Average and instantaneous rates of change.Velocity and acceleration of a particle moving along a line.Curve sketching: increasing and decreasing functions relative and absolute maximum and minimum points concavity points of inflection.Use of L'Hospital's Rule (quotient and indeterminate forms).Relation between differentiability and continuity.Statement of the Mean Value Theorem applications and graphical illustrations.Corresponding characteristics of graphs of f, f ' and f ''.Derivative of the inverse of a function (including a r c s i n x and a r c t a n x).Derivative of a composite function (chain rule), e.g., s i n ( a x + b ), a e k x, l n ( k x ).Derivatives of sums, products and quotients (including t a n x and c o t x.Definitions of the derivative, e.g., f ′ a = lim x → a f ( x ) - f ( a ) x - a and f ′ x = lim h → 0 f ( x + h ) - f ( x ) h.Limit calculations, including limits involving infinity, e.g., lim x → 0 sin x x = 1, lim x → 0 1 x is nonexistent, and lim x → ∞ sin x x = 0ĭifferential Calculus (50%) The Derivative.Statement of properties, e.g., limit of a constant, sum, product or quotient.
The percentages next to the main topics indicate the approximate percentage of exam questions on that topic. The subject matter of the Calculus exam is drawn from the following topics. Solving nonroutine problems involving an understanding of the concepts and applications of calculus (approximately 50% of the exam).Solving routine problems involving the techniques of calculus (approximately 50% of the exam).Questions on the exam require candidates to demonstrate the following abilities: Generate a table of values for a function.Find points of intersection of graphs of functions.Perform calculations (e.g., exponents, roots, trigonometric values, and logarithms).In order to answer some of the questions in Section 2 of the exam, students may be required to use the online graphing calculator in the following ways: Visit ETS to learn more and to practice using the scientific calculator. Students are expected to know how and when to make appropriate use of the calculator.
#COLLEGE CALCULUS MATH HOW TO#
Information about how to use the calculator is available in the Help icon under the Calculator tab. To use the calculator during the exam, students need to select the Calculator icon.
Only some of the questions actually require the graphing calculator.
#COLLEGE CALCULUS MATH SOFTWARE#
Only some of the questions will require the use of the calculator.Ī graphing calculator, the TI-84 Plus CE, is integrated into the exam software and available to students during Section 2 of the exam. The use of an online graphing calculator (non-CAS) is allowed for this section.
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