Correlation of

Correlation of

Calculus for AP?, by Ron Larson/ Paul Battaglia, ? 2017,

ISBN: 9781305674912

to

South Carolina College- and Career -Readiness Standards

Mathematics Calculus

CORRELATION TO SOUTH CAROLINA'S COLLEGE- AND CAREER -READINESS STANDARDS ? MATHEMATICS CALCULUS

CALCULUS FOR AP?, BY RON LARSON/ PAUL BATTAGLIA, ? 2017,

ISBN: 9781305674912 NATIONAL GEOGRAPHIC LEARNING | CENGAGE

COMPETENCY/OBJECTIVE

In South Carolina College- and Career-Ready (SCCCR) Calculus, students build on the conceptual knowledge and the problem-solving skills they learned in previous mathematics courses. This course prepares students for postsecondary mathematical study but is not designed to prepare students for an Advanced Placement exam. SCCCR Calculus focuses on a conceptual understanding of calculus as well as computational competency. The standards promote a multi-representational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. These representations facilitate an understanding of the connections among limits, derivatives, and integrals. In this course, students are expected to apply mathematics in meaningful ways to solve problems that arise in the workplace, society, and everyday life through the process of modeling. Modeling involves choosing or creating appropriate equations, graphs, functions, or other mathematical representations to analyze real-world situations and answer questions. Use of technological tools, such as hand-held graphing calculators, is important in creating and analyzing mathematical representations used in the modeling process and should be used during instruction and assessment. However, technology should not be limited to hand-held graphing calculators. Students should use a variety of technologies, such as graphing utilities, spreadsheets, and computer algebra systems, to solve problems and to master standards in all Key Concepts of this course.

Key Concepts: Limits and Continuity

C.LC.1 Understand the concept of a limit graphically, numerically, analytically, and contextually.

a. Estimate and verify limits using tables, graphs of functions, and technology.

PAGE REFERENCES

pp. 65-75, Section 1.2, Finding Limits Graphically and Numerically; pp. 76-86, Section 1.3, Evaluating Limits Analytically pp. 65-75, Section 1.2, Finding Limits Graphically and Numerically

b. Calculate limits, including one-sided limits, algebraically using direct substitution, simplification, rationalization, and the limit laws for constant multiples, sums, differences, products, and quotients.

c. Calculate infinite limits and limits at infinity. Understand that infinite limits and limits at infinity provide information regarding the asymptotes of certain functions, including rational, exponential and logarithmic functions.

pp. 76-86, Section 1.3, Evaluating Limits Analytically; pp. 87-99, Section 1.4, Continuity and One-Sided Limits

pp. 100-107, Section 1.5, Infinite Limits; pp. 108-117, Section 1.6, Limits at Infinity

Calculus for AP? ? SC, Calculus

Page 2 of 5

ngl. / 888.915.3276

CORRELATION TO SOUTH CAROLINA'S COLLEGE- AND CAREER -READINESS STANDARDS ? MATHEMATICS CALCULUS

CALCULUS FOR AP?, BY RON LARSON/ PAUL BATTAGLIA, ? 2017,

ISBN: 9781305674912 NATIONAL GEOGRAPHIC LEARNING | CENGAGE

COMPETENCY/OBJECTIVE

C.LC.2 Understand the definition and graphical interpretation of continuity of a function.

a. Apply the definition of continuity of a function at a point to solve problems.

PAGE REFERENCES

pp. 87-99, Section 1.4, Continuity and One-Sided Limits

pp. 87-88; p. 96, Exercises 29-32

b. Classify discontinuities as removable, jump, or infinite. Justify that classification using the definition of continuity.

c. Understand the Intermediate Value Theorem and apply the theorem to prove the existence of solutions of equations arising in mathematical and real-world problems.

Derivatives

C.D.1 Understand the concept of the derivative of a function geometrically, numerically, analytically, and verbally.

a. Interpret the value of the derivative of a function as the slope of the corresponding tangent line.

pp. 87-88; p. 96, Exercises 37-62; p.98, Exercise 106 p. 94-95, The Intermediate Value Theorem; p.98, Exercises 93-102

pp. 124-133, Section 2.1, The Derivative and the Tangent Line Problem pp. 124-133, Section 2.1, The Derivative and the Tangent Line Problem; p. 267, Tangent Line Approximation

b. Interpret the value of the derivative as an instantaneous rate of change in a variety of real-world contexts such as velocity and population growth.

p. 124, Section 2.1; p. 127, The Derivative of a Function; p. 134, Section 2.2; p. 141, Rates of Change; p. 144, How do You See It?; p. 145, Exercises 89-94; p. 146, Exercise 106p. 147, Section 2.3; p. 158, Section 2.4

c. Approximate the derivative graphically by finding the slope of the tangent line drawn to a curve at a given point and numerically by using the difference quotient.

d. Understand and explain graphically and analytically the relationship between differentiability and continuity.

e. Explain graphically and analytically the relationship between the average rate of change and the instantaneous rate of change.

pp. 124-133, Section 2.1; pp. 134-146, Section 2.2; pp. 147-157, Section 2.3; pp. 158-172, Section 2.4

p. 129, Differentiability and Continuity; p. 130, Theorem 2.1; p. 133, Exercises 71-74, 87 p. 144, How do You See It?; p. 127, The Derivative of a Function; p. 141, Rates of Change; p. 145, Exercises 89-94; p. 146, Exercise 106

f. Understand the definition of the derivative and use this definition to determine the derivatives of various functions.

