HONORS MATHEMATICS TESTING INFORMATION If you are interested in the Honors Mathematics program, please read the Criteria for Honors Advancement in the Guidance Department Course Guide under Mathematics. The Course Guide is on the NBTHS website. Specific information on testing for entrance into Honors Mathematics is provided below. Please read the documents that are listed. Math Honors Testing Information (page 2) Math Honors Testing Registration Form (page 3) complete and give to current math teacher by May 12 (Linwood MS or NBTHS). You must return the completed registration form in order to test. You must also study the list of topics that will be tested for entry into the indicated courses. These lists are provided on the pages indicated. Topics for Entry into Honors Geometry (pages 4 5) Topics for Entry into Honors Algebra II (pages 6 9) Topics for Entry into Honors Math Analysis (pages 10 12) Topics for Entry into AP Calculus AB/BC (pages 13 15) For information on entry into AP Computer Science, please call Mrs. Aloisio, Supervisor of Mathematics (732-289-3700 Ext.73054) Please feel free to call Mrs. Aloisio, Supervisor of Mathematics (732-289-3700 X73054) for additional information. 1
NORTH BRUNSWICK TOWNSHIP HIGH SCHOOL Raider Road North Brunswick, NJ 08902 Phone: 732-289-3700 Fax: 732-821-8342 Dear Student, You have requested enrollment into an honors mathematics course for the next school year. To enter the honors math program, you are required to take a comprehensive honors exam on the prerequisite course content and earn a minimum score of 85%. Please review the information below. Who can test into Honors The following criteria will be used to determine if a student qualifies for honors testing: A- or higher in current college prep course; AND Teacher recommendation How will testing be done PREREGISTRATION: o You must inform your current teacher and guidance counselor of your interest. Based on your teacher s recommendation, your teacher will provide you with a registration form. Or you may download the attached form and give it to your teacher. o All registration forms must be completed by May 12. o Once registrations are turned in, the HS math supervisor will provide any additional textbooks. (LMS students should see Mrs. Lanphear, LMS Math Supervisor) TESTING o You will be tested on topics you learned in your college prep math course plus additional topics covered in honors. Not all topics will be tested but it is expected that you learn/can do all problems in the covered concepts. You will receive a list of topics for studying. o The comprehensive exam will be given at 7:45 a.m. on Tuesday, June 20, 2017, at North Brunswick Township High School. Please bring a calculator, pencils, and any textbooks you borrowed. This is a 2-hour exam so transportation should be arranged for pick-up at approximately 10:15 a.m. The test will be held in Room 707 (2 nd floor NBTHS). o After the test is graded, you will be notified by mail as to whether you earned the necessary passing grade of 85%. Retakes for comprehensive exams are not given under any circumstance so come prepared. A graphing calculator is allowed only on the entrance to Honors Math Analysis or higher course exams. For all other exams, scientific calculators are allowed. Results should be expected within two weeks of testing. o Note all Honors math courses require completion of a summer assignment. Please obtain a copy by the end of June. Additional time to complete the assignment will not be given. If there are any questions please contact me at 732-289-3700 X73054. Sincerely, Mrs. Kari Aloisio Supervisor of Mathematics, NBTHS 2
MATHEMATICS DEPARTMENT NORTH BRUNSWICK TOWNSHIP HIGH SCHOOL TESTING FOR ENTRY INTO HONORS MATHEMATICS - REGISTRATION FORM 1. Read the information letter attached to this form. 2. Complete all required information listed below before May 12. Late submission means you have less time to prepare! 3. Obtain current math teacher recommendation and signature. 4. Obtain parent/guardian signature. 5. Return to current math teacher, who will submit the form to the Supervisor of Mathematics. Student s Last Name Student ID Number Student First Name Current Math Course 1 st 2 nd 3 rd Marking Period Grades Requested Honors Math Course recommend do not recommend Current Math Teacher Please provide explanation for recommendation or not: Teacher Signature We have read the information letter and request that the above named student be given the comprehensive mathematics entry exam for the requested course. Student Signature Parent/Guardian Signature Date Date Registration Deadline is May 12 3
