College · intermediate
Calculus
Limits, derivatives, and integrals — practiced until automatic.
Skills
29 skills in 4 sections — fundamentals first, then more specific topics. Practice each until Mastery Score 100.
A.Limits4 skills
- A.1 Polynomial LimitsPractice →Evaluate limits of polynomials by direct substitution.
- A.2 Limits of Rational FunctionsPractice →Evaluate removable limits by factoring and canceling.
- A.3 Limits at InfinityPractice →Find horizontal asymptote values via leading coefficients.
- A.4 Trigonometric LimitsPractice →Evaluate limits built on sin(kx)/x as x → 0.
B.Derivative rules10 skills
- B.1 Derivative from DefinitionPractice →Use the difference quotient for f(x)=x².
- B.2 Power Rule DerivativesPractice →Differentiate monomials with the power rule.
- B.3 Differentiating PolynomialsPractice →Differentiate multi-term polynomials with the power rule.
- B.4 Product RulePractice →Differentiate products of simple functions.
- B.5 Quotient Rule (Linears)Practice →Differentiate quotients of linear functions.
- B.6 Chain Rule (Powers)Practice →Differentiate (ax+b)^n compositions.
- B.7 Derivatives of Sine & CosinePractice →Differentiate a sin x + b cos x.
- B.8 Derivatives of ExponentialsPractice →Differentiate c·e^(kx).
- B.9 Second DerivativesPractice →Differentiate twice to find f''.
- B.10 Derivative at a PointPractice →Evaluate f'(a) for a polynomial.
C.Applications of derivatives10 skills
- C.1 Tangent Slope from a GraphPractice →Read the slope of a drawn tangent to y = x².
- C.2 Secant Slope from a GraphPractice →Find average rate of change from a secant drawn through two curve points.
- C.3 Critical PointsPractice →Solve f'(x) = 0 for a quadratic.
- C.4 Critical Point from a GraphPractice →Identify a critical number and local extremum from a smooth graph.
- C.5 Concavity & InflectionPractice →Use f'' to find inflection or concavity direction.
- C.6 Implicit DifferentiationPractice →Find dy/dx on x² + y² = r² at a point.
- C.7 Related Rates (Circle)Practice →Relate dA/dt to dr/dt for A = πr².
- C.8 Tangent Line EquationsPractice →Write the tangent line to a parabola at a point.
- C.9 Position & VelocityPractice →Differentiate a position function and evaluate velocity.
- C.10 Basic OptimizationPractice →Maximize area or product under a simple constraint.
D.Integrals & area5 skills
- D.1 Basic AntiderivativesPractice →Find indefinite integrals of power functions (+ C omitted).
- D.2 FTC Definite IntegralsPractice →Evaluate ∫ 2x dx on [a,b] with the Fundamental Theorem.
- D.3 Area Under a CurvePractice →Compute area as ∫ x dx from 0 to b.
- D.4 Area Under a Graphed LinePractice →Use a shaded graph to evaluate a simple definite integral geometrically.
- D.5 Average Value of a FunctionPractice →Find the average value of a function on an interval.