Honors Precalculus - HIGH SCHOOL INFORMATION AV · 1. Apply critical thinking skills to precalculus topics: analytic geometry, algebraic functions, trigonometric functions, complex

Honors Precalculus Gorman Learning Center (052344)

Basic Course Information

Title: Honors Precalculus Transcript abbreviations: H Pre Calc A / H Pre Calc B Length of course: Full Year Subject area: Mathematics ("c") / Advanced Mathematics UC honors designation? Yes Prerequisites: ALgebra 1 (Required) Geometry (Required) Algebra 2 (Required) Co-requisites: None Integrated (Academics / CTE)? No Grade levels: 10th, 11th, 12th Course learning environment: Classroom Based

Course Description

Course overview:

This rigorous, honors course is an in-depth preparation for Calculus and, in fact, includes some introductory Calculus topics. It concentrates on properties and language of algebraic, exponential, and logarithmic functions, conic sections with an emphasis on circular and trigonometric functions and their applications, limits of sequences, series, and an introduction to the concept of limits through sequences and series functions and derivatives and their applications is introduced in the second half of the course. Analytic geometry is studied using a vector approach. Problem solving techniques are emphasized and more challenging problems are explored. Instructor-approved graphing calculator is required.

This course combines many of the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus and strengthens their conceptual understanding of problems and mathematical reasoning in solving problems. Precalculus uses the techniques that students have previously learned from the study of algebra and geometry and apply those to more analytical and advanced trigonometric and algebraic manipulations. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Students learn the techniques of matrix manipulation so that they can solve systems of linear equations in any number of variables. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college. To achieve this knowledge, numerous applications, examples, graphical interpretations, and multi-level exercises are presented. Topics include angles, arcs, and sectors, trigonometric functions, triangle trigonometry, properties of functions, inverse and logarithmic functions, polar coordinates, vectors, the binomial theorem, polar coordinates, conic sections, parametric equations, sequences, and series. Technology is integrated throughout to prepare the student for participation in a technological society. Communication skills are stressed—emphasizing reading, writing, discussion, and visual thinking.

Upon completion of course, students will be able to:

1. Apply critical thinking skills to precalculus topics: analytic geometry, algebraic functions, trigonometric functions, complex numbers, vectors, and sequences and series

2. Discuss non-routine and open-ended precalculus problems in collaborative teams, verbalizing concepts, solution strategies and constructing written solutions

3. Compare and contrast different approaches to problems; discuss the relative merit of each method

4. Use technology to solve applied mathematical problems

5. Develop collaborative working relationships with other students

6. Select appropriate problem solving strategies for a given application

7. Adapt general problem solving techniques to a specific application

8. Analyze different forms of solutions to determine which are equivalent

9. Organize a portfolio of problem-solving situations and related solutions Course content: Unit 1

Module 1:

Students will complete weekly Precalculus with Limits readings and will engage in problem solving, answer critical thinking questions, conduct applied and sometimes open-ended mathematics investigations, complete chapter quizzes and chapter assessments (with questions from publisher, SAT Math 2 sample subject tests, and “Smarter Balanced”-style exams) on:

Diagnostic review topics; Lines in the Plane; Functions and Their Graphs—

Rectangular Coordinates, Graphs of Equations, Analyzing Graphs of Functions; Shifting, Reflecting, and Stretching Graphs; Transformations of Functions; Mathematical Modeling and Variation; Combinations of Functions; Inverse Functions; Constructing scatter plots and interpreting correlation; Using scatter plots and a graphing utility to find linear models for data; Quadratic Functions and Models; Polynomial Functions of Higher Degree.

Upon completion of Module 1, students will be able to:

Find the slopes of lines; write linear equations given points on lines and their slopes.

Use slope-intercept forms of linear equations to sketch lines; use slope to identify parallel and perpendicular lines.

Decide whether relations between two variables represent a function; use function notation and evaluate functions.