For entry into Honors Geometry Topics taught in Honors Algebra I Textbook: Algebra I, Glencoe, 2014 Chapter 0 0-1 to 0-13 Chapter 1 1-1 to 1-8 Chapter 2 2-1 to 2-9 Analyze real world problems Classify and use real numbers Graph real numbers as solutions to equations and inequalities Find square roots as solutions to quadratic equations Computations with real numbers Using percents and proportions to solve problems Solve problems using geometric properties Find probability and odds of simple and compound events Use permutations and combinations to find probabilities Find and apply measures of central tendency Use statistics and populations parameters Represent and analyze data using visual models Use variables and expressions to model relationships Perform orders of operations and evaluate variable expressions Apply the properties of real numbers Solve equations in one and two variables Represent relations and interpret their graphs Classify relations as functions Represent functions using rules and graphs Evaluate function rules Describe the characteristics of a function graph using proper mathematical terminology Use equations to model problems Solve one-step, two step and multi-step equations Solve equations with variables on both sides Solve equations involving absolute value Solve problems using ratios, proportions and percent change Solve literal equations Chapter 3 3-1 to 3-6 Chapter 4 4-1 to 4-7 (Omit 4-6) Chapter 5 5-1 to 5-6 Chapter 6 6-1 to 6-6 Use formulas to solve real world problems Solve mixture and uniform motion problems Analyze key features of linear graphs Identify linear equations, intercepts and zeros Graph linear equations Solve linear equations by graphing Estimate solutions to an equation by graphing Use rate of change to solve problems Find the slope of a line Write and graph direct variation equations Solve problems using direct variation Recognize arithmetic sequences and relate them to linear functions Write equations for proportional and nonproportional relationships Write and graph equations in slope-intercept form and point-slope form Model real world data with linear equations Write equations for parallel and perpendicular lines Interpret relationships using scatter plots Use lines of best fit to make and evaluate predictions Find the inverse of a relation and a linear function Solve linear inequalities using addition, subtraction, multiplication and division properties Solve multi-step and compound inequalities Solve inequalities involving absolute value Graph inequalities in two variables Solving systems of equations by graphing, substitution, elimination Solve real world problems by writing a system of equations Graph linear inequalities Solve systems of linear inequalities by graphing Use systems of linear inequalities to solve real world problems 4
Chapter 7 7-1 to 7-6 (Omit 7-7 to 7-8) Chapter 8 8-1 to 8-9 Chapter 9 9-1 to 9-5 (Omit 9-6 to 9-7) Chapter 10 (Omit 10-6) Simplify expressions using multiplication and division properties of exponents Simplify expressions with zero and negative exponents Evaluate and rewrite expressions involving rational exponents Solve equations involving expressions with rational exponents Write numbers from scientific notation to standard notation and vice versa Find products and quotients of numbers in scientific notation Graph exponential functions Identify data that displays exponential behavior Solve problems involving exponential growth and decay Add, subtract, and multiply polynomials Factor polynomials Analyze the characteristics of the graphs of quadratic functions Graph quadratic functions in vertex form and using transformations Find the vertex when in standards form and in vertex form Find the minimum and maximum values Solve quadratic equations by graphing, factoring, completing the square and quadratic formula Solve problems using quadratic models Graph and analyze graphs of radical functions Simplify radical expressions Add, subtract, multiply and divide radical expressions Solve radical equations including those with extraneous roots Find the domain of a radical expression Solve problems using the Pythagorean Theorem. Chapter 11 11-1 to 11-8 Identify, use and graph inverse relations Graph rational functions using asymptotes Identify the domain of rational functions Simplify rational expressions using addition, subtraction, multiplication and division Solve rational equations. 5
Entry into Honors Algebra II requires demonstration of proficiency in both Honors Algebra I and Honors Geometry. Topics taught in Honors Algebra I Textbook: Algebra I, Glencoe, 2014 Chapter 0 0-1 to 0-13 Chapter 1 1-1 to 1-8 Chapter 2 2-1 to 2-9 Analyze real world problems Classify and use real numbers Graph real numbers as solutions to equations and inequalities Find square roots as solutions to quadratic equations Computations with real numbers Using percents and proportions to solve problems Solve problems using geometric properties Find probability and odds of simple and compound events Use permutations and combinations to find probabilities Find and apply measures of central tendency Use statistics and populations parameters Represent and analyze data using visual models Use variables and expressions to model relationships Perform orders of operations and evaluate variable expressions Apply the properties of real numbers Solve equations in one and two variables Represent relations and interpret their graphs Classify relations as functions