CBSE 12 Math · U3
Calculus
Continuity and differentiability, applications of derivatives, integrals, applications of integrals, and differential equations.
Test yourself
A focused, distraction-free run through 50 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 3.1
Continuity and Differentiability
Continuity at a point, removable definitions, differentiability, and corner cases.
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Topic 3.2
Derivative Rules and Standard Functions
Chain rule, derivatives of inverse trigonometric, exponential, and logarithmic functions.
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Topic 3.3
Implicit, Parametric, Logarithmic, and Second Derivatives
CBSE differentiation techniques beyond direct formulas, including second derivatives.
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Topic 3.4
Applications of Derivatives: Rates and Monotonicity
Rate of change, marginal quantities, and increasing/decreasing intervals.
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Topic 3.5
Applications of Derivatives: Maxima and Minima
First derivative and second derivative tests, simple optimization, and board-style extrema problems.
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Topic 3.6
Indefinite Integrals and Substitution
Integration as the inverse of differentiation, standard forms, and substitution.
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Topic 3.7
Integration by Parts and Partial Fractions
CBSE integration techniques: parts, partial fractions, and choosing a method.
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Topic 3.8
Definite Integrals, Properties, and FTC
Definite integral evaluation, fundamental theorem of calculus, and standard properties.
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Topic 3.9
Applications of Integrals
Area under simple curves and area between two curves using definite integrals.
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Topic 3.10
Differential Equations
Order and degree, separation of variables, homogeneous equations, and first-order linear differential equations.
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