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Specialist MathematicsQ&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 conjugate0Q&A pairs
- Represent complex numbers in Cartesian and polar form, perform arithmetic, and apply de Moivre's theorem1Q&A pairs
- State and apply de Moivre's theorem to evaluate integer powers of complex numbers and derive trigonometric identities0Q&A pairs
- Factorise polynomials over the complex numbers using the conjugate root theorem and the fundamental theorem of algebra1Q&A pairs
- Sketch rational functions, reciprocal and modulus graphs, and use transformations and asymptotic behaviour4Q&A pairs
- Differentiate inverse trig functions, use implicit differentiation, and integrate rational functions, partial fractions and trig forms0Q&A pairs
- Define the inverse circular functions with their restricted domains and ranges and sketch their graphs1Q&A pairs
- 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 equations0Q&A pairs
- Multiply and divide complex numbers in polar form, interpreting the result as rotation and scaling0Q&A pairs
- Sketch graphs of rational functions, identifying intercepts, vertical, horizontal and oblique asymptotes1Q&A pairs
- Sketch the reciprocal of a function, relating zeros to asymptotes and turning points to turning points0Q&A pairs
- Describe and sketch subsets of the complex plane defined by equations and inequalities in modulus and argument0Q&A pairs
- Find the nth roots of a complex number and the nth roots of unity, and represent them on the Argand plane0Q&A pairs
- Compute the scalar (dot) product of vectors in three dimensions and use it for angles, perpendicularity and projections0Q&A pairs
- Represent complex numbers on the Argand plane and find modulus and argument, converting to polar form2Q&A pairs
- Write vector and parametric equations of curves and convert between vector, parametric and cartesian forms1Q&A pairs
- Compute the vector (cross) product in three dimensions and use it to find perpendicular vectors and areas0Q&A pairs
- Use vector functions of time and differentiate them to find velocity, speed and acceleration along a path0Q&A pairs
- Use 3D vectors with the dot product and cross product to find lengths, angles, projections and areas1Q&A pairs
Unit 4
- Find the area between curves using definite integration, accounting for intersection points and which curve is on top0Q&A pairs
- State the central limit theorem and use it to compute probabilities for the sample mean0Q&A pairs
- Construct and interpret confidence intervals for a population mean and find the required sample size0Q&A pairs
- Set up and solve the exponential growth-decay equation and the logistic equation and interpret their solutions0Q&A pairs
- Resolve a rational function into partial fractions and integrate each term0Q&A pairs
- Integrate by substitution, changing the variable and the limits to evaluate definite and indefinite integrals0Q&A pairs
- Integrate using substitution, partial fractions and trig identities, and apply integration to volumes and differential equations0Q&A pairs
- Integrate trigonometric functions by first applying double-angle, Pythagorean and product identities0Q&A pairs
- Use 2x2 matrices for arithmetic, determinants and inverses, and as linear transformations of the plane1Q&A pairs
- Prove statements by mathematical induction, including summation, divisibility and inequality results1Q&A pairs
- Describe the sampling distribution of the sample mean, including its mean and the standard error0Q&A pairs
- Solve separable first-order differential equations and apply an initial condition to find the particular solution1Q&A pairs
- Interpret and sketch slope (direction) fields for first-order differential equations and sketch solution curves0Q&A pairs
- Use the distribution of the sample mean and the central limit theorem to build confidence intervals for a population mean0Q&A pairs
- Write vector and parametric equations of lines and planes and find intersections, distances and angles0Q&A pairs
- Find the volume of a solid generated by rotating a region about the x-axis or y-axis using the disc method1Q&A pairs