Find the domains of functions; use functions to model and solve real-life problems. Evaluate difference quotients.

Find the domains and ranges of functions and use the Vertical Line Test for functions; determine intervals on which functions are increasing, decreasing, or constant.

Determine relative maximum and relative minimum values of functions; identify and graph step functions and other piecewise-defined functions.

Identify even and odd functions.

Recognize graphs of common function; use vertical and horizontal shifts and reflections to graph functions.

Use nonrigid transformations to graph functions.

Add, subtract, multiply, and divide functions; find compositions of one function with another function.

Use combinations of functions to model and solve real-life problems.

Find inverse functions informally and verify that two functions are inverse functions of each other.

Use graphs of functions to decide whether functions have inverse functions.

Determine if functions are one-to-one; find inverse functions algebraically.

Module 2:


Polynomial and Rational Functions:

Quadratic Functions; Polynomial Functions of Higher Degree—Polynomial and Synthetic Division; Complex Numbers; Zeros of Polynomial Functions.

Real Zeros of Polynomial Functions; Complex Numbers—Rational Functions; Nonlinear Inequalities.

The Fundamental Theorem of Algebra; Rational Functions and Asymptotes—Exponential Functions and Their Graphs; Logarithmic Functions and Their Graphs; Properties of Logarithms. Graphs of Rational Functions; Exploring Data: Quadratic Models—Exponential and Logarithmic Equations; Exponential and Logarithmic Models.


Analyze graphs of quadratic functions; write quadratic functions in standard from and use the results to sketch graphs of functions.

Find minimum and maximum values of functions in real-life applications.

Use transformations to sketch graphs of polynomial functions; use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions.

Find and use zeros of polynomial functions as sketching aids; use the Intermediate Value Theorem to help locate zeros of polynomial functions.

Use long division to divide polynomials by other polynomials; use synthetic division to divide polynomials by binomials of the form (x-k).

Use the Remainder and Factor Theorems; use the Rational Zero Test to determine possible rational zeros of polynomials functions.

Use Descarte's Rule of Signs and the Upper and Lower Bound Rules to find zeros of polynomials.

Use the imaginary unit / to write complex numbers; add, subtract, and multiply complex numbers.

Use complex conjugates to write the quotient of two complex numbers in standard form; plot complex numbers in the complex plane.

Use the Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function; find all zeros of polynomial functions, including complex zeros.

Find conjugate pairs of complex zeros; find zeros of polynomials by factoring.

Find the domains of rational functions; find horizontal and vertical asymptotes of graphs of rational functions. Use rational functions to model and solve real-life problems.

Analyze and sketch graphs of rational functions; sketch graphs of rational functions that have slant asymptotes. Use rational functions to model and solve real-life problems.

Classify scatter plots; use scatter plots and a graphing utility to find quadratic models for data.

Choose a model that best fits a set of data.

Module 3:


Exponential and Logarithmic Functions:

Exponential Functions and Their Graphs; Logarithmic Functions and Their Graphs—

Trigonometric Functions—The Unit Circle; Right Triangle Trigonometry; Trigonometric Functions of Any Angle; Radian and Degree Measure; Solving Trigonometric Equations; Sum and Difference Formulas; Multiple Angle and Product-Sum Formulas.

Properties of Logarithms; Solving Exponential and Logarithmic Equations—

Graphs of Sine and Cosine Functions; Graphs of Other Trigonometric Functions; Inverse Trigonometric Functions; Applications and Models.

Exponential and Logarithmic Models; Exploring Data: Nonlinear Models—

Using Fundamental Identities; Verifying Trigonometric Identities.

During Module 3 students also complete:

Mid-term Exam

Portfolio project development.


Recognize and evaluate exponential functions with base a; graph exponential functions.

Recognize, evaluate, and graph exponential functions with base e; use exponential functions to model and solve real-life problems.

Recognize and evaluate logarithmic functions with base a; graph logarithmic functions.