Represent functions using rules and graphs Evaluate function rules Describe the characteristics of a function graph using proper mathematical terminology Use equations to model problems Solve one-step, two step and multi-step equations Solve equations with variables on both sides Solve equations involving absolute value Solve problems using ratios, proportions and percent change Solve literal equations Chapter 3 3-1 to 3-6 Chapter 4 4-1 to 4-7 (Omit 4-6) Chapter 5 5-1 to 5-6 Chapter 6 6-1 to 6-6 Use formulas to solve real world problems Solve mixture and uniform motion problems Analyze key features of linear graphs Identify linear equations, intercepts and zeros Graph linear equations Solve linear equations by graphing Estimate solutions to an equation by graphing Use rate of change to solve problems Find the slope of a line Write and graph direct variation equations Solve problems using direct variation Recognize arithmetic sequences and relate them to linear functions Write equations for proportional and nonproportional relationships Write and graph equations in slope-intercept form and point-slope form Model real world data with linear equations Write equations for parallel and perpendicular lines Interpret relationships using scatter plots Use lines of best fit to make and evaluate predictions Find the inverse of a relation and a linear function Solve linear inequalities using addition, subtraction, multiplication and division properties Solve multi-step and compound inequalities Solve inequalities involving absolute value Graph inequalities in two variables Solving systems of equations by graphing, substitution, elimination Solve real world problems by writing a system of equations Graph linear inequalities Solve systems of linear inequalities by graphing Use systems of linear inequalities to solve real world problems 6
Chapter 7 7-1 to 7-6 (Omit 7-7 to 7-8) Chapter 8 8-1 to 8-9 Chapter 9 9-1 to 9-5 (Omit 9-6 to 9-7) Chapter 10 (Omit 10-6) Chapter 11 11-1 to 11-8 Simplify expressions using multiplication and division properties of exponents Simplify expressions with zero and negative exponents Evaluate and rewrite expressions involving rational exponents Solve equations involving expressions with rational exponents Write numbers from scientific notation to standard notation and vice versa Find products and quotients of numbers in scientific notation Graph exponential functions Identify data that displays exponential behavior Solve problems involving exponential growth and decay Add, subtract, and multiply polynomials Factor polynomials Analyze the characteristics of the graphs of quadratic functions Graph quadratic functions in vertex form and using transformations Find the vertex when in standards form and in vertex form Find the minimum and maximum values Solve quadratic equations by graphing, factoring, completing the square and quadratic formula Solve problems using quadratic models Graph and analyze graphs of radical functions Simplify radical expressions Add, subtract, multiply and divide radical expressions Solve radical equations including those with extraneous roots Find the domain of a radical expression Solve problems using the Pythagorean Theorem. Identify, use and graph inverse relations Graph rational functions using asymptotes Identify the domain of rational functions Simplify rational expressions using addition, subtraction, multiplication and division Solve rational equations. Honors Geometry Topics for Entry into Honors Algebra II Textbook: Geometry Common Core, Prentice Hall, 2012 Chapter 1 Make isometric and orthographic drawings. Draw nets for 3-D figures. Understand basic terms and postulates of geometry. Find and compare lengths of segments Find and compare lengths of angles Identify special angle pairs and use their relationships to find angle measures Make basic constructions using a straightedge and a compass Find midpoint of a segment. Find the distance between two points in the coordinate plane Find the perimeter of circumference of basic shapes. Find the area of basic shapes Chapter 2 Chapter 3 Use inductive reasoning to make conjectures. Recognize conditional statements and their parts. Write converses, inverses, and contrapositives of conditionals. Write biconditionals and recognize good definitions Use the Law of Detachment and the Law of Syllogism Connect reasoning in algebra and geometry Prove and apply theorems about angles Identify relationships between figures in space. Identify formed by two lines and a transversal Prove theorems about parallel lines; Use properties of parallel lines to find angle measures. Determine whether two lines are parallel Relate parallel and perpendicular lines Use parallel lines to prove a theorem about triangles. Find measures of angles of triangles. Construct parallel and perpendicular lines Graph and write linear equations Relate slope parallel and perpendicular lines 7
