Curriculum Map - West Point Public Schools

Town of West Point Public Schools

Pre-Calculus Dual Enrollment Curriculum Map

Version: December, 2012 Based on: Rappahannock Community College Curriculum and the Math Analysis SOLs Adopted, 2009

West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment Assessment Map *denotes assessment points with notes to guide assessment creation

STRAND/ TOPIC (Organizing Concepts)

FUNCTIONS

1st Quarter RCC.I.5 RCC.I.6 MA.1/RCC.I.8 MA.2/RCC.I.7 MA.3 RCC.I.9

2nd Quarter MA.2/RCC.I.7 MA.9/RCC.I.8

3rd Quarter RCC.II.1 RCC.II.7

ANALYTICAL GEOMETRY

Revised: Dec. 10, 2012

MA.7 – if time allows

MA.4 MA.5/RCC.II.13 RCC.II.14 RCC.II.15

DISCRETE MATHEMATICS

EQUATIONS

4th Quarter

RCC.I.1 RCC.I.3 RCC.I.4 RCC.I.10

RCC.I.1 MA.14 – systems only/RCC.I.2 RCC.I.10

MA.10 MA.12 RCC.II.9 MA.11/RCC.II.11 MA.13/RCC.II.8 RCC.II.2 RCC.II.3 RCC.II.4 RCC.II.5 RCC.II.6 RCC.II.12

MA.8/RCC.II.10

West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment Instructional Outline STRAND/ TOPIC

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

(Organizing Concepts)

Functions

RCC.I.5 RCC.I.6 MA.1/RCC.I.8 MA.2/RCC.I.7 MA.3 RCC.I.9

MA.2/RCC.I.7 MA.9/RCC.I.8

RCC.II.1 RCC.II.7

MA.4 MA.5/RCC.II.13 RCC.II.14 RCC.II.15

Discrete Mathematics

Equations


RCC.I.1 RCC.I.3 RCC.I.4 RCC.I.10

Analytical Geometry


RCC.I.1 MA.14 – systems only/RCC.I.2 RCC.I.10

MA.10 MA.12 RCC.II.9 MA.11/RCC.II.11 MA.13/RCC.II.8 RCC.II.2 RCC.II.3 RCC.II.4 RCC.II.5 RCC.II.6 RCC.II.12

MA.8/RCC.II.10

West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment 1st QUARTER - Pre-Calculus I (Math 163) STRAND/ TOPIC

SOL/ Objective #(s)

Essential Skills/Concepts


RCC.I.5

Identify functions graphically and algebraically and be able to determine their domain and range.

RCC.I.6

Perform operations on functions.

MA.1/ RCC.1.8

Determine graphs of polynomial and rational functions by exploring characteristics and components of the functions:  Identify a polynomial function or rational function, given an equation or graph  Sketch the graph of a polynomial or rational function  Identify zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes, points of discontinuity, end behavior, maximum and minimum points, intervals on which the function is increasing or decreasing Explain all general characteristics of polynomial functions and inverses of the functions, both with and without a graphing calculator.

Functions MA.2/ RCC.1.7 MA.3


Find compositions and inverses of functions and their domains and ranges. Be able to find inverse functions and explain the relationship of a function and its inverse. Investigate and describe the continuity of functions:  Investigate the continuity of absolute value, step, rational, and piece-wise functions  Use transformations to sketch absolute value, step, and rational functions  Verify the accuracy of the sketches by using a graphing calculator

Formative/Summative Assessments (Tests, Projects, etc.) Quizzes and tests when appropriate Vocabulary quizzes 9-week test Secret Message project Polynomial Equation – Volume of Box project

Instructional Resources SmartBoard Note packets Online notes

West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment STRAND/ TOPIC

SOL/ Objective #(s)


(Organizing Concepts) RCC.1.9

Equations

Use a graphing calculator to find curve of best fit when given real data.

RCC.I.1

Solve equations of various types and systems of equations, analytically and graphically.

