Rockingham County Public Schools
Visitors | Employees | Parents | K-5 Students | 6-12 Students | Schools | Search Tools | Site Index | Home
Calculus & AP Calculus
SOLs | Resources by Textbook Chapters | Resources by SOL | Overview | D.O.E. Resources | Curriculum Home
Standards of Learning Resources: Click on the SOL number to view the resources
APC.1 The student will define and apply the properties of elementary functions, including algebraic, trigonometric, exponential, and composite functions and their inverses, and graph these functions using a graphing calculator. Properties of functions will include domains, ranges, combinations, odd, even, periodicity, symmetry, asymptotes, zeros, upper and lower bounds, and intervals where the function is increasing or decreasing. APC.2 The student will define and apply the properties of limits of functions. This will include limits of a constant, sum, product, quotient, one-sided limits, limits at infinity, infinite limits, and nonexistent limits. APC.3 The student will state the definition of continuity and determine where a function is continuous or discontinuous. This will include: continuity at a point; continuity over a closed interval; application of the Intermediate Value Theorem; and graphical interpretation of continuity and discontinuity. APC.4 The student will find the derivative of an algebraic function by using the definition of a derivative. This will include investigating and describing the relationship between differentiability and continuity. APC.5 The student will apply formulas to find the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses. APC.6 The student will apply formulas to find the derivative of the sum, product, quotient, inverse, and composite (chain rule) of elementary functions. APC.7 The student will find the derivative of an implicitly defined function. APC.8 The student will find the higher order derivatives of algebraic, trigonometric, exponential, and logarithmic functions. APC.9 The student will use logarithmic differentiation as a technique to differentiate nonlogarithmic functions. APC.10 The student will state (without proof) the Mean Value Theorem for derivatives and apply it both algebraically and graphically. APC.11 The student will use l'Hopital's rule to find the limit of functions whose limits yield the indeterminate forms: 0/0 and infinity/infinity APC.12 The student will apply the derivative to solve problems, including tangent and normal lines to a curve, curve sketching, velocity, acceleration, related rates of change, Newton's method, differentials and linear approximations, and optimization problems. APC.13 The student will find the indefinite integral of algebraic, exponential, logarithmic, and trigonometric functions. The special integration techniques of substitution (change of variables) and integration by parts will be included. APC.14 The student will identify the properties of the definite integral. This will include the Fundamental Theorem of Calculus and the definite integral as an area and as a limit of a sum as well as the fundamental theorem: The integral from a to x of f(t)d(t) dt/dx = f(x) APC.15 The student will apply the definite integral to solve problems. These problems will include finding distance traveled on a line and velocity from acceleration with initial conditions, growth and decay problems, solutions of separable differential equations, the average value of a function, area between curves, volumes of solids of revolution about the axes or lines parallel to the axes using disc/washer and shell methods, and volumes of solids with known cross-sectional areas. APC.16 The student will compute an approximate value for a definite integral. This will include numerical calculations using Riemann Sums and the Trapezoidal Rule. Back to top.   Objective: APC.1 The student will define and apply the properties of elementary functions, including algebraic, trigonometric, exponential, and composite functions and their inverses, and graph these functions using a graphing calculator.Properties of functions will include domains, ranges, combinations, odd, even, periodicity, symmetry, asymptotes, zeros, upper and lower bounds, and intervals where the function is increasing or decreasing. Text Resources: Sections A.1-A.3, P.1-P.3, 3.3 Related Web Sites: http://www.hofstra.edu/~matscw/Calcsummary1.html Suggested Manipulatives: Technology Resources: Graphing calculator Other Resources: Assessment Suggestions: 1988 AP EXAM MC #2,31,32,42,44 1985 AP EXAM MC #12,15,19,21,26,35 (MC = Multiple choice section) Suggestions for Integration: . Back to top. Objective: APC.2 The student will define and apply the properties of limits of functions. This will include limits of a constant, sum, product, quotient, one-sided limits, limits at infinity, infinite limits, and nonexistent limits. Text Resources: Sections 1.1-1.5 Related Web Sites: http://www.npac.syr.edu/REU/reu94/williams/ch2/section3_1.html Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1985 AP EXAM MC # 5, 37, 41 Suggestions for Integration: . Back to top. Objective: APC.3 The student will state the definition of continuity and determine where a function is continuous or discontinuous.This will include: continuity at a point; continuity over a closed interval; application of the Intermediate Value Theorem; and graphical interpretation of continuity and discontinuity. Text Resources: Section 1.4 Related Web Sites: http://www.npac.syr.edu/REU/reu94/williams/ch2/subsection3_4_2.html http://chaos.math.temple.edu/cgi-bin/manager Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1985 AP EXAM MC #29 Suggestions for Integration: . Back to top. Objective: APC.4 The student will find the derivative of an algebraic function by using the definition of a derivative. This will include investigating and describing the relationship between differentiability and continuity. Text Resources: Section 2.1 Related Web Sites: http://www.math.montana.edu/~frankw/ccp/calculus/deriv/compare/learn.htm Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #27, 29, 41 1985 AP EXAM