Mississippi

NQ Number and Quantity

• NQ.A Compute and determine the reasonableness of results in mathematical and real world situations

  • NQ.1 Estimate limits from graphs or tables.

    • Find limits using graphs (C-A.1)
    • Find one-sided limits using graphs (C-A.2)
    • Find limits at vertical asymptotes using graphs (C-C.1)

  • NQ.2 Estimate numerical derivatives from graphs or tables of data.

  • NQ.3 Prove statements using mathematical induction.

A Algebra

• A.A Demonstrate basic knowledge of functions, including their behavior and characteristics

  • A.4 Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and end behavior).

    • Determine end behavior using graphs (C-D.1)
    • Determine end behavior of polynomial and rational functions (C-D.2)

  • A.5 Investigate, describe, and determine asymptotic behavior using tables, graphs, and analytical methods

  • A.6 Determine and justify the continuity and discontinuity of functions

    • Identify graphs of continuous functions (C-E.1)
    • Determine continuity using graphs (C-E.2)
    • Determine one-sided continuity using graphs (C-E.3)
    • Find and analyze points of discontinuity using graphs (C-E.4)
    • Determine continuity on an interval using graphs (C-E.5)

• A.B Evaluate limits and communicate an understanding of the limiting process

  • A.7 Solve mathematical situations and application problems involving or using derivatives, including exponential, logarithmic, and trigonometric functions.

    • Find derivatives of sine and cosine functions (C-H.3)
    • Find derivatives of other trigonometric functions (C-H.4)
    • Find derivatives of exponential functions (C-H.5)
    • Find derivatives of logarithmic functions (C-H.6)

  • A.8 Calculate limits using algebraic methods.

    • Find limits using addition, subtraction, and multiplication laws (C-B.1)
    • Find limits using the division law (C-B.2)
    • Find limits using power and root laws (C-B.3)
    • Find limits using limit laws (C-B.4)
    • Find limits of polynomials and rational functions (C-B.5)
    • Find limits involving factorization and rationalization (C-B.6)
    • Find limits involving absolute value functions (C-B.7)
    • Find limits involving trigonometric functions (C-B.8)

  • A.9 Verify the behavior and direction of non-determinable limits.

    • Find limits at vertical asymptotes using graphs (C-C.1)
    • Find the limit at a vertical asymptote of a rational function I (C-C.2)
    • Find the limit at a vertical asymptote of a rational function II (C-C.3)

• A.C Use the definition and formal rules of differentiation to compute derivatives

  • A.10 State and apply the formal definition of a derivative.

    • Find values of derivatives using limits (C-F.5)
    • Find the slope of a tangent line using limits (C-F.6)
    • Find equations of tangent lines using limits (C-F.7)

  • A.11 Apply differentiation rules to sums, products, quotients, and powers of functions.

    • Sum and difference rules (C-G.1)
    • Product rule (C-G.2)
    • Quotient rule (C-G.3)
    • Power rule I (C-G.4)
    • Power rule II (C-G.5)
    • Find derivatives using the product rule I (C-H.9)
    • Find derivatives using the product rule II (C-H.10)
    • Find derivatives using the quotient rule I (C-H.11)
    • Find derivatives using the quotient rule II (C-H.12)

  • A.12 Use the chain rule and implicit differentiation.

    • Chain rule (C-G.6)
    • Find derivatives using the chain rule I (C-H.14)
    • Find derivatives using the chain rule II (C-H.15)
    • Find derivatives using implicit differentiation (C-I.1)

  • A.13 Describe the relationship between differentiability and continuity.

• A.D Apply derivatives to find solutions in a variety of situations

  • A.15 Define a derivative and explain the purpose/utility of the derivative.

  • A.16 Apply the derivative as a rate of change in varied contexts, including velocity, speed, and acceleration.

    • Find instantaneous rates of change (C-F.3)
    • Velocity as a rate of change (C-F.4)

  • A.17 Apply the derivative to find tangent lines and normal lines to given curves at given points.

    • Find equations of tangent lines using limits (C-F.7)
    • Find tangent lines using implicit differentiation (C-I.2)

  • A.18 Predict and explain the relationships between functions and their derivatives.

  • A.19 Model rates of change to solve related rate problems.

  • A.20 Solve optimization problems.

C Calculus

• C.A Employ various integration properties and techniques to evaluate integrals

  • C.21 State and apply the First and Second Fundamental Theorem of Calculus.

  • C.22 Apply the power rule and u-substitution to evaluate indefinite integrals.

G Geometry

• G.A Use geometric concepts to gain insights into, answer questions about, and graph various implications of differentiation

  • G.23 Demonstrate and explain the differences between average and instantaneous rates of change.

  • G.24 Apply differentiation techniques to curve sketching

  • G.25 Apply Rolle's Theorem and the Mean Value Theorem and their geometric consequences.

  • G.26 Identify and apply local linear approximations.

  • G.27 Analyze curves with attention to non-decreasing functions (monotonicity) and concavity.

SP Statistics and Probability

• SP.A Adapt integration methods to model situations to problems

  • SP.28 Apply integration to solve problems of area.

  • SP.29 Utilize integrals to model and find solutions to real-world problems such as calculating displacement and total distance traveled.

• SP.B Apply appropriate techniques, tools, and formulas to determine values for the definite integral

  • SP.30 Interpret the concept of definite integral as a limit of Riemann sums over equal subdivisions.