Australia (New South Wales) — NESA
Free online calculators for HSC Mathematics Advanced and Extension. Practice calculus, statistics, trigonometry and algebra questions with step-by-step solutions.
Ages 16-18 · October to November (approx. mid-October — mid-November 2026)
NESA-approved scientific calculators are permitted in all HSC Mathematics papers. CAS calculators are NOT allowed.
These 10 calculators cover key topics from Mathematics Advanced, Extension 1, and Extension 2. Each provides step-by-step workings to help you learn the method.
Calculate derivatives of any function step by step. Supports higher-order derivatives, partial derivatives, and common functions. Free online tool.
Calculate indefinite integrals (antiderivatives) of functions. Symbolic integration with step-by-step display. Free online integral calculator.
Calculate definite integrals with upper and lower bounds. Numerical integration using Simpson's rule. Free online definite integral calculator.
Calculate probability of events, complements, unions, and intersections. Free online probability calculator for statistics.
Calculate standard deviation, variance, mean, and more for any dataset. Supports population and sample statistics. Free online tool.
Calculate triangle sides, angles, area, and perimeter. Supports SSS, SAS, ASA, AAS configurations. Free online triangle calculator.
Solve quadratic equations using the quadratic formula. Find roots, discriminant, and vertex. Free online quadratic formula calculator.
Solve algebraic equations for x. Handles linear, quadratic, polynomial, and simple equations. Free online equation solver.
Calculate logarithms with any base. Find natural log (ln), log base 10, and custom base logarithms. Free online log calculator.
Calculate probabilities for normal distributions. Find areas under the bell curve, percentiles, and inverse values. Free online tool.
Practice with these HSC-style questions. Each example shows the full working and links to the relevant calculator.
Problem:
Find the derivative of y = x³ − 6x² + 9x + 2.
Solution:
dy/dx = 3x² − 12x + 9. To find stationary points, set dy/dx = 0: 3x² − 12x + 9 = 0, giving 3(x − 1)(x − 3) = 0, so x = 1 or x = 3.
Answer: dy/dx = 3x² − 12x + 9
Problem:
Find the area enclosed between y = x² and y = 4.
Solution:
Intersection: x² = 4, so x = ±2. Area = integral from −2 to 2 of (4 − x²) dx = [4x − x³/3] from −2 to 2 = (8 − 8/3) − (−8 + 8/3) = 32/3.
Answer: 32/3 ≈ 10.67 square units
Problem:
Solve log₂(x) + log₂(x − 2) = 3.
Solution:
log₂(x(x − 2)) = 3, so x(x − 2) = 8. x² − 2x − 8 = 0. (x − 4)(x + 2) = 0. Since x > 2 (domain restriction), x = 4.
Answer: x = 4
Problem:
A test has 10 multiple-choice questions with 4 options each. Find the probability of getting at least 7 correct by guessing.
Solution:
P(X ≥ 7) = P(7) + P(8) + P(9) + P(10) where X ~ Binomial(10, 0.25). This equals approximately 0.0035.
Answer: 0.0035 (0.35%)
Problem:
Solve 2sin(x) − 1 = 0 for 0 ≤ x ≤ 2π.
Solution:
sin(x) = 1/2. In the range 0 to 2π: x = π/6 or x = 5π/6.
Answer: x = π/6 or x = 5π/6
Common questions about HSC Mathematics exams and calculator use.
Yes. NESA-approved scientific calculators are permitted in all HSC Mathematics papers (Advanced, Extension 1, and Extension 2).
No. Unlike VCE in Victoria, NSW HSC exams do not permit CAS or graphing calculators. Only NESA-approved scientific calculators are allowed.
HSC exams run from mid-October to mid-November each year. Mathematics Advanced, Extension 1, and Extension 2 are typically scheduled in late October or early November.
HSC Mathematics Advanced covers functions, trigonometric functions, calculus (differentiation and integration), exponential and logarithmic functions, statistical analysis, and financial mathematics.
Advanced is the standard HSC maths course. Extension 1 adds combinatorics, further calculus, and vectors. Extension 2 (the most challenging) includes complex numbers, proof, and further integration techniques.
The HSC mark combines your school assessment (50%) and exam performance (50%). This is then scaled into an ATAR. Extension courses carry additional weighting in ATAR calculations.