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Try this with Specialist Mathematics

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Practice paper focus areas

• Exam 1 — Unit 3 further complex numbers: De Moivre's theorem, roots of z^n, conjugate root theorem, factorisation over C; Unit 3 mathematical induction: summation and divisibility proofs; Unit 3 vectors in 3D: cross product, area/volume, lines and planes, point-plane distance
• Exam 2 — Unit 3 further complex numbers: De Moivre's theorem, nth roots, conjugate root theorem, polynomial factorisation over C; Unit 3 mathematical induction: summation and divisibility proofs; Unit 3 vectors in 3D: cross products, vector/Cartesian equations of lines and planes, distance formulae
• Exam 3 — Further complex numbers: De Moivre's theorem, powers/roots, conjugate root theorem, polynomial factorisation over C; Mathematical induction: summation and divisibility proofs; Vectors in 3D: lines, planes, cross products, distance formulae, spheres, projectile & circular motion via vector calculus
• Exam 4 — Statistical inference: sampling distribution of the sample mean, constructing and interpreting confidence intervals for a population mean (known sigma), and required sample size — set in a respiratory-illness clinical-trial recovery-time context; Further complex numbers: De Moivre's theorem, powers and nth roots, polynomial factorisation over C, conjugate root theorem; Mathematical induction: summation identities and divisibility proofs
• Exam 5 — Vectors in 3D: vector/Cartesian equations of lines and planes, cross products, concurrent vs skew roof-beam intersections, shortest-distance and point-to-plane formulae, spheres; Further complex numbers: De Moivre's theorem, powers and roots, conjugate root theorem, factorisation over C; Mathematical induction: summation and divisibility proofs
• Exam 6 — Unit 3 further complex numbers: De Moivre's theorem, modulus-argument form, conjugate root theorem, factorisation over C; Unit 3 mathematical induction: summation and divisibility proofs; Unit 3 vectors in 3D: dot/cross products, lines and planes, distance formulae, spheres
• Exam 7 — Unit 3 further complex numbers: De Moivre's theorem, nth roots, conjugate root theorem, polynomial factorisation over C; Unit 3 mathematical induction: summation and divisibility proofs; Unit 3 vectors in 3D: cross products, lines/planes, distances, line-plane intersection
• Exam 8 — Unit 3 further complex numbers: factorising z^4+4 over C, conjugate root theorem, De Moivre for powers/roots and argument calculations (cryptography framing); Mathematical induction: summation and divisibility proofs; Vectors in 3D: lines, planes, cross product, distance formulae, spheres
• Exam 9 — Unit 3 further complex numbers: De Moivre's theorem, powers and nth roots, conjugate root theorem and factorisation over C; Unit 3 mathematical induction: summation and divisibility proofs; Unit 3 vectors in 3D: cross product, scalar/vector equations of lines and planes, point-to-plane distance, spheres
• Exam 10 — Unit 3 further complex numbers: De Moivre's theorem, roots of unity, polynomial factorisation over C, conjugate root theorem; Signal-processing thread: proving Fourier harmonic-sum trig identities via the complex geometric series z=e^{i theta} (Dirichlet kernel, odd-harmonic sum); Mathematical induction: summation and divisibility proofs
• Exam 11 — Paper 1 (technology-free): De Moivre's theorem and complex arithmetic, conjugate root theorem, mathematical induction (summation and divisibility), 3D vectors (dot/cross product, lines/planes, distance, spheres), integration techniques (inverse trig, partial fractions, by parts, substitution), applications (areas, volumes of revolution, PDFs), differential equations (separable, implicit, related rates), SHM and projectile motion, Gaussian elimination, and statistical inference (sampling distribution of the mean, confidence intervals for mu, sample size).; Paper 2 (technology-active): heavier computation and applied modelling on the same Units 3 & 4 topics, with the quality-control-in-manufacturing context (sampling distributions, batch sample sizes, 95% CI for mean component length) recurring across confidence-interval and sample-size items, plus Simpson's rule, volumes of revolution, logistic/separable DEs and slope fields, projectile and circular motion, and complex-number modelling.; Cognitive spread: ~60% simple familiar, ~20% complex familiar, ~20% complex unfamiliar across Select, Recall-and-use, Apply, Analyse-and-reason and Communicate, with Band A model solutions showing full method, precise notation and contextual interpretation of results.
