Mathematics · Grades 11–12
Introductory calculus · Formula sheet
Rules, conditions and small examples in one printable reference.
Remember this
Power-rule derivatives
Multiply by the exponent and reduce that exponent by one. These tasks use positive integer powers.
d(axⁿ)/dx = an xⁿ⁻¹
f′(x) = 14x^1; f′(3) = 42
Definite integrals of powers
Use an antiderivative at the upper bound minus its value at the lower bound.
∫₀ᵇ axⁿ dx = abⁿ⁺¹/(n + 1), n ≠ −1
[6x^3]₀^4 = 384
Limits of polynomials
Polynomials are continuous at every real input, so direct substitution applies.
lim(x→a) p(x) = p(a) for a polynomial p
9 × (-6)² + 10 = 334
A derivative at a point
Differentiate term by term before substituting x.
d(ax³ + bx² + cx)/dx = 3ax² + 2bx + c
3×2×(0)² + 2×4×(0) + (1) = 1
Integrate a linear function
Evaluate the antiderivative at the upper limit minus the lower limit.
∫(ax + b) dx = ax²/2 + bx + C
F(9) − F(1) = 944; F(x) = 11x² + 8x
Further reading and review references
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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.