvolve to the circumvolve.

Standard 1000.C.five
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle every bit the abiding of proportionality; derive the formula for the area of a sector.

Strand: GEOMETRY - Expressing Geometric Properties With Equations (G.GPE)
Translate between the geometric description and the equation for a conic section (Standard G.GPE.i). Apply coordinates to evidence simple geometric theorems algebraically. Include elementary proofs involving circles (Standard Thou.GPE.four). Use coordinates to prove uncomplicated geometric theorems algebraically (Standard Chiliad.GPE.6).

Standard G.GPE.one
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the middle and radius of a circumvolve given by an equation.

Standard G.GPE.4
Use coordinates to bear witness simple geometric theorems algebraically. For example, bear witness or disprove that a effigy defined past iv given points in the coordinate aeroplane is a rectangle; prove or disprove that the signal (1, √iii) lies on the circumvolve centered at the origin and containing the indicate (0, 2).

Standard One thousand.GPE.vi
Find the betoken on a directed line segment betwixt two given points that partitions the segment in a given ratio.

Strand: GEOMETRY - Geometric Measurement and Dimension (1000.GMD)
Explain volume formulas and apply them to solve problems (Standards G.GMD.i, 3).

Standard G.GMD.one
Give an informal statement for the formulas for the circumference of a circle, surface area of a circumvolve, volume of a cylinder, pyramid, and cone. Informal arguments for area formulas can brand use of the way in which expanse scale nether similarity transformations: when 1 figure in the plane results from another by applying a similarity transformation with scale factor 1000, its expanse is g ^two times the area of the first. Use dissection arguments, Cavalieri�south principle, and informal limit arguments.

Standard G.GMD.3
Use book formulas for cylinders, pyramids, cones, and spheres to solve problems. Informal arguments for volume formulas tin brand utilise of the way in which book scale nether similarity transformations: when one figure results from another by applying a similarity transformation, volumes of solid figures scale past chiliad ³ under a similarity transformation with calibration gene k.^★

Strand: STATISTICS - Interpreting Categorical and Quantitative Information (S.ID)
Summarize, represent, and interpret information on 2 categorical or quantitative variables (Standard S.ID.five).

Standard S.ID.5
Summarize categorical information for two categories in two-style frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and condition reltive frequencies). Recognize possible associations and trends in the date.

Strand: STATISTICS - Conditional Probability and the Rules of Probability (S.CP)
Sympathise independence and conditional probability and use them to interpret data (Standards S.CP.one, 4�5). Employ the rules of probability to compute probabilities of chemical compound events in a uniform probability model (Standard S.CP.half dozen).

Standard S.CP.1
Draw events equally 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").

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

Standard S.CP.5
Recognize and explain the concepts of conditional probability and independence in everyday linguistic communication and everyday situations. For example, compare the chance of having lung cancer if y'all are a smoker with the chance of being a smoker if yous take lung cancer.

Standard S.CP.6
Discover the conditional probability of A given B equally the fraction of B's outcomes that also belong to A, and interpret the respond in terms of the model.

HONORS - Strand: NUMBER AND QUANTITY - Circuitous Number Organisation (Due north.CN)
Perform arithmetics operations with complex numbers (Standard N.CN.iii). Stand for complex numbers and their operations on the complex plane (Standards N.CN.4�five).

HONORS - Standard Due north.CN.iii
Notice the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

HONORS - Standard N.CN.iv
Represent circuitous numbers on the complex plane in rectangular form, and explain why the rectangular class of a given complex number represents the same number.

HONORS - Standard N.CN.5
Correspond addition, subtraction, and multiplication geometrically on the circuitous airplane; employ properties of this representation for ciphering. For case, (-ane + √3 i)3 = viii considering (-1 + √3 i) has modulus 2 and argument 120°.

HONORS - Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)
Solve systems of equations (Standards A.REI.8�ix).

HONORS - Standard A.REI.8
Stand for a system of linear equations equally a unmarried-matrix equation in a vector variable.

HONORS - Standard A.REI.9
Find the inverse of a matrix if information technology exists, and use it to solve systems of linear equations (using applied science for matrices of dimension 3 x iii or greater).

HONORS - Strand: FUNCTIONS - Interpreting Functions (F.IF)
Analyze functions using different representations (Standards F.IF.ten�11).

HONORS - Standard F.IF.10
Use sigma notation to represent the sum of a finite arithmetics or geometric series.

HONORS - Standard F.IF.11
Represent series algebraically, graphically, and numerically.

HONORS - Strand: GEOMETRY - Expressing Geometric Properties With Equations (M-GPE)
Translate between the geometric description and the equation for a conic section (Standards G.GPE.ii�3).

HONORS - Standard 1000.GPE.2
Derive the equation of a parabola given a focus and directrix.

HONORS - Standard Thou.GPE.iii
Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is abiding.

HONORS - Strand: STATISTICS AND PROBABILITY - Provisional Probability and the Rules of Probability (S.CP)
Understand independence and provisional probability and use them to interpret data (Standards S.CP.2�3). Apply the rules of probability to compute probabilities of chemical compound events in a uniform probability model (Standards Southward.CP.7�eight).

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

HONORS - Standard Due south.CP.iii
Understand the provisional probability of A given B equally P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of B given A is the same as the probability of B.

HONORS - Standard Due south.CP.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) � P(A and B), and translate the answer in terms of the model.

HONORS - Standard Southward.CP.8
Employ the full 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 terms of the model.

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