NSW · NESAQ&A
Maths Extension 2Q&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 plane2Q&A pairs
- Sketch curves and regions in the complex plane defined by conditions on modulus and argument, such as circles, perpendicular bisectors, rays and half-planes0Q&A pairs
- Use de Moivre's theorem to find powers and nth roots of complex numbers and to derive the roots of unity and their geometric arrangement0Q&A pairs
- Express complex numbers in modulus-argument form and use it to multiply and divide, interpreting these operations geometrically as scaling and rotation1Q&A pairs
- Solve quadratic equations with complex coefficients and factorise polynomials over the complex field, using the conjugate root theorem for real polynomials1Q&A pairs
Further Integration (MEX-C1)
- Apply integration by parts to evaluate integrals of products, including repeated application and the recovery of the original integral0Q&A pairs
- Decompose rational functions into partial fractions and use the decomposition to integrate, including linear, repeated and irreducible quadratic factors2Q&A pairs
- Evaluate integrals using trigonometric substitution and the t = tan(x/2) substitution, including completing the square to reach standard inverse-trigonometric and logarithmic forms1Q&A pairs
Applications of Calculus to Mechanics (MEX-M1)
- Analyse projectile motion using calculus, resolving into horizontal and vertical components, and extend to projectiles experiencing a resistance proportional to velocity1Q&A pairs
- Model rectilinear motion under gravity with a resistive force proportional to velocity or to the square of velocity, and determine terminal velocity0Q&A pairs
- Derive and apply the equations of simple harmonic motion, relating acceleration, velocity, displacement, amplitude and period for an oscillating particle0Q&A pairs
- Apply calculus to rectilinear motion where acceleration is expressed as a function of displacement or velocity, using the forms a = v dv/dx and a = d(v^2/2)/dx1Q&A pairs
Proof (MEX-P2)
- Prove results involving sums, divisibility and inequalities for all integers using the principle of mathematical induction2Q&A pairs
- Prove inequalities using algebraic manipulation, the fact that squares are non-negative, and standard results such as the arithmetic mean-geometric mean inequality0Q&A pairs
- Use the language of proof, prove results by contradiction and contrapositive, and disprove statements by counterexample1Q&A pairs
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 sphere1Q&A pairs
- Prove geometric results using vectors, including properties of triangles, parallelograms and the diagonals of quadrilaterals, by expressing points as position vectors0Q&A pairs
- Compute the projection of one vector onto another, distinguishing the scalar projection from the vector projection, and resolve a vector into parallel and perpendicular components0Q&A pairs