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Cheat sheet

CLEP Calculus cheat sheet

A condensed reference for the formulas, graph-reading rules, and must-know facts most worth reviewing before exam day.

Rules to know cold

  • Limit definition of the derivative: f'(x) = lim (h→0) [f(x+h) - f(x)] / h.
  • Power rule: d/dx[x^n] = n·x^(n-1). Integration reverses it: ∫x^n dx = x^(n+1)/(n+1) + C (n ≠ -1).
  • Product, quotient, and chain rules for derivatives.
  • d/dx[sin x] = cos x, d/dx[e^x] = e^x, d/dx[ln x] = 1/x; ∫(1/x) dx = ln|x| + C, ∫e^x dx = e^x + C.
  • Fundamental Theorem of Calculus: ∫ from a to b of f(x) dx = F(b) - F(a), where F is an antiderivative of f (F' = f).

Applications and limits

  • Derivative = instantaneous rate of change / slope of the tangent line.
  • Optimization: set the derivative to 0 to find maxima and minima.
  • Related rates: differentiate a relationship with respect to time; look for 'how fast is ... changing.'
  • L'Hopital's rule: for a 0/0 or ∞/∞ limit, take the derivative of the numerator and denominator.
  • Definite integral = area under the curve; used for accumulated change (distance, total).

Practice this first: Derivatives - Differentiation rules and their applications are the largest share.

Now put it to work - practice CLEP Calculus free

Reviewing the sheet is step one. Passers are usually hitting about 70-80% on realistic practice before test day, so the fastest way to know you are ready is to start answering real questions.