(continued) For entry into Honors Algebra II Topics taught in Honors Geometry Chapter 4 Chapter 5 Recognize congruent figures and their corresponding parts Prove two triangles congruent using SSS and SAS Prove two triangles congruent using ASA and AAS Use triangle congruence and corresponding parts of congruent triangles to prove parts of 2 triangles are congruent State and apply properties of isosceles and equilateral triangles. Prove right triangles congruent using the Hypotenuse Leg Theorem Identify congruent overlapping triangles. Prove two triangles congruent using other congruent triangles. Use properties of midsegments to solve problems Use properties of perpendicular and angle bisectors. Identify properties of perpendicular and angle bisectors Identify properties of medians and altitudes of a triangle Use indirect reasoning to write proofs Use inequalities involving sides and angles of triangles. Apply inequalities to two triangles Chapter 8 Chapter 9 Use the Pythagorean theorem and its converse Use properties of 45-45-90 and 30-60-90 triangles The sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles. Use angles of elevation and depression to solve problems. Apply the Law of Sines Apply the Law of Cosines Identify isometries and find translation images of figures Find reflection images of figures Draw and identify rotation images of figures Find compositions of isometries, including glide reflections. Classify isometries. Identify congruence transformations. Prove triangle congruence using isometries. Understand dilation images of figures. Identify similarity transformations and verify properties of similarity. Chapter 6 Chapter 7 Find the sum of the measures of the interior and exterior angles of a polygon. Use relationships among sides and angles and among diagonals of a parallelogram. Determine whether a quadrilateral is a parallelogram Define and classify special types of parallelograms. Use properties of diagonals of rhombuses and rectangles. Verify and use properties of trapezoids and kites. Classify polygons in the coordinate plane Name coordinates of special figures by using their properties Prove theorems using figures in the coordinate plane Write ratios and solve proportions Identify and apply similar polygons Use AA, SAS and SSS similarity theorems. Use similarity to find indirect measurements Find and use relationships in similar right triangles Use the Side-splitter theorem and the Triangle-Angle- Bisector Theorem Chapter 10 Find the area of parallelograms and triangles Find area of a trapezoid, rhombus, or kite Find the area of a regular polygon Find the perimeters and areas of similar polygons Find areas of regular polygons and triangles using trigonometry Find the measures of central angles and arcs; find the circumference and arc length Find areas of circles, sectors, and segments of circles Use segment and area models to find the probabilities of events 8
(continued) For entry into Honors Algebra II Topics taught in Honors Geometry Chapter 11 Recognize polyhedra and their parts; visualize cross sections of space figures Find surface area of prisms and cylinders Find surface area of pyramids and cones Find volumes of prisms and cylinders Find volumes of pyramids and cones Find surface area and volume of a sphere Compare and find areas and volumes of similar solids Chapter 12 Use properties of a tangent to a circle Use congruent chords, arcs, and central angles Find the measure of an inscribed angle; find the measure of and angle formed by a tangent and a chord. Find measures of angles formed by chords, secants, and tangents. Find lengths of segments associated with a circle Write the equation of a circle;find the center and radius of a circle Draw and describe a locus Chapter 13 Calculate experimental and theoretical probability Make and use frequency tables and probability distributions Use permutations and combinations to solve problems Identify independent and dependent events; find compound probabilities Construct and use probability models Understand and calculate conditional probabilities Understand random numbers; use probabilities in decision-making 9
For Entry into Honors Math Analysis Topics taught in Honors Algebra II Textbook: Algebra & Trigonometry by Blitzer, Prentice Hall, 2010 Prerequisite Chapter Chapter 1 OBJ P.1: Evaluate and simplify algebraic expressions. Recognize subsets and identify properties of real numbers. Use inequality symbols. Evaluate absolute value and use it to express distance. OBJ P.2: Use the product, quotient, zero-exponent, negative-exponent, and power rules. Find the power of a product and quotient. Simplify exponential expressions. Use scientific notation. OBJ P.3: Evaluate and simplify square roots. Add and subtract square roots. Rationalize denominators. Understand and use rational exponents. OBJ P.4: Add, subtract, and multiply polynomials. Perform operations with polynomials in several variables. OBJ P.5: Use various techniques to factor polynomials. Factor algebraic expressions containing fractional and negative exponents. OBJ P.6: Specify numbers that must be excluded from the domain of a rational expression. Simplify, multiply, divide, add, and