Recognize, evaluate, and graph natural logarithmic functions; use logarithmic functions to model and solve real-life problems.

Rewrite logarithms with different bases; use properties of logarithms to evaluate or rewrite logarithmic expressions.

Use properties of logarithms to expand or condense logarithmic expressions; use logarithmic functions to model and solve real-life problems.

Solve simple exponential and logarithmic equations; solve more complicated exponential equations.

Solve more complicated logarithmic equations; use exponential and logarithmic equations to model and solve real-life problems.

Recognize the five most common types of models involving exponential or logarithmic functions; use exponential growth and decay functions to model and solve real-life problems.

Use Gaussian functions to model and solve real-life problems; use logistic growth functions to model and solve real-life problems.

Use logarithmic functions to model and solve real-life problems.

Classify scatter plots; use scatter plots and a graphing utility to find models for data and choose a model that best fits a set of data.

Use a graphing utility to find exponential and logistic models for data.

Describe angles; user radian measure.

Use degree measure and convert between degree and radian measure; use angles to model and solve real-life problems.

Identify a unit circle and describe its relationship to real numbers; evaluate trigonometric functions using the unit circle.

Use domain and period to evaluate sine and cosine functions; use a calculator to evaluate trigonometric functions.

Module 4:


Trigonometric Functions:

Right Triangle Trigonometry; Trigonometric Functions of Any Angle.

Graphs of Sine and Cosine Functions; Graphs of Other Trigonometric Functions.—Law of Sines, Law of Cosines, Vectors in the Plane Vectors and Dot Products,

Inverse Trigonometric Functions; Applications and Models,—Trigonometric Form of a Complex Number.

Analytic Trigonometry:

Using Fundamental Identities; Verifying Trigonometric Identities.


Evaluate trigonometric functions of acute angles; use the fundamental trigonometric identities.

Use a calculator to evaluate trigonometric functions; use trigonometric functions to model and solve real-life problems.

Evaluate trigonometric functions of any angle; use reference angles to evaluate trigonometric functions. Evaluate trigonometric functions of real numbers.

Sketch the graphs of basic sine and cosine functions; use amplitude and period to help sketch the graphs of sine and cosine functions.

Sketch translations of graphs of sine and cosine functions; use sine and cosine functions to model real-life data. Sketch the graphs of tangent functions; sketch the graphs of cotangent functions.

Sketch the graphs of secant and cosecant functions; sketch the graphs of damped trigonometric functions.

Evaluate inverse sine functions; evaluate other inverse trigonometric functions. Evaluate compositions of trigonometric functions.

Solve real-life problems involving right triangles; solve real-life problems involving directions bearings. Solve real-life problems involving harmonic motion.

Recognize and write the fundamental trigonometric identities.

Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions.

Verify trigonometric identities.

Evaluate inverse sine functions; evaluate other inverse trigonometric functions. Evaluate compositions of trigonometric functions.

Solve real-life problems involving right triangles.

Solve real-life problems involving directions bearings. Solve real-life problems involving harmonic motion.

Module 5:


Analytic Trigonometry:

Multiple-Angle and Product-to-Sum Formulas.

Solving Trigonometric Equations; Sum and Difference Formulas.

Additional Topics in Trigonometry:

Law of Sines—Areas of Oblique Triangles, solve real life problems on location, measuring distance, angles of evaluation, altitude, engineering and design.

Law of Cosines; Vectors in the Plane—Linear and Nonlinear Systems of Equations; Two-Variable Linear Systems; Multi-Variable Linear Systems.

Vectors and Dot Products—Trigonometric Form of a Complex Number—Partial Fractions; Systems of Inequalities; Linear Programming.


Use standard algebraic techniques to solve trigonometric equations; solve trigonometric equations of quadratic type.

Solve trigonometric equations involving multiple angles; use inverse trigonometric functions to solve trigonometric equations.

