CLEP Calculus study guide
CLEP Calculus · Work through your exam, one topic at a time.
The CLEP Calculus exam is a College Board credit-by-examination test that assesses an intuitive understanding of calculus at the level of a one-semester college course. It is aimed at students who already know algebra, geometry, trigonometry, and analytic geometry and who want to demonstrate that knowledge rather than sit through the course. The exam draws roughly 60% of its questions from limits and differential calculus and 40% from integral calculus, covering derivatives and their applications, antiderivatives and techniques of integration, the definite integral and the Fundamental Theorem, and applications such as area and average value. Algebraic, trigonometric, exponential, and logarithmic functions all appear. Topics on this exam: Limits, Differential Calculus, and Integral Calculus. The CLEP Calculus study guide has 3 sections and about 799 words.
01Limits and Continuity
A limit describes the value a function approaches , not necessarily the value it attains. Candidates must be fluent with one-sided limits, two-sided limits, infinite limits (vertical asymptotes), and limits at infinity (horizontal asymptotes and end behavior). Know the limit laws, the Squeeze Theorem, and the special limits {x 0} x/x=1 and {x 0}1- x/x=0 . Continuity at a point requires three things: the function is defined there, the limit exists, and the two agree.
277 words, about 1 min02Derivatives and Their Applications
The derivative is a limit of a difference quotient and represents instantaneous rate of change and slope of the tangent line. Master the power, product, quotient, and chain rules, plus derivatives of x , x , e^x , and x . Implicit differentiation handles curves not written as y=f(x) . Applications drive most questions: tangent and normal lines, linear approximation, related rates, and optimization.
275 words, about 1 min03Integration and the Fundamental Theorem
Antiderivatives reverse differentiation, and the indefinite integral carries a constant +C . The definite integral is a limit of Riemann sums and equals signed area. The Fundamental Theorem of Calculus connects the two: a^b f(x)\,dx=F(b)-F(a) where F'=f , and d/dx a^x f(t)\,dt=f(x) . Know the power rule for integrals, integrals of x , x , e^x , and 1/x , and how to use substitution (u-substitution reverses the chain rule).
247 words, about 1 min