VCE Mathematical Methods Practice Exams with Worked Solutions

The 20 practice exams inside the VCE Mathematical Methods Mastery Pack, each set out like the real paper with a separate worked-solution guide. Open any paper to see what it covers.

1. Practice Exam 1120 marks · 33 questions · 3 sections
   • 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
   • Probability and statistics in a biological-sampling context: normal distribution, binomial distribution, and approximate confidence intervals for a population proportion
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2. Practice Exam 2120 marks · 31 questions · 3 sections
   • 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
   • Probability: binomial distribution, the normal distribution and confidence intervals for a proportion
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3. Practice Exam 3120 marks · 32 questions · 3 sections
   • 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
   • Statistical inference: sample proportions and approximate 95% confidence intervals
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4. Practice Exam 4120 marks · 31 questions · 3 sections
   • 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
   • Technology-free fluency: exact-value trig, by-hand product/quotient/chain differentiation, and exact definite integration
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5. Practice Exam 5120 marks · 32 questions · 3 sections
   • 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
   • Application/modelling: translating a manufacturing context (cost, revenue, profit, material, depreciation, quality control) into functions and interpreting results in context
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6. Practice Exam 6120 marks · 30 questions · 3 sections
   • 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
   • Probability & statistics: binomial distribution, continuous random variables and pdfs, normal distribution and approximate confidence intervals for a population proportion
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7. Practice Exam 7120 marks · 33 questions · 3 sections
   • 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
   • Core technology-free calculus and algebra: product/quotient differentiation, tangents, exact definite integrals, exponential/trigonometric equations, index and log laws, plus calculus optimisation of a cost model
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8. Practice Exam 8120 marks · 33 questions · 3 sections
   • 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
   • Technology-free core skills: product/quotient rules, first principles, antidifferentiation, log/index equations and binomial probabilities
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9. Practice Exam 9120 marks · 32 questions · 3 sections
   • 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
   • Algebra and index/log laws: solving exponential and quadratic-in-disguise equations
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10. Practice Exam 10120 marks · 31 questions · 3 sections
    • 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
    • Exponential modelling via Newton's Law of Cooling: forming/interpreting T = A + Be^(-kt), rates of change, limiting behaviour
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11. Practice Exam 11120 marks · 31 questions · 3 sections
    • 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
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12. Practice Exam 12120 marks · 33 questions · 3 sections
    • 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
    • Probability and statistics in a finance context: the normal distribution (z-scores, percentiles) and the binomial distribution
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13. Practice Exam 13120 marks · 32 questions · 3 sections
    • 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
    • Technology-free fluency: exact-value differentiation, antidifferentiation, tangents/normals and trigonometric equations over a restricted domain
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14. Practice Exam 14120 marks · 32 questions · 3 sections
    • 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
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15. Practice Exam 15120 marks · 33 questions · 3 sections
    • Normal distribution & tolerances
    • Binomial distribution
    • Sample proportions & confidence intervals
    • Calculus & probability density functions
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16. Practice Exam 16120 marks · 33 questions · 3 sections
    • 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
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17. Practice Exam 17120 marks · 31 questions · 3 sections
    • 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
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18. Practice Exam 18120 marks · 34 questions · 3 sections
    • 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)
    • Algebra & functions (exponential/log/simultaneous equation solving, tangents, inverse functions)
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19. Practice Exam 19120 marks · 31 questions · 3 sections
    • 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
    • Statistics and algebra: sample proportions and confidence intervals, exact-value solution of exponential/log/trig equations, inverse and hybrid functions
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20. Practice Exam 20120 marks · 31 questions · 3 sections
    • 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
    • Calculus applied to response/uptake models: differentiation, optimisation, definite integrals and average value
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