Use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations. Use multiple-angle formulas to rewrite and evaluate trigonometric functions; use power-reducing formulas to rewrite and evaluate trigonometric functions.

Use half-angle formulas to rewrite and evaluate trigonometric functions; use product-to-sum and sum-to-product formulas to rewrite and evaluate trigonometric functions.

Use the Law of Sines to solve oblique triangles (AAS or ASA); use the Law of Sines to solve oblique triangles (SSA).

Find areas of oblique triangles; us the Law of Sines to model and solve real-life problems.

Use the Law of Cosines to solve oblique triangles (SSS or SAS); use the Law of Cosines to model and solve real-life problems on mapping routes and location, measuring distance, alngles of evlaulation, altitutde, engineering and design.

Use Heron's Area Formula to find areas of triangles.

Represent vectors as directed line segments; write the component from of vectors.

Write vectors as linear combinations of unit vectors; find the direction angles of vectors. Use vectors to model and solve real-life problems.

Find the dot product of two vectors and use properties of the dot product; find angles between vectors and determine whether two vectors are orthogonal.

Write vectors as sums of two vector components; use vectors to find the work done by a force.

Find absolute values of complex numbers; multiply and divide complex numbers written in trigonometric form. Write trigonometric forms of complex numbers; use DeMoivre's Theorem to find powers of complex numbers. Find nth roots of complex numbers.

In Module 5 students will also complete:

Portfolio Preparation

Cumulative Final Exam Chapters 1-6

Portfolio Presentation

Portfolio Submission

Self-Reflection Analysis

Module 6:


Linear Systems and Matrices:

Solving Systems of Equations; Systems of Linear Equations in Two Variables—Matrices and Systems of Equations; Operations with Matrices; The Inverse of a Square Matrix; The determinant of a Square Matrix.

Operations with Matrices Linear Systems and Matrices—Applications of Matrices and Determinants Sequences and Series; Arithmetic Sequences and Partial Sums; Geometric Sequences and Series.


Use the method of substitution and the graphical method to solve systems of equations in two variables; use systems of equations to model and solve real-life problems.

Use the method of elimination to solve systems of linear equations in two variables; graphically interpret the number of solutions of a system of linear equations in two variables.

Use systems of linear equations in two variables to model and solve real-life problems.

Use back-substitution to solve linear systems in row-echelon form; use Gaussian elimination to solve systems of linear equations.

Solve nonsquare systems of linear equations; graphically interpret three-variable linear systems.

Use systems of linear equations to write partial fraction decompositions of rational expressions; use systems of linear equations in three or more variables to model and solve real-life problems.

Write matrices and identify their orders; perform elementary row operations on matrices.

Use matrices and Gaussian elimination to solve systems of linear equations; use matrices and Gauss-Jordan elimination to solve systems of linear equations.

Decide whether two matrices are equal; add and subtract matrices and multiply matrices by a scalar.

Multiply tow matrices; use matrix operations to model and solve real-life problems.

Verify that two matrices are inverses of each other; use Gauss-Jordan elimination to find inverse of matrices.

Use a formula to find inverses of 2x2 matrices; use inverse matrices to solve systems of linear equations.

Find the determinants of 2x2 matrices; find minors and cofactors of square matrices. Find the determinants of square matrices; find the determinants of triangular matrices.

Use determinants to find areas of triangles; use determinants to decide whether points are collinear. Use Cramer's Rule to solve systems of linear equations; use matrices to encode and decode messages.

During Module 7 students also complete:

Mid-term Exam

Portfolio project development.

Module 7:


Sequences, Series, and Probability:

Sequences and Series; Arithmetic Sequences and Partial Sums—Mathematical Induction; The Binomial Theorem Counting Principles.

Geometric Sequences and Series—factorial notation, calculating and writing the nth term; using mathematical induction to prove statements and to find finite differences of sequences.