• Exam 12 — Rates of change & separable differential equations applied to traffic-flow (Greenshields) modelling: setting up and solving dk/dt and dq/dk; Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts; Applications of integral calculus: areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Exam 13 — Vector calculus: differentiation of vector functions, velocity/speed/acceleration, projectile and circular/elliptical motion (astronomy satellite context); Further complex numbers: modulus-argument form, De Moivre's theorem, roots over C, conjugate root theorem, polynomial factorisation; Mathematical induction: summation and divisibility proofs
• Exam 14 — Unit 4 integration techniques — partial-fraction decomposition of proper rational functions and integration to logarithmic form, anchored in a CT-dosimetry absorption-rate context; De Moivre's theorem, conjugate root theorem and factorisation of polynomials over the complex field (Unit 3); Mathematical induction — summation and divisibility proofs (Unit 3)
• Exam 15 — Continuous probability density functions modelled on an ecological fish-weight survey (normalisation constant, mean, median, mode, variance, interval probabilities); Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts; Unit 4 applications of integration: areas between curves, volumes of revolution, Simpson's rule
• Exam 16 — Vectors in 3D: cross products, moment of a force (r×F), scalar triple product, lines/planes, distance formulae, spheres; Further complex numbers: De Moivre's theorem, nth roots, conjugate root theorem, factorisation over C; Mathematical induction: summation and divisibility proofs
• Exam 17 — Paper 1 (technology-free): De Moivre's theorem, conjugate root theorem, 3D vectors (dot/cross products, planes, distance), inverse-trig and partial-fraction integration, integration by parts, separable DEs, implicit differentiation, mathematical induction, and Gaussian elimination — all hand-computable.; Paper 2 (technology-active): Gaussian elimination for the intersection of two planar ore seams and a drill line (geology/mining stimulus), volumes of revolution, related rates, Newton's law of cooling, simple harmonic motion, circular motion, area between curves, and statistical inference (sampling distribution, 95% CI for μ, sample size).; QCAA EA marks-based standard across five assessment objectives (Select; Recall & use; Apply; Analyse & reason; Communicate) at simple familiar (~60%), complex familiar (~20%) and complex unfamiliar (~20%) levels, 120 marks total (Paper 1 = 60, Paper 2 = 60).
• Exam 18 — Unit 4 integration techniques — inverse-trig integrals, substitution, partial fractions, and integration by parts (the paper's stimulus thread: present value of a continuous income stream with exponential decay, PV = ∫ R(t)e^{-rt} dt); Unit 4 applications of integral calculus — areas between curves, volumes of revolution, Simpson's rule, probability density functions; Unit 3 further complex numbers — De Moivre's theorem, conjugate root theorem, factorisation over C
• Exam 19 — Mathematical induction (summation and divisibility proofs) framed through a sports-science cumulative fatigue index; Further complex numbers: De Moivre's theorem, powers and roots, conjugate root theorem, factorisation over C; Vectors in 3D: cross products, lines and planes, point-plane distance, spheres, and vector calculus (projectile/circular motion)
• Exam 20 — Rates of change and separable differential equations — Newton's law of cooling modelled as dT/dt = -k(T - Ts), solved by separation of variables; The time constant tau = 1/k, its interpretation (excess temperature falls to 1/e of its initial value) and half-life reasoning; Statistical inference — sampling distribution of the mean, z-based confidence intervals for a population mean mu, and minimum sample size