subtract rational expressions. Simplify complex rational expressions. OBJ 1.1: Plot points and graph equations in the rectangular coordinate system. Use a graph to determine intercepts. Interpret information given by graphs. OBJ 1.2: Solve linear equations in one variable and those containing fractions. Solve rational equations with variables in the denominators. Recognize identities, conditional equations, and inconsistent equations. Solve applied problems using mathematical models. OBJ 1.3: Use linear equations to solve problems. Solve a formula for a variable. OBJ 1.4: Add, subtract, multiply, and divide complex numbers. Perform operations with square roots of negative numbers. Chapter1 continued Chapter2 OBJ 1.5: Solve quadratic equations by factoring, using the square root property, completing the square, and using the Quadratic Formula. Use the discriminant to determine the number and type of solutions. Solve problems modeled by quadratic equations. OBJ 1.6: Solve equations that involve factoring, radicals, rational exponents, quadratic type, and absolute value. Solve problems modeled by equations. OBJ 1.7: Use interval notation. Find intersections and unions of intervals. Solve linear, compound, and absolute value inequalities. Recognize inequalities with no solution or all real numbers as solutions. OBJ 2.1: Find the domain and range of a relation. Determine whether a relation is a function and whether an equation represents a function. Evaluate a function. Graph a function by plotting points and obtain information about the function, including its domain, range, and intercepts. Use the Vertical Line Test to identify functions. OBJ 2.2: Identify intervals on which a function increases, decreases, or is constant. Use graphs to locate relative maxima or minima. Identify even or odd functions and recognize their symmetries. Understand and use piecewise functions. Find and simplify a function s difference quotient. OBJ 2.3: Calculate a line s slope. Write the point-slope form of the equation of a line. Write and graph the slope-intercept form of the equation of a line. Graph horizontal and vertical lines. Recognize and use the general form of a line s equation, and use intercepts to graph it. Model data with linear functions and make predictions. OBJ 2.4: Find slopes and equations of parallel and perpendicular lines. Interpret slope as rate of change. Find a function s average rate of change. 10
For entry into Honors Math Analysis (continued) Chapter2 continued Chapter 3 OBJ 2.5: Recognize graphs of common functions. Use vertical / horizontal shifts, reflections, and vertical / horizontal stretching and shrinking to graph functions. Graph functions involving a sequence of transformations. OBJ 2.6: Find the domain of a function. Combine functions using the algebra of functions, specifying domains. Form and determine the domain for composite functions. Write functions as compositions. OBJ 2.7: Verify inverse functions. Find the inverse of a function and graph both functions on the same axes. Use the horizontal line test to determine if a function has an inverse. Use the graph of a one-to-one function to graph its inverse function. OBJ 2.8: Find the distance between two points. Find the midpoint of a line segment. Write the standard form of a circle s equation. Give the center and radius of a circle whose equation is in standard form. Convert the general form of a circle s equation to standard form. OBJ 3.1: Recognize characteristics of, and graph, parabolas. Determine a quadratic function s minimum and maximum values, and solve problems involving them. OBJ 3.2: Identify polynomial functions and recognize characteristics of their graphs. Determine end behavior. Use factoring to find zeros of polynomial functions and identify their multiplicities. Use the Intermediate Value Theorem. Understand the relationship between degree and turning points. Graph polynomial functions. OBJ 3.3: Use long and synthetic division to divide polynomials. Evaluate a polynomial using the Remainder Theorem. Use the Factor Theorem to solve a polynomial equation. OBJ 3.4: Use the Rational Zero Test to find possible rational zeros of polynomial functions. Solve polynomial equations. Use the Linear Factorization Theorem to find polynomials with given zeros. Use Descartes Rule of Signs. Chapter 3 continued Chapter 11 Chapter 4 OBJ 3.5: Find the domains of rational functions. Use arrow notation. Identify vertical and horizontal asymptotes. Use transformations to graph rational functions. Identify slant asymptotes. Solve applied problems involving rational functions. OBJ 3.6: Solve polynomial inequalities. Solve rational inequalities. Solve problems modeled by polynomial and rational inequalities. OBJ 3.7: Solve direct, inverse, combined, and joint variation problems. OBJ 11.6: Use the Fundamental Counting Principle. Use the permutations and combinations formula. Distinguish between permutation problems and combination problems. OBJ 11.7: Compute empirical probability. Compute theoretical probability. Find the