The Binomial Theorem; Counting Principles— using the Binomial Theorem to calculate binomial coefficients, how using Pascal’s Triangle, using permutations and combinations; probability of mutually exclusive, independent and complements of events.

Topics in Analytic Geometry:

Introduction to Conics— Lines, Parabolas, Ellipses, Hyperbolas, Rotation of ConicsUpon completion of Module 7, students will be able to:

Use sequence notation to write the terms of sequences; use factorial notation.

Use summation notation to write sums; find sums of infinite series; use sequences and series to model and solve real-life problems.

Recognize, write, and find the nth terms of arithmetic sequences; find nth partial sums of arithmetic sequences. Use arithmetic sequences of model and solve real-life problems.

Recognize, write, and find the nth terms of geometric sequences; find nth partial sums of geometric sequences. Find sums of infinite geometric series.

Use geometric sequences to model and solve real-life problems.

Use mathematical induction to prove statements involving a positive integer n; find the sums of powers of integers.

Find finite differences of sequences.

Use the Binomial Theorem to calculate binomial coefficients; Use Pascal's Triangle to calculate binomial coefficients.

Use binomial coefficients to write binomial expansions.

Solve simple counting problems; use the Fundamental Counting Principle to solve more complicated counting problems.

Use permutations to solve counting problems; use combinations to solve counting problems.

Find probabilities of events; find probabilities of mutually exclusive events.

Find probabilities of independent events; find probabilities of complements of events.

Recognize a conic as the intersection of a plane and a double-napped cone; write equations of parabolas in standard form.

Use the reflective property of parabolas to solve real-life problems.

Module 8:


Topics in Analytic Geometry:

Rotation and Systems of Quadratic Equations—Parametric Equations.

More on Conics—Ellipses; Hyperbolas; Parametric Equations; Polar Coordinates; Graphs of Polar Equations; Polar Equations of Conics; The Three Dimensional Coordinate System; Vectors in Space.


Write equations of ellipses in standard form; use properties of ellipses to model and solve real-life problems. Find eccentricities of ellipses.

Write equations of hyperbolas in standard form; find asymptotes of hyperbolas; use properties of hyperbolas to solve real-life problems. Classify conics from their general equations.

Rotate the coordinate axes to eliminate the xy-term in equations of conics; use the discriminant to classify conics.

Solve systems of quadratic equations.

Evaluate sets of parametric equations for given values of the parameter; graph curves that are represented by sets of parametric equations.

Rewrite sets of parametric equations as single rectangular equations by eliminating the parameter; find sets of parametric equations for graphs.

Plot points and find multiple representations of points in the polar coordinate system; convert points from rectangular to polar form and vice versa.

Convert equations from rectangular to polar form and vice versa.

Graph polar equations by point plotting; use symmetry as a sketching aid.

Use zeros and maximum r-values as sketching aids; recognize special polar graphs.

Module 9:


Analytic Geometry in Three Dimensions:

The Three-Dimensional Coordinate Plane—Vectors in Space; The Cross Product of Two Vectors; Lines and Planes in Space;

Limits and an Introduction to Calculus:

Introduction to Limits; Techniques for Evaluating Limits; The Tangent Line Problem.


Review for Final Exam

Prep for SAT Subject Tests


Define conics in terms of eccentricities; write and graph equations of conics in polar form. Use equations of conics in polar form to model real-life problems.

Plot points in the three-dimensional coordinate system; find distances between points in space and find midpoints of line segments joining points in space.

Write equations of spheres in standard form and find traces of surfaces in space.

Find the component forms of, the unit vectors in the same direction of, the magnitudes of, the dot products of, and the angles between vectors in space.

Determine whether vectors in space are parallel or orthogonal; use vectors in space to solve real-life problems.

Find cross products of vectors in space; use geometric properties of cross products of vectors in space.

Use triple scalar products to find volumes of parallelepipeds.

Find parametric and symmetric equations of lines in space; find equations of planes in space. Sketch planes in space; find distances between points and planes in space.