RCC.I.3

Solve linear, quadratic, polynomial, and rational inequalities.

RCC.I.4

Solve problems involving complex numbers.

RCC.I.10

Solve real world problems using algebra.


Formative/Summative Assessments (Tests, Projects, etc.)

West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment 2nd QUARTER - Pre-Calculus I (Math 163) STRAND/ TOPICS

SOL/ Objective

#(s)



MA.2/ RCC.1.7

Find compositions and inverses of functions and their domains and ranges Be able to find inverse functions and explain the relationship of a function and its inverse.

MA.9/ RCC.1.8

Investigate and identify characteristics of exponential and logarithmic functions  Identify exponential and logarithmic functions from an equation or graph  Define e, and know its approximate value  Write logarithmic equations in exponential form and vice versa  Identify common and natural logarithms  Use laws of exponents and logarithms to solve equations and simplify expressions  Model practical problems using exponential and logarithmic functions  Graph exponential and logarithmic functions, using a graphing calculator  Identify asymptotes, intercepts, domain, and range Explain the general characteristics of exponential and logarithmic functions and the inverses of the functions, both with and without a graphing calculator.

Functions

RCC.1.1

Equations

Solve equations of various types and systems of equations, algebraically and graphically.

MA.14/ RCC.1.2

The student will use matrices to organize data and solve systems of equations. Explain the meaning of simultaneous equations and be able to translate them into matrix form and solve these matrices.

RCC.1.10

Solve real world problems using algebra.


Formative/Summative Assessments (Tests, Projects, etc.) Quizzes and tests when appropriate Vocabulary quizzes 18-week test


West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment 3rd QUARTER – Pre-Calculus II (Math 164) STRAND/ TOPIC

SOL/ Objective

#(s)


Functions


RCC.II.1

Explain the relationship between circular and trigonometric functions.

RCC.II.7 MA.10

Explain inverse functions as applied to trigonometric functions. Investigate and identify the characteristics of the graphs of polar equations: (using a graphing calculator)  Recognize polar equations (rose, limacon, lemniscate, spiral, and circle), given the graph or the equation  Determine the effects of changes in the parameters of polar equations on the graph, using a graphing calculator  Convert complex numbers from rectangular form to polar form and vice versa  Find the intersection of the graphs of two polar equations, using a graphing calculator

Equations MA.12

Use parametric equations to model and solve applications problems:  Graph parametric equations, using a graphing calculator  Use parametric equations to model motion over time  Determine solutions to parametric equations, using a graphing calculator  Compare and contrast traditional solution methods with parametric methods

RCC.II.9

Solve trigonometric equations.


Formative/Summative Assessments (Tests, Projects, etc.) Quizzes and tests when appropriate Vocabulary Quizzes 27-week test Flagpole project



SOL/ Objective


#(s)


MA.11/ RCC.II.11

Analytical Geometry MA.13/ RCC.II.8

RCC.II.2 RCC.II.3 RCC.II.4 Revised: Dec. 10, 2012

Perform operations with vectors in the coordinate plane and solve practical problems using vectors:  Use vector notation  Perform the operations of addition, subtraction, scalar multiplication, and dot product on vectors  Graph vectors and resultant vectors  Express complex numbers in vector notation  Define unit vector, and find the unit vector in the same direction as a given vector  Identify properties of vector addition, scalar multiplication, and dot product  Find vector components  Find the magnitude (norm) of a vector  Use vectors in simple geometric proofs Find the component of vectors and perform operations of vectors. Identify, create, and solve practical problems involving triangles:  Solve and create problems, using trigonometric functions  Solve and create problems, using the Pythagorean Theorem  Solve and create problems, using the Law of Sines and the Law of Cosines Find parts of non-right triangles using Laws of Sines and Cosines. Calculate radian and angular measurement and shift from one to another. Find the values of trigonometric functions given the value of one trigonometric function. Find, without the aid of a calculator, the values of trigonometric functions of special angles.



