§-Maths Extension 2 Q&A
NSW · NESA← Maths Extension 2
Maths Extension 2 Q&A by dot point
A short Q&A bank for every NSW Maths Extension 2 syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Introduction to Complex Numbers (MEX-N1)
Represent complex numbers in Cartesian and polar form, perform arithmetic, and interpret modulus, argument and conjugate geometrically on the Argand plane
Sketch curves and regions in the complex plane defined by conditions on modulus and argument, such as circles, perpendicular bisectors, rays and half-planes
Use de Moivre's theorem to find powers and nth roots of complex numbers and to derive the roots of unity and their geometric arrangement
Express complex numbers in modulus-argument form and use it to multiply and divide, interpreting these operations geometrically as scaling and rotation
Solve quadratic equations with complex coefficients and factorise polynomials over the complex field, using the conjugate root theorem for real polynomials
Further Integration (MEX-C1)
Apply integration by parts to evaluate integrals of products, including repeated application and the recovery of the original integral
Decompose rational functions into partial fractions and use the decomposition to integrate, including linear, repeated and irreducible quadratic factors
Evaluate integrals using trigonometric substitution and the t = tan(x/2) substitution, including completing the square to reach standard inverse-trigonometric and logarithmic forms
Integrate powers and products of trigonometric functions: powers of sin and cos (odd and even), powers of tan and sec, the integral of sec x, and products of sines and cosines via product-to-sum identities
Applications of Calculus to Mechanics (MEX-M1)
Use Newton's laws to resolve forces and form the equation of motion: weight, tension, normal and resistive forces, equilibrium of concurrent forces, and the conical pendulum
Analyse projectile motion using calculus, resolving into horizontal and vertical components, and extend to projectiles experiencing a resistance proportional to velocity
Model rectilinear motion under gravity with a resistive force proportional to velocity or to the square of velocity, and determine terminal velocity
Derive and apply the equations of simple harmonic motion, relating acceleration, velocity, displacement, amplitude and period for an oscillating particle
Apply calculus to rectilinear motion where acceleration is expressed as a function of displacement or velocity, using the forms and
Proof (MEX-P2)
Prove results involving sums, divisibility and inequalities for all integers using the principle of mathematical induction
Prove inequalities using algebraic manipulation, the fact that squares are non-negative, and standard results such as the arithmetic mean-geometric mean inequality
Use the language of proof, prove results by contradiction and contrapositive, and disprove statements by counterexample
Further Work with Vectors (MEX-V1)
Represent three-dimensional vectors in component form, compute the scalar product and magnitude, and find vector equations of lines and the equation of a sphere
Prove geometric results using vectors, including properties of triangles, parallelograms and the diagonals of quadrilaterals, by expressing points as position vectors
Compute the projection of one vector onto another, distinguishing the scalar projection from the vector projection, and resolve a vector into parallel and perpendicular components