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Practice paper focus areas

• Exam 1 — de Moivre and polar powers (3.1); composite-function domain (3.2); partial fractions (4.1)
• Exam 2 — loci in the Argand plane (3.1); rational function sketching (3.2); trigonometric substitution (4.1)
• Exam 3 — roots of unity (3.1); inverse functions (3.2); volume of revolution about the y-axis (4.1)
• Exam 4 — conjugate roots of a quartic (3.1); y = 1/f(x) and y = |f(x)| (3.2); separable differential equation (4.2)
• Exam 5 — multiplication as rotation (3.1); f(|x|) and absolute value equations (3.2); area between curves in y (4.1)
• Exam 6 — polar form and modulus-argument identities (3.1); oblique asymptotes (3.2); integral of f'(x)/f(x) (4.1)
• Exam 7 — complex polynomial and factor theorem (3.1); composite of graphs given as sketches (3.2); volume about the x-axis (4.1)
• Exam 8 — regions bounded by Arg and modulus (3.1); one-to-one restriction (3.2); sin^2 and cos^2 integrals (4.1)
• Exam 9 — nth roots of a complex number (3.1); rational function from features (3.2); partial fractions and areas (4.1)
• Exam 10 — geometry of complex numbers as vectors (3.1); inverse graph reflection (3.2); substitution with exact limits (4.1)
• Exam 11 — de Moivre to derive a trigonometric identity (3.1); absolute value graphs (3.2); volume of a vessel to depth h (4.1)
• Exam 12 — loci |z - a| = k|z - b| (3.1); composite function range (3.2); Newton's-law-of-cooling style DE (4.2)
• Exam 13 — polynomial with given complex roots (3.1); rational functions with holes and asymptotes (3.2); area between two curves (4.1)
• Exam 14 — roots of unity sum and product (3.1); inverse of a rational function (3.2); volume about the y-axis by shells-free disc method (4.1)
• Exam 15 — modulus-argument proof (3.1); y = f(|x|) and y = |f(x)| together (3.2); integration by substitution (4.1)
• Exam 16 — complex transformation sequences (3.1); composite and inverse from a table (3.2); volume of a torus-style solid (4.1)
• Exam 17 — cube roots of a complex number (3.1); reciprocal function sketch (3.2); partial fractions with ln (4.1)
• Exam 18 — Arg of differences and quadrilaterals in the plane (3.1); rational function with oblique asymptote (3.2); area with x = f(y) (4.1)
• Exam 19 — polar powers and quadrant of z^n (3.1); one-to-one and inverse with restricted domain (3.2); volume of a vase (4.1)
• Exam 20 — complex polynomial equation solving (3.1); absolute value equation with infinite solutions (3.2); trigonometric identity integrals (4.1)