SOL/ Objective


#(s)


RCC.II.5

Calculate lengths of sides and measures of angles of a right triangle using trigonometric functions.

RCC.II.6

Transform from one trigonometric form to another using identities.

RCC.II.12

Represent complex numbers in trigonometric form and perform their addition, subtraction, multiplication, and division.



West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment 4th QUARTER - Pre-Calculus II (Math 164)

STRAND/ TOPIC

SOL/ Objective

#(s)


Functions


MA.4

Find the limit of an algebraic function, if it exists, as the variable approaches either a finite number or infinity:  Find the limit of a function algebraically or numerically, and verify with a graphing calculator  Verify intuitive reasoning about the limit of a function, using a graphing calculator Expand binomials having positive integral exponents by using the Binomial Theorem, Pascal’s Triangle, and the formula for combinations

MA.5/ RCC.II.13

Solve practical problems involving arithmetic and geometric sequences and series:  Use and interpret the notation: ∑, n, nth, and an  Given the formula, find the nth term, an, for an arithmetic or geometric sequence  Given the formula, find the sum, Sn, for an arithmetic or geometric series  Model and solve problems, using sequence and series information  Distinguish between a convergent and divergent series  Discuss convergent series in relation to the concept of a limit Define a sequence and explain what it means to add an infinite sequence.

RCC.II.14

Identify the various common forms of series.

RCC.II.15

Determine the nth term of sequences and the sum of finite/infinite convergent series.

MA.8/ RCC.II.10

Investigate and identify the characteristics of conic section equations in (h, k) and standard forms:  Given a translation or rotation matrix, find an equations for the transformed function or conic section  Investigate and verify graphs of transformed conic sections, using a graphing

Discrete Mathematics

Analytical Geometry



Formative/Summative Assessments (Tests, Projects, etc.) Quizzes and tests when appropriate Vocabulary quizzes Final Exam Number puzzle project



SOL/ Objective



#(s)

calculator Determine the form of a conic section from its equation and graph these equations.



West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment Pre-Calculus Dual-Enrollment Rappahannock Community College

Pre-Calculus I (Math 163): 1st Semester – Students will be able to: Solve equations of various types and systems of equations, analytically and graphically. Explain the meaning of simultaneous equations and be able to translate them into matrix form and solve these matrices. Solve linear, quadratic, polynomial, and rational inequalities. Solve problems involving complex numbers. Identify functions graphically and algebraically and be able to determine their domain and range. Perform operations on functions. Be able to find inverse functions and explain the relationship of a function and its inverse. Explain the general characteristics of polynomial, exponential and logarithmic functions and graph all types of basic functions: linear, quadratic, exponential, logarithmic, polynomials, and inverses of the functions, both with and without the graphing calculator. 9. Use a graphing calculator to find curve of best fit when given real data. 10. Solve real world problems using algebra.

I. 1. 2. 3. 4. 5. 6. 7. 8.

Pre-Calculus II (Math 164): II.

2nd Semester – Students will be able to: 1. Explain the relationship between circular and trigonometric functions. 2. Calculate radian and angular measurement and shift from one to another. 3. Find the values of trigonometric functions given the value of one trigonometric function. 4. Find, without the aid of a calculator, the values of trig functions of special angles. 5. Calculate lengths of sides and measures of angles of a right triangle using trig functions. 6. Transform from one trigonometric form to another using identities. 7. Explain inverse functions as applied to trig functions. 8. Find parts of non-right triangles using Laws of Sines and Cosines. 9. Solve trigonometric equations. 10. Determine the form of a conic section from its equation and graph these equations.


West Point Public School Curriculum Map Rappahannock Community College Pre-Calculus Dual Enrollment

11. Find the component of vectors and perform operations of vectors. 12. Represent complex numbers in trigonometric form and perform their addition, subtraction, multiplication, and division. 13. Define a sequence and explain what it means to add an infinite sequence. 14. Identify the various common forms of series. 15. Determine the nth term of sequences and the sum of finite/infinite convergent series