probability that an event will not occur, that one event or a second event occurring, or one event and a second event were occurring. OBJ 4.1: Evaluate and graph exponential functions. Evaluate functions with base e. Use compound interest formulas. OBJ 4.2: Change from logarithmic form to exponential form and vice-versa. Evaluate logarithms. Use basic logarithmic properties. Graph a logarithmic function and find its domain. Use common and natural logarithms. OBJ 4.3: Use the product, quotient, and power rules. Expand and condense logarithmic expressions. Use the change-of-base property. OBJ 4.4: Use like bases and logarithms to solve exponential equations. Use the definition of a logarithm and the one-to-one property of logarithms to solve logarithmic equations. 11
For entry into Honors Math Analysis (continued) Chapter 5 OBJ 5.1: Recognize and use the vocabulary of angles. Use degree and radian measure. Convert between radians and degrees. Draw angles in standard position. Find coterminal angles and length of a circular arc. Use linear and angular speed to describe motion on a circular path. OBJ 5.2: Use right triangles to evaluate trigonometric functions and to solve applied problems. Find function 0 values for 0 30, 0 45, and 60. Recognize and 6 4 3 use fundamental identities. Use equal cofunctions of complements. Evaluate trigonometric functions with a calculator. OBJ 5.3: Use the definitions of trigonometric functions of any angle. Use the signs of the trigonometric functions. Find reference angles. Use reference angles to evaluate trigonometric functions. OBJ 5.4: Use a unit circle to define trigonometric functions of real numbers. Recognize the domain and range of sine and cosine functions. Use even and odd trigonometric functions. Use periodic properties. OBJ 5.5: Understand the graph of y = sin x and y = cos x. Graph variations of y = sin x and y = cos x. Use vertical shifts of sine and cosine curves. Model periodic behavior OBJ 5.8: Solve a right triangle. Chapter 8 continued Chapter 10 OBJ 8.4: Recognize systems of nonlinear equations in two variables. Solve nonlinear systems by substitution and addition. Solve problems using systems of nonlinear equations OBJ 8.5: Graph a linear and nonlinear inequality in two variables. Use mathematical models involving linear inequalities. Graph a system of inequalities. OBJ 8.6: Write an objective function describing a quantity that must be maximized or minimized. Use inequalities to describe limitations in a situation. Use linear programming to solve problems. OBJ 10.1: Graph ellipses centered and not centered at the origin. Write equations of ellipses in standard form. Solve applied problems involving ellipses. OBJ 10.2: Locate a hyperbola s vertices and foci. Write equations of hyperbolas in standard form. Graph hyperbolas centered and not centered at the origin. Solve applied problems involving hyperbolas. OBJ 10.3: Graph parabolas with vertices at the origin and not at the origin. Write equations of parabolas in standard form. Solve applied problems involving parabolas Chapter 8 OBJ 8.1: Decide whether an ordered pair is a solution of a linear system. Solve linear systems by substitution and addition. Identify systems that do not have exactly one ordered-pair solution. Solve problems using systems of linear equations. OBJ 8.2: Verify the solutions of a system of linear equations in three variables. Solve systems of linear equations in three variables. Solve problems using systems in three variables. OBJ 8.3: Decompose P, where Q has only distinct linear Q factors, repeated linear factors, non-repeated prime quadratic factor, or a prime repeated quadratic factor 12
For Entry into AP Calculus AB (EXTRA topics for entry into AP Calculus BC are starred) Topics taught in Precalculus and/or Honors Math Analysis Textbook: Precalculus; Prentice Hall, 2007 P.1 P.4 Solve Equations Complex Numbers Solve Inequalities Modeling Functions all concepts for entry into AP Calculus AB Solve equations: linear, quadratic, absolute value, and radical Parametric Equations* Inverse Functions Transformations Linear and Quadratic Functions Compute with complex numbers; find complex zeros of quadratic functions Solve inequalities: quadratic, absolute value, polynomial and rational Use tables, graphs, equations to model and solve real-world problems Represent functions numerically, algebraically, and graphically Determine domain and range Analyze characteristics of functions: exteme values, symmetry, asymptotes, end behavior Recognize graphs of basic functions and combine to create new functions Determine compositions of functions and effects on the domain Graph, write and solve parametric equations Find the inverse of a relation. Determine if a function is one-to-one Algebraically verify that two functions are inverses of each other Algebraically and graphically represent transformations Recognize and graph linear and quadratic functions, and use them to model and solve real world situations Polynomial, Power and Rational Functions Sketch the graph of polynomial