§-Specialist Mathematics Q&A
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Specialist Mathematics Q&A by dot point
A short Q&A bank for every WA Specialist Mathematics 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.
Unit 3
Perform addition, subtraction, multiplication and division of complex numbers in Cartesian form using the conjugate
Represent complex numbers in Cartesian and polar form, perform arithmetic, and apply de Moivre's theorem
State and apply de Moivre's theorem to evaluate integer powers of complex numbers and derive trigonometric identities
Factorise polynomials over the complex numbers using the conjugate root theorem and the fundamental theorem of algebra
Sketch rational functions, reciprocal and modulus graphs, and use transformations and asymptotic behaviour
Differentiate inverse trig functions, use implicit differentiation, and integrate rational functions, partial fractions and trig forms
Define the inverse circular functions with their restricted domains and ranges and sketch their graphs
Sketch graphs of the modulus functions y equals the absolute value of f of x and y equals f of the absolute value of x, and solve modulus equations
Multiply and divide complex numbers in polar form, interpreting the result as rotation and scaling
Sketch graphs of rational functions, identifying intercepts, vertical, horizontal and oblique asymptotes
Sketch the reciprocal of a function, relating zeros to asymptotes and turning points to turning points
Describe and sketch subsets of the complex plane defined by equations and inequalities in modulus and argument
Find the nth roots of a complex number and the nth roots of unity, and represent them on the Argand plane
Compute the scalar (dot) product of vectors in three dimensions and use it for angles, perpendicularity and projections
Represent complex numbers on the Argand plane and find modulus and argument, converting to polar form
Write vector and parametric equations of curves and convert between vector, parametric and cartesian forms
Compute the vector (cross) product in three dimensions and use it to find perpendicular vectors and areas
Use vector functions of time and differentiate them to find velocity, speed and acceleration along a path
Use 3D vectors with the dot product and cross product to find lengths, angles, projections and areas
Unit 4
Find the area between curves using definite integration, accounting for intersection points and which curve is on top
State the central limit theorem and use it to compute probabilities for the sample mean
Construct and interpret confidence intervals for a population mean and find the required sample size
Set up and solve the exponential growth-decay equation and the logistic equation and interpret their solutions
Resolve a rational function into partial fractions and integrate each term
Integrate by substitution, changing the variable and the limits to evaluate definite and indefinite integrals
Integrate using substitution, partial fractions and trig identities, and apply integration to volumes and differential equations
Integrate trigonometric functions by first applying double-angle, Pythagorean and product identities
Use 2x2 matrices for arithmetic, determinants and inverses, and as linear transformations of the plane
Prove statements by mathematical induction, including summation, divisibility and inequality results
Describe the sampling distribution of the sample mean, including its mean and the standard error
Solve separable first-order differential equations and apply an initial condition to find the particular solution
Interpret and sketch slope (direction) fields for first-order differential equations and sketch solution curves
Use the distribution of the sample mean and the central limit theorem to build confidence intervals for a population mean
Write vector and parametric equations of lines and planes and find intersections, distances and angles
Find the volume of a solid generated by rotating a region about the x-axis or y-axis using the disc method