HSC Extension Two Maths Papers

Explore free HSC extension 2 maths questions organised into exam style topic tests with worked solutions. Each test contains 5 multiple choice questions and 3 15 mark short answer segments in the style of the HSC, for a total of 50 marks. The questions are designed to be harder than usual, but not impossible, and the worked solutions should help with understanding them. For any questions or concerns about these papers, feel free to contact me and I’ll reply as soon as possible.

The HSC extension two maths syllabus includes five topics, below is a skills checklist based on the syllabus with everything you should understand going into the final exam.

Proof:

  • Understand the formal language and symbols of proof

  • Understand proof by contradiction

  • Use examples and counter examples

  • Prove results involving inequalities

  • Prove equality, inequality, divisibility, calculus, geometric, probability and recursive results by induction

Vectors:

  • Understand basic notations and operations in three dimensions

  • Calculate the magnitude of a three dimensional vector

  • Convert a vector into a unit vector by dividing by its length

  • Understand the dot product in three dimensions

  • Prove geometric results using vectors

  • Understand the equations of spheres

  • Use vector equations of curves involving a parameter

  • Understand the vector equation of a line

Complex numbers:

  • Perform basic operations with complex numbers

  • Understand complex conjugates

  • Represent a complex number in the complex plane

  • Convert a complex number to polar and exponential forms

  • Understand the principal argument

  • Find powers of complex numbers using exponential form

  • Use De Moivre’s theorem to prove trigonometric identities

  • Solve quadratic equations with both real and complex coefficients

  • Solve polynomials with real coefficients by using complex conjugates

  • Represent complex numbers as vectors on the complex plane

  • Calculate the nth roots of a complex number and plot them on the complex plane

  • Identify subsets of the complex plane determined by relations

Integration:

  • Understand integration by substitution

  • Use partial fractions

  • Use integration by parts

  • Derive and use recurrence relationships

Mechanics:

  • Understand simple harmonic motion

  • Prove a particle is undergoing simple harmonic motion

  • Understand the relationship between displacement, velocity and acceleration

  • Use Newton’s laws

  • Derive and use the equations of motion for a particle travelling in a straight line resisted and unresisted

  • Solve problems involving particles in resistive mediums

  • Understand the concept of terminal velocity

  • Use parametric and cartesian equations to solve projectile motion questions

  • Solve projectile motion questions for particles in resistive mediums and under the influence of gravity