functions. Predict end behavior of polynomial functions Find the real zeros of polynomial functions Divide a polynomial using long or synthetic division Apply the Remainder and Factor Theorems Use Descartes Rule of Signs to determine number of possible positive and negative real roots. Test if an integer is a lower or upper bound. Factor polynomials and determine all complex zeros Exponential and Logarithmic Functions Describe the graph of a basic rational function using transformations. Identify horizontal and vertical asymptotes and end behavior models Sketch the graph of rational functions. Use the end behavior model to determine if a rational function has a horizontal asymptote and what that asymptote is. Solve equations and inequalities involving polynomials and rational functions using both algebraic and graphical techniques Evaluate exponential expressions Identify and graph exponential and logistic functions Identify and graph logarithmic functions Convert equations between exponential and logarithmic form Evaluate common and natural logarithms Apply properties of logarithms to expand exponential and logarithmic expressions Solve exponential and logarithmic equations Use exponents and logarithms to solve real world problems (growth, decay, regression, compound interest, annuities) 13
For entry into AP Calculus AB or BC* o Discrete Math* Use the counting principle to solve problems Determine permutations and combinations. Use Pascal's Triangle to expand powers of binomials. Use the binomial formula to determine the binomial coefficients and expand binomial powers. Solve probability problems using basic definition and counting principle and binomial formula Determine if two events are mutually exclusive or independent and use the appropriate rules to determine probabilities Express arithmetic and geometric sequences explicitly and recursively Find the limit of convergent sequences Use summation notation Find finite sums of terms of arithmetic and geometric sequences Find sums of convergent geometric series Use principles of mathematical induction to prove mathematical generalizations. Distinguish between categorical and quantitative variables in data Use various graphs to display data: scatterplot, box plot, normal distribution curve Use measures of center, the five-number summary, standard deviation to describe quantitative data Trigonometric Functions Analytic Trigonometry Convert between radian and degrees; find arc length, convert to nautical miles and trace a path using a compass bearing Define the six trigonometric functions using the lengths of the sides of a right triangle. Solve problems involving the trigonometric functions of real numbers and the properties of sine and cosine as periodic functions. Graph the six trigonometric functions and various transformations of these functions Graph combinations of trigonometric and algebraic functions Use periodic functions and trigonometry to solve real world problems. Use fundamental identities to simplify trigonometric expressions and solve trigonometric equations. Verify identities using the basic trig identities. State and apply sum/ difference, double-angle, power-reducing, and half-angle identities. Solve trigonometric equations for a restricted value or for all possible values. Use Law of Sines to solve triangles and real world problems. Determine the number of triangles and the ambiguous case. Use the Law of Cosines to solve triangles and real world problems. Find the area of a triangle using sines or Heron's formula. 14
For entry into AP Calculus AB or BC Applications of Trigonometry Apply arithmetic of vectors and use to solve real world problems Calculate the dot product of vectors Graph curves parametrically Solve motion problems using parametric equations Convert points and equations from polar to rectangular coordinates and vice versa Graph polar equations Determine maximum r-value and symmetry of a polar graph Represent complex numbers in trig form and perform operations on them. Use DeMoivre's theorem Find the nth roots of a complex number Introduction to Calculus* Calculate instantaneous velocities and derivatives using limits Calculate definite integrals using areas Use the properties of limits and evaluate onesided limits, two-sided limits, and limits involving infinity Estimate derivatives and integrals using numerical techniques Systems and Matrices* Conics (Analytic Geometry) Solve systems of equations algebraically and graphically Find sums, differences, products and inverses of matrices Solve linear systems using Gaussian elimination, the row echelon elimination or an inverse matrix. Decompose rational expressions into partial fractions Solve linear programming problems and systems of linear inequalities Write equations for conic sections in standard form: parabola, ellipse, hyperbola Identify key features of a conic (focus (foci), directrix, vertices) and use to graph conic sections by hand Graph conic sections involving transformations. Draw three dimensional figures and analyze vectors in space 15