Use the definition of a limit to estimate limits; determine whether limits of functions exist. Use properties of limits and direct substitution to evaluate limits.

Module 10:


Limits and an Introduction to Calculus:

Techniques for Evaluating Limits—More on The Tangent Line Problem; Limits at Infinity; Limits of Sequences; The Area Problem.


SAT Subject test or mock Test

Portfolio Preparation


Portfolio Submission

Self-Reflection Analysis

Cumulative Written Final Exam (including applied Smarter Balanced-style problem solving format)


Use the dividing out technique to find limits of functions; use the rationalizing technique to find limits of functions.

Approximate limits of functions graphically and numerically; evaluate one-sided limits function. Evaluate limits of difference quotients from calculus.

Use a tangent line to approximate the slope of a graph at a point; use the limit definition of slope to find exact slopes of graphs.

Find derivatives of functions and use derivatives to find slopes of graphs.

Evaluate limits of functions at infinity; find limits of sequences.

Find limits of summations; use rectangles to approximate areas of plane regions. Use limits of summations to find areas of plane regions.

Successfully complete SAT subject tests in mathematics.

Think mathematically and apply Precalculus and some Calculus to solve real-life problems.

Unit 2

Students will complete Precalculus with Limits: A Graphing Approach readings to engage in problem solving involving detailed mathematical calculations daily. Much attention is paid to using the graphing calculator as a tool. In tandem with chapter and supplemental readings, students will be assigned Problems of the Week (POW) critical thinking, problem solving questions, which require written analyses to support findings, frequently derived from complex calculations connected to other subject areas including physical and biological sciences, navigation, finance and economics, and other real world statistical analyses. All daily problem sets include applied, “real world” quantitative reasoning problems as well as questions that introduce SAT- and/or Smarter Balanced-style question sets (multiple choice, short answer, and team problem solving activities.)

Students complete self-check quizzes weekly.

Students are frequently asked to self-check answers and analyze, “What went wrong” and compose written analyses explaining their missteps in problem solving when applicable.

Students conduct mathematical investigations and compose formal write-ups in portfolios which they present each semester.

Students design and implement demonstrations/models to illustrate key concepts. (One+ per semester.)

Students complete reflective, written self-evaluations each term.

Unit 3

Students complete a variety of formative and summative assessments each semester.

Homework

Homework is expected to be self-corrected, which is checked for completion. Select problems are checked and scored for accuracy and self-evaluation each week.

Class Work

Students are graded on participation of Problems of the Week and other practical, modeling assignments, since so much class time is devoted to them.

Quizzes, Tests/Exams

Students complete section regular quizzes, chapter tests, a mid-term exam, and a final exam each semester. Tests include SAT-style Short Answer and Smarter Balanced-style applied mathematics questions.


Portfolios are assessed both throughout and at the end of the semester. Modeling demonstrations are included in portfolio presentations and graded each semester.

Self-Evaluation

Students complete self-evaluations weekly, when reviewing homework answers and complete written, self-reflective analyses of progress and “polish” each semester.

(Rubrics are employed to evaluate performance and skill-based learning goals.)

Unit 4

Honors Precalculus is intensely hands-on and student-driven and the role of the teacher in this course is one of a subject area specialist/facilitator, rather than as a lecturer, although of primary importance is the teacher’s role in presenting new material, demonstrations, and monitoring students’ paths of inquiry. Very little content delivery is through direct instruction and presentations with class time primarily being devoted to reviewing homework (with a close focus on self-evaluation efficacy of math applications) and on demonstrations and hands-on, group and individual problem solving tasks. Students are asked to be very self motivated and complete all research readings and follow up critical thinking questions (designed to cover and extend the content), almost entirely independently. Students are provided with syllabi of module content each month and are expected to stay on track with the fast-paced outline. Progress on homework assignments is monitored weekly and students have access to solution sets to self-evaluate, tutors, and subject area specialists to help guide research extension assignments and to support progress on daily assignments and SAT exam preparations as needed.