C.D.2 Apply the rules of differentiation to functions.

pp. 124-133, Section 2.1; pp. 134-146, Section 2.2; pp. 147-157, Section 2.3; pp. 158-172, Section 2.4 pp. 123-210, Chapter 2, Differentiation

a. Know and apply the derivatives of constant, power, trigonometric, inverse trigonometric, exponential, and logarithmic functions.

pp. 147-157, Section 2.3, Product and Quotient Rules and Higher Order Derivatives; pp. 158-172, Section 2.4

Calculus for AP? ? SC, Calculus

Page 3 of 5

ngl. / 888.915.3276

CORRELATION TO SOUTH CAROLINA'S COLLEGE- AND CAREER -READINESS STANDARDS ? MATHEMATICS CALCULUS

CALCULUS FOR AP?, BY RON LARSON/ PAUL BATTAGLIA, ? 2017,

ISBN: 9781305674912 NATIONAL GEOGRAPHIC LEARNING | CENGAGE

COMPETENCY/OBJECTIVE

b. Use the constant multiple, sum, difference, product, quotient, and chain rules to find the derivatives of functions.

c. Understand and apply the methods of implicit and logarithmic differentiation.

C.D.3 Apply theorems and rules of differentiation to solve mathematical and real-world problems.

a. Explain geometrically and verbally the mathematical and real-world meanings of the Extreme Value Theorem and the Mean Value Theorem.

b. Write an equation of a line tangent to the graph of a function at a point.

PAGE REFERENCES

p. 134, The Constant Rule; p. 135, The Power Rule; p. 137, The Constant Multiple Rule; p. 138, The Sum and Difference Rules; p. 147, Section 2.3, Product and Quotient Rules and Higher Order Derivatives; p. 149, The Quotient Rule pp. 173-181, Section 2.5, Implicit Differentiation

pp. 123-210, Chapter 2, Differentiation; pp. 211-278, Chapter 3, Applications of Differentiation p. 212, Extrema on an Interval; p. 220-223, Section 3.2, Rolle's Theorem and the Mean Value Theorem; p. 224, Exercises 29-30; p. 225, Exercises 57-58; p. 226, Exercises 63-64 p. 136, Example 4; p. 143, Exercises 31-38

c. Explain the relationship between the increasing/decreasing behavior of and the signs of . Use the relationship to generate a graph of given the graph of , and vice versa, and to identify relative and absolute extrema of .

d. Explain the relationships among the concavity of the graph of , the increasing/decreasing behavior of and the signs of . Use those relationships to generate graphs of , , and given any one of them and identify the points of inflection of .

e. Solve a variety of real-world problems involving related rates, optimization, linear approximation, and rates of change.

pp. 174-178, Implicit Differentiation; p. 212, Extrema on an Interval; p. 239, Points of Inflection; p. 245-256, Section 3.5, A Summary of Curve Sketching

pp. 237-244, Section 3.4, Concavity and the Second Derivative Test

pp. 141-142, Rates of Change; p. 145, Exercises 89-94; p. 146, Exercise 105; p. 156, Exercise 92; p. 171, Exercises 169, 172; pp. 189-197, Section 2.7, Related Rates; pp. 257-266, Section 3.6, Optimization Problems; p. 267, Tangent Line Approximation;

Integrals C.I.1 Understand the concept of the integral of a function geometrically, numerically, analytically, and contextually.

a. Explain how the definite integral is used to solve area problems.

pp. 279-366, Chapter 4 p. 305-306, Theorem 4.5; p. 312-313, Exercises 15-36

b. Approximate definite integrals by calculating Riemann sums using left, right, pp. 302-316, Section 4.3, Riemann Sums and Definite Integrals and mid-point evaluations, and using trapezoidal sums.

Calculus for AP? ? SC, Calculus

Page 4 of 5

ngl. / 888.915.3276

CORRELATION TO SOUTH CAROLINA'S COLLEGE- AND CAREER -READINESS STANDARDS ? MATHEMATICS CALCULUS

CALCULUS FOR AP?, BY RON LARSON/ PAUL BATTAGLIA, ? 2017,

ISBN: 9781305674912 NATIONAL GEOGRAPHIC LEARNING | CENGAGE

COMPETENCY/OBJECTIVE

c. Interpret the definite integral as a limit of Riemann sums.

PAGE REFERENCES

pp. 304-305, Definite Integrals

d. Explain the relationship between the integral and derivative as expressed in both parts of the Fundamental Theorem of Calculus. Interpret the relationship in terms of rates of change.

C.I.2 Apply theorems and rules of integration to solve mathematical and realworld problems.

a. Apply the Fundamental Theorems of Calculus to solve mathematical and real-world problems.

b. Explain graphically and verbally the properties of the definite integral. Apply these properties to evaluate basic definite integrals.

c. Evaluate integrals using substitution.

pp. 317-331, Section 4.4, The Fundamental Theorem of Calculus

pp. 279-366, Chapter 4

p. 322, Example 5; pp. 326-327, Examples 9, 10; pp. 329-331, Exercises 62, 64-67, 99-108; pp. 307-309, Properties of Definite Integrals; p. 313, Exercises 37-46; p. 362, Exercises 29-30 pp. 332-344, Section 4.5, Integration by Substitution

"National Geographic," "National Geographic Society" and the "Yellow Border Design" are registered trademarks of the National Geographic Society? Marcas Registradas. AP? or Advanced Placement? is a trademark registered and/or owned by the College Board, which was not involved in the production of, and does not endorse, this product.

Calculus for AP? ? SC, Calculus

Page 5 of 5

ngl. / 888.915.3276

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download