Assessment and exam practice.

Try this with Mathematical Methods

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2. Start with one timed section or task and record where you spent the most time.
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Practice paper focus areas

• Exam 1 — Calculus applied to a logistic population-growth model: rates of change, optimisation of growth rate, average value and definite integrals; Functions, transformations and inverse functions arising from exponential/logistic models, with domain and range; Algebra: index and log laws, solving exponential and logarithmic equations exactly over a domain
• Exam 2 — Calculus: differentiation rules, definite integrals, optimisation and stationary points applied to projectile motion; Algebra: solving exponential, logarithmic and trigonometric equations over a domain; Functions: quadratic and circular models, transformations, domain/range
• Exam 3 — Calculus of exponential decay models (derivatives, rates, tangents, antidifferentiation, definite integrals/AUC, average value); Exponential and logarithmic algebra: index/log laws and solving equations exactly over a domain; Probability: discrete random variables, binomial distribution, continuous pdfs and the normal distribution
• Exam 4 — Circular (trig) functions: modelling periodic tidal motion with sinusoids — amplitude, period, mean, range, and solving trig equations over a domain; Calculus applied to trig models: derivatives, rates of change, slack water (stationary points), fastest rise/fall (points of inflection), average value via definite integrals; Probability & statistics in context: binomial distribution (mean/variance), the normal distribution (z-scores), and approximate 95% confidence intervals for a population proportion
• Exam 5 — Calculus: differentiation (product/chain rules, derivatives of e^x and log), antidifferentiation, definite integrals, area between curves, average value, and optimisation via stationary points; Algebra: solving exponential equations (quadratic-in-disguise), circular equations over a domain, literal/inverse functions and tangents; Probability & statistics: binomial distribution (E(X), Var(X)), the normal distribution (z-scores), and approximate confidence intervals for a population proportion
• Exam 6 — Calculus: differentiation of exponential models, tangents, rates of change, antidifferentiation and definite integrals (area, average value) in technology-free form; Algebra: index and log laws, solving exponential and logarithmic equations exactly over a domain, half-life modelling; Functions: exponential and log functions, transformations, inverse and composite functions, asymptotes and domain/range
• Exam 7 — Binomial distribution in a quality-control context: exact by-hand probabilities (Section A) and full CAS modelling with E(X), Var(X), conditional probability and minimum-sample-size (Section C); Sample proportions and approximate 95%/90% confidence intervals for a population proportion of defectives, including margin-of-error sample-size design; Continuous random variables: constructing a probability density function, mean, median, variance and interval probabilities for a manufacturing dimension
• Exam 8 — The normal distribution: probabilities, conditional probability, quantiles/inverse, and standardisation (z-scores); Sample proportions and approximate confidence intervals for a population proportion; Calculus modelling: differentiation, stationary points, average value and definite integrals applied to context
• Exam 9 — Sample proportions and approximate confidence intervals for a population proportion; Binomial distribution (mean np, variance np(1-p)) and the normal approximation; Calculus: differentiation, stationary points and rates of change applied to a modelling context
• Exam 10 — Calculus: differentiation (product/chain), antidifferentiation & definite integrals, stationary points and their nature, average value; Algebra: solving exponential equations (quadratic-in-e^x), trigonometric equations over a domain, inverse functions with domain/range; Probability & statistics: binomial distribution, continuous PDFs, the normal distribution and approximate confidence intervals for a proportion
• Exam 11 — Circular function modelling: differentiation, max rate, period/range and solving trig equations over a domain (Ferris wheel height); Calculus applications: tangents, average value via definite integral, optimisation and area under exponential models; Probability & statistics: binomial occupancy, normal distribution z-scores, sample proportion confidence intervals and continuous pdfs
• Exam 12 — Exponential and logarithmic models for compound growth (index/log laws, e^x, solving exponential and log equations technology-free); Calculus of growth models: differentiation of exponential/product forms, rates of change, antidifferentiation and definite integrals; Financial modelling with first-order recurrence relations (reducing-balance loans, annuities) and continuous vs periodic compounding using CAS
• Exam 13 — Calculus in context: derivatives, rates of change, stationary/inflection points and definite-integral measures (average value, total change) applied to exponential and logistic growth models; Exponential and logarithmic algebra: index/log laws, solving exponential & log equations, inverse/composite functions and transformations (technology-free); Probability & statistics: binomial distribution, the normal distribution (z-scores, percentiles) and approximate confidence intervals for a population proportion
• Exam 14 — Calculus: rates of change, related rates, optimisation and definite integrals applied to a water-tank context; Functions and graphs: quadratic, exponential and circular models with domain/range and asymptotic behaviour; Technology-free differentiation (product/chain rule, first principles) and exact-value solving of log/exponential/trig equations
• Exam 15 — Normal distribution & tolerances; Binomial distribution; Sample proportions & confidence intervals
• Exam 16 — Calculus in a projectile context: differentiation, tangents/first principles, antidifferentiation, definite integrals, average value and optimisation; Functions and algebra: exponential/log/trig equations over a domain, inverse and composite functions, hybrid-function continuity and differentiability; Probability and statistics: binomial distribution, the normal distribution with z-scores, and confidence intervals for a population proportion
• Exam 17 — Calculus in context (rates of change, average value, optimisation) applied to a sinusoidal temperature model; Circular functions: amplitude/period/midline, exact-value equation solving, and transformations; Probability and statistics: normal distribution, binomial, and confidence intervals for a population proportion
• Exam 18 — Differential & integral calculus (product rule, stationary points, antidifferentiation, definite integrals, average value, optimisation); Probability distributions (binomial E(X)/Var(X), continuous pdfs, the normal distribution, conditional probability); Statistical inference (sample proportions and approximate confidence intervals for a population proportion)
• Exam 19 — Differential calculus: product/chain/quotient rules, stationary points and nature, tangents, rates of change; Integral calculus: antidifferentiation, definite integrals, area, average value of a function; Probability: binomial distribution, the normal distribution, continuous random variables and probability density functions
• Exam 20 — Sample proportions and approximate confidence intervals for a population proportion; Binomial distribution: exact probabilities, mean np and variance np(1-p), conditional probability; The normal distribution: z-scores, percentiles, and the sampling distribution of a sample proportion