Honors Final Exam Details:

Honors Pre-Calculus

Final Exam

Gorman Learning Center

Use your paper as necessary and attach

1. 1. (5 points) Evaluate the function 2. b. c. d.

2. (5 points) Find the domain of the given function. Write your answer in interval notation. 3. b.

3. (15 points) Solve each exponential equation 4. b.

1. d.

4. (10 points) Solve for in degrees giving all solutions. 5. b. c. undefined

See next page

5. (5 points) Find the inverse of the function algebraically. Also find any restrictions on the domain of

the inverse function.

6. (5 points) Find the area of ABC if b = 32, c = 27, and = 108

7. (10 points) The path of a diver is approximated by where is the height

(in feet) and is the horizontal distance (in feet) from the end of a diving board. What is the

Maximum height of the diver?

8. (10 points) Evaluate the following 9.

See next page

9. (15 points) Use a graphing utility to graph the function and determine the open intervals on which the

function is increasing, decreasing or constant. Write your answers in interval notation. Also, identify

any relative minimum or relative maximum values of the function.

10. (10 points) Determine algebraically if the given function is even, odd or neither. 11. b. c.

11. (20 points) Use the first and second derivative to identify the local max and min, inflection point/s

and determine the intervals where the curve is concave up and concave down. Then graph the

function. (Do not use a graphing calculator)

Local Max_______________________

Local Min________________________

Pt. of Inflection___________________

Intervals:

Concave Up______________________

Concave Down____________________

See next page

12. (10 points) Solve for if

13. (10 points) A satellite in a circular orbit 1125 KM above a planet makes one complete revolution

Every 120 minutes. Assuming that the planet is a sphere of radius 6400 km, find the linear speed of

the satellite in kilometers per minute. Round your answer to the nearest whole number.

14. (15 points) Solve the logarithmic equations. 15. b. c.

15. (15 points) Convert the following into polar form: 16. b. c.

16. (10 points) Condense

1. b.

See next page

17. 17. (20 points) Given and

1. Describe the sequence of transformations (in order) from

1. Sketch the graph of below 2. Use function notation to write in terms of

18. (10 points) Find all real and imaginary roots of the following

19. (15 points) Given and. Find the indicated values in simplest form. 20. b. d.

See next page

20. (5 points) John stands 150 meters from a water tower and sights the top at an angle of elevation of

21. 36. How tall is the tower?

21. (10 points) Given , find 22. Amplitude_____________________ 23. Period________________________ 24. Phase Shift____________________ 25. Vertical Shift___________________ 26. (15 points) Given the series 27. Does it converge or diverge?

1. Find the sum, if possible.

23. (10 points) Find all real zeros of . Use the rational root theorem

and synthetic division.

See next page

24. (10 points) Convert the following into rectangular form. 25. b.

25. (15 points) Use the difference quotient, , to find the derivative.

26. (15 points) If 250 mg of ibuprofen has a half-life of 3 hours, then how much ibuprofen is in a person’s

bloodstream after the following:

1. 7 hours b. hours

See next page

27. (5 points) The point is on the terminal side of an angle in standard position. Determine the exact

values of the six trigonometric functions of the angle in simplified form.

28. (15 points) Simply the following:

1. b. ) c.

29. (15 points) If , find the following in form:

1. b. c.

30. (20 points) Find the equation of the tangent line to the given curve:

when

Course Materials

Textbooks

Title Author Publisher Edition Website Primary Precalculus with Limits: A Graphing Approach

Larson, Hostetler, Edwards

Houghton Mifflin College 5 [ empty

] Yes

Documents

Honors Precalculus - HIGH SCHOOL INFORMATION AV · 1. Apply critical thinking skills to precalculus topics: analytic geometry, algebraic functions, trigonometric functions, complex