MC #25 Suggestions for Integration: . Back to top. Objective: APC.5 The student will apply formulas to find the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses. Text Resources: Sections 2.2, 2.3, 5.1, 5.4 Related Web Sites: http://www.math.ou.edu/calculus/sec3_6/sec3-6.html http://www.hofstra.edu/~matscw/trig/trig3.html Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #24 1985 AP EXAM MC #6,10,12, 20 Suggestions for Integration: . Back to top. Objective: APC.6 The student will apply formulas to find the derivative of the sum, product, quotient, inverse, and composite (chain rule) of elementary functions. Text Resources: Sections 2.2-2.4, 5.3 Related Web Sites: http://www.math.ou.edu/calculus/sec3_4/sec3-4.html Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #1,6,15 1985 AP EXAM MC #3, 18, 23 Suggestions for Integration: . Back to top. Objective: APC.7 The student will find the derivative of an implicitly defined function. Text Resources: Section 2.5 Related Web Sites: http://www.math.ou.edu/calculus/sec2_10/sec2_10.html http://www.math.ou.edu/calculus/sec3_5/sec3_5.html Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #9, 40 1985 AP EXAM MC #13 Suggestions for Integration: . Back to top. Objective: APC.8 The student will find the higher order derivatives of algebraic, trigonometric, exponential, and logarithmic functions. Text Resources: Sections 2.3, 5.1, 5.4 Related Web Sites: Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #18 1985 AP EXAM MC #2 Suggestions for Integration: . Back to top. Objective: APC.9 The student will use logarithmic differentiation as a technique to differentiate nonlogarithmic functions. Text Resources: Section 5.1 Related Web Sites: Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: Suggestions for Integration: . Back to top. Objective: APC.10 The student will state (without proof) the Mean Value Theorem for derivatives and apply it both algebraically and graphically. Text Resources: Sections 3.2, 3.9 Related Web Sites: http://forum.swarthmore.edu/dr.math/problems/mean_value_thm.html Suggested Manipulatives: Technology Resources: Graphing calculator Other Resources: Assessment Suggestions: Suggestions for Integration: . Back to top. Objective: APC.11 The student will use l'Hopital's rule to find the limit of functions whose limits yield the indeterminate forms: 0/0 and infinity/infinity Text Resources: Section 7.7 Related Web Sites: http://www.npac.syr.edu/REU/reu94/williams/ch3/subsection3_4_4.html http://chaos.math.temple.edu/cgi-bin/manager Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #23 Suggestions for Integration: . Back to top. Objective: APC.12 The student will apply the derivative to solve problems, including tangent and normal lines to a curve, curve sketching, velocity, acceleration, related rates of change, Newton's method, differentials and linear approximations, and optimization problems. Text Resources: Sections 2.1-2.3, 2.6-3.8 Related Web Sites: http://www.hofstra.edu/~matscw/Calcsummary5.html http://calculus.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-2/CalcIMMA-2-1-1.html http://www.seresc.k12.nh.us/www/alvirne.html http://www.seresc.k12.nh.us/www/archiv97.html http://www.math.psu.edu/dna/graphics.html http://archives.math.utk.edu/visual.calculus/ Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #3,4,8,11,16,20,33,37,45 1985 AP EXAM MC #8,11,16,28,31,33,36,39,43 Suggestions for Integration: . Back to top. Objective: APC.13 The student will find the indefinite integral of algebraic, exponential, logarithmic, and trigonometric functions. The special integration techniques of substitution (change of variables) and integration by parts will be included. Text Resources: Sections 4.1, 4.5, 5.2, 5.4, 5.9, 7.1, 7.2 Related Web Sites: hhttp://www.hofstra.edu/~matscw/Calcsummary6.html http://www.hofstra.edu/~matscw/Calcsummary7.html http://www.hofstra.edu/~matscw/Calcquestintegral.html Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC#5, 7, 26 1985 AP EXAM MC #4, 30 Suggestions for Integration: . Back to top. Objective: APC.14 The student will identify the properties of the definite integral. This will include the Fundamental Theorem of Calculus and the definite integral as an area and as a limit of a sum as well as the fundamental theorem: The integral from a to x of f(t)d(t) dt/dx = f(x) Text Resources: Sections 4.2-4.4 Related Web Sites: http://www.ies.co.jp/math/java/perime/perime.html http://mss.math.vanderbilt.edu/~pscrooke/MSS/definiteintegral.html Suggested Manipulatives: Technology Resources: Other Resources: Assessment Suggestions: 1988 AP EXAM MC #10,13,14, 17,19,21,25,28,34,38,39 1985 AP EXAM MC #1, 9, 17, 22, 27, 32, 34, 38, 40, 42 Suggestions for Integration: . Back to top. Objective: APC.15 The student will apply the definite integral to solve problems. These problems will include finding distance traveled on a line and velocity from acceleration with initial conditions, growth and decay problems, solutions of separable differential equations, the average value of a function, area between curves, volumes of solids of revolution about the axes or lines parallel to the axes using disc/washer and shell methods, and volumes of solids with known cross-sectional areas. Text Resources: Sections 4.4, 5.5-5.7, 6.1-6.3, 7.1 Related Web Sites: http://www.math.psu.edu/dna/calculus/crosssecs/crosssecs.gif Suggested Manipulatives: Technology Resources: Graphing calculator Other Resources: Assessment Suggestions: 1988 AP EXAM MC #30, 36, 43, 45 1985 AP EXAM MC #14, 24, 44 Suggestions for Integration: . Back to top. Objective: APC.16 The student will compute an approximate value for a definite integral. This will include numerical calculations using Riemann Sums and the Trapezoidal Rule. Text Resources: Section 4.3 Related Web Sites: http://www2.wheatonma.edu/academic/academicdept/MathCS/faculty/tratliff/writing/calculus-II/carpeting.html Suggested Manipulatives: Technology Resources: Graphing calculator Other Resources: Assessment Suggestions: Suggestions for Integration: . Back to top.
When it comes to learning, we click!