Free resources for Calculus in Mathematics: lessons, PDFs and video courses. Calculus study material for ATAR, HSC, VCE, NAPLAN with Khan Academy, Wikipedia and video solutions.
Calculus is the branch of mathematics that studies continuous change. It has two main pillars: differential calculus, which deals with rates of change and slopes of curves (derivatives), and integral calculus, which deals with accumulation of quantities and areas under curves. Both are connected by the Fundamental Theorem of Calculus.
The derivative f'(x) measures how fast a function changes at a point and is defined as the limit of the difference quotient. Core rules include the power rule (xⁿ)' = n·xⁿ⁻¹, the product rule, the quotient rule, and the chain rule for composite functions. Integrals reverse differentiation: the indefinite integral ∫f(x)dx = F(x) + C, while the definite integral computes exact area between bounds.
Calculus is central to SAT Subject level, AP Calculus AB/BC, A-Level Maths, and first-year university courses. Typical exam questions cover limits, tangent lines, optimization, related rates, and area/volume by integration. Mastering algebra and trigonometry first makes calculus significantly easier.
Pick the correct answer — instant feedback!
1. What is the derivative of x³?
2. What is ∫2x dx?
3. The derivative of a constant function equals:
4. Which rule is used to differentiate composite functions?
Calculus models anything that changes: physics (velocity, acceleration), economics (marginal cost), biology (population growth), and engineering. It is required for most STEM degrees.
A derivative measures the instantaneous rate of change of a function; an integral accumulates quantities, such as the area under a curve. They are inverse operations.
The standard SAT does not test calculus directly, but AP Calculus AB/BC and many university entrance exams worldwide do.
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