Australia (New South Wales) — NESA
HSC Maths Calculator
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)
Calculator Allowed
NESA-approved scientific calculators are permitted in all HSC Mathematics papers. CAS calculators are NOT allowed.
- Mathematics Advanced: 3-hour paper — approved scientific calculator permitted throughout
- Mathematics Extension 1: 2-hour paper — approved scientific calculator permitted throughout
- Mathematics Extension 2: 3-hour paper — approved scientific calculator permitted throughout
- NESA maintains a list of approved calculators (updated annually)
- CAS and graphing calculators are NOT permitted in any HSC Mathematics exam
- Phone calculators and smartwatches are NOT allowed
Calculators for HSC Maths
These calculators cover key topics from Mathematics Advanced, Extension 1, and Extension 2. Each provides step-by-step workings to help you learn the method.
Derivative Calculator
Calculate derivatives of any function step by step. Supports higher-order derivatives, partial derivatives, and common functions. Free online tool.
Integral Calculator
Calculate indefinite integrals (antiderivatives) of functions. Symbolic integration with step-by-step display. Free online integral calculator.
Definite Integral Calculator
Calculate definite integrals with upper and lower bounds. Numerical integration using Simpson's rule. Free online definite integral calculator.
Probability Calculator
Calculate probability of events, complements, unions, and intersections. Free online probability calculator for statistics.
Standard Deviation Calculator
Calculate standard deviation, variance, mean, and more for any dataset. Supports population and sample statistics. Free online tool.
Triangle Calculator
Calculate triangle sides, angles, area, and perimeter. Supports SSS, SAS, ASA, AAS configurations. Free online triangle calculator.
Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula. Find roots, discriminant, and vertex. Free online quadratic formula calculator.
Solve For X Calculator
Solve algebraic equations for x. Handles linear, quadratic, polynomial, and simple equations. Free online equation solver.
Log Calculator
Calculate logarithms with any base. Find natural log (ln), log base 10, and custom base logarithms. Free online log calculator.
Normal Distribution Calculator
Calculate probabilities for normal distributions. Find areas under the bell curve, percentiles, and inverse values. Free online tool.
Worked Examples
Practice with these HSC-style questions. Each example shows the full working and links to the relevant calculator.
1Differentiation
standard
Differentiation
standardProblem:
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
2Integration (Area Under Curve)
standard
Integration (Area Under Curve)
standardProblem:
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
3Logarithmic Equations
standard
Logarithmic Equations
standardProblem:
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
4Probability (Binomial)
higher
Probability (Binomial)
higherProblem:
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%)
5Trigonometric Equation
standard
Trigonometric Equation
standardProblem:
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
Frequently Asked Questions
Common questions about HSC Mathematics exams and calculator use.
Can I use a calculator in HSC Maths?
Yes. NESA-approved scientific calculators are permitted in all HSC Mathematics papers (Advanced, Extension 1, and Extension 2).
Are CAS calculators allowed in HSC Maths?
No. Unlike VCE in Victoria, NSW HSC exams do not permit CAS or graphing calculators. Only NESA-approved scientific calculators are allowed.
When are the HSC Maths exams?
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.
What topics are covered in HSC Mathematics Advanced?
HSC Mathematics Advanced covers functions, trigonometric functions, calculus (differentiation and integration), exponential and logarithmic functions, statistical analysis, and financial mathematics.
What is the difference between Advanced, Extension 1, and Extension 2?
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.
How is the HSC ATAR calculated for maths?
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.