HSC Mathematics Advanced Practice Exams with Worked Solutions

The 20 practice exams inside the HSC Mathematics Advanced 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 1100 marks · 22 questions · 2 sections
   • Functions and graphing techniques (rational, exponential, logarithmic) as the dominant theme
   • Differential and integral calculus including the second derivative and areas
   • Trigonometric functions and graph transformations
   • Financial mathematics (annuity/superannuation modelling)
   • Statistical analysis (bivariate regression and the normal distribution)
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2. Practice Exam 2100 marks · 22 questions · 2 sections
   • Trigonometric Functions and Graphs (transformations, equations, modelling, area)
   • Differential Calculus (product rule, tangents, stationary points, concavity/inflection)
   • Integral Calculus (area between curves, trapezoidal rule, applications)
   • Financial Mathematics (annuities, reducing-balance loans)
   • Statistical Analysis (descriptive, bivariate regression, normal & continuous random variables)
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3. Practice Exam 3100 marks · 22 questions · 2 sections
   • Calculus (differential calculus, the second derivative, integral calculus) — ~50 of 90 marks
   • Financial Mathematics — reducing-balance loan modelling
   • Statistical Analysis — normal distribution, bivariate regression, continuous random variables
   • Trigonometric Functions and Graphs
   • Functions and graphing techniques (curve sketching)
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4. Practice Exam 4100 marks · 21 questions · 2 sections
   • Financial Mathematics — Modelling Financial Situations (reducing-balance loans via recurrence, superannuation annuities, depreciation and geometric series): 26 dedicated marks
   • Statistical Analysis — Descriptive Statistics, Bivariate Data Analysis and Random Variables (continuous PDFs and the normal distribution): 33 marks
   • Calculus — Differential Calculus, the Second Derivative and Integral Calculus (curve sketching, tangents, area and the trapezoidal rule): 17 marks
   • Functions (Graphing Techniques) and Trigonometric Functions and Graphs (inverses, transformations, equation solving and periodic modelling): 14 marks
   • Multi-part real-world modelling with full mark-by-mark band 6 solutions, every figure recomputed and stated with units
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5. Practice Exam 5100 marks · 21 questions · 2 sections
   • Statistical Analysis — Descriptive Statistics & Bivariate Data (5-number summary, boxplots, outliers, least-squares regression, correlation, interpretation)
   • Statistical Analysis — Random Variables (discrete probability distributions, E(X), Var(X), linear transformations; the normal distribution, z-scores, empirical rule)
   • Calculus — differential (product/chain rule, stationary points, second derivative, concavity) and integral (area under/between curves, trapezoidal rule)
   • Financial Mathematics and exponential modelling (annuities/superannuation; Newton's law of cooling)
   • Trigonometric functions and graphs (solving equations, area under a sinusoidal curve)
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6. Practice Exam 6100 marks · 21 questions · 2 sections
   • Functions (Graphing Techniques) — rational functions, transformations, curve sketching with calculus
   • Calculus — differential, second derivative, integral (area + trapezoidal rule)
   • Trigonometric functions and graphs
   • Financial Mathematics — reducing-balance loan modelling
   • Statistical Analysis — bivariate regression and continuous/normal random variables
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7. Practice Exam 7100 marks · 22 questions · 2 sections
   • Trigonometric Functions and Graphs
   • Calculus (Differential & Integral)
   • Financial Mathematics
   • Statistical Analysis
   • Functions (Graphing Techniques)
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8. Practice Exam 8100 marks · 21 questions · 2 sections
   • Calculus: Differential Calculus, The Second Derivative, Integral Calculus (heavily weighted)
   • Trigonometric Functions and Graphs
   • Financial Mathematics (Modelling Financial Situations)
   • Statistical Analysis (Bivariate Data; Random Variables incl. continuous & normal)
   • Functions and applied modelling (optimisation, kinematics, exponential growth)
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9. Practice Exam 9100 marks · 20 questions · 2 sections
   • Financial Mathematics (Modelling Financial Situations) — annuities, reducing-balance loans, depreciation, present-value comparison, recurrence/geometric savings models
   • Calculus — differential (stationary points, second-derivative test, concavity/inflection) and integral (definite integrals, area)
   • Statistical Analysis — least-squares regression and correlation, continuous random variables, normal distribution / empirical rule
   • Functions (graphing techniques) and Trigonometric Functions and Graphs
   • Realistic HSC weighting, varied difficulty, and a 15-mark multi-part financial modelling task
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10. Practice Exam 10100 marks · 22 questions · 2 sections
    • Statistical Analysis weighted heaviest (~40 of 90 marks): descriptive statistics, bivariate data analysis, discrete and continuous random variables
    • Full Year 12 coverage: graphing techniques, trigonometric functions, differential and integral calculus, the second derivative, financial mathematics
    • Two 9-mark multi-part modelling/application questions (bivariate+RV market data; particle kinematics via calculus)
    • Every numerical answer recomputed and verified in Python (SymPy/SciPy); units stated throughout
    • Band-6 model answers with full working and mark-by-mark allocation that sums to each question total
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11. Practice Exam 11100 marks · 22 questions · 2 sections
    • Functions and Graphing Techniques (rational, quadratic, inverse, transformations)
    • Differential and Integral Calculus (including the second derivative and curve sketching)
    • Trigonometric Functions and Graphs
    • Financial Mathematics (modelling financial situations)
    • Statistical Analysis (descriptive, bivariate and random variables)
    See what this paper covers →
12. Practice Exam 12100 marks · 22 questions · 2 sections
    • Trigonometric Functions and Graphs (graphing, equations, identities, modelling)
    • Differential and Integral Calculus including the second derivative
    • Financial Mathematics — modelling financial situations (annuities/superannuation)
    • Statistical Analysis — random variables and bivariate data
    • Functions and graphing techniques
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13. Practice Exam 13100 marks · 21 questions · 2 sections
    • Differential Calculus (product/quotient/chain rules, stationary points)
    • The Second Derivative (concavity, points of inflection, curve sketching)
    • Integral Calculus (areas, trapezoidal rule, kinematics)
    • Financial Mathematics, Statistical Analysis and Trigonometric modelling
    • Multi-step calculus modelling/optimisation applications
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14. Practice Exam 14100 marks · 19 questions · 2 sections
    • Financial Mathematics (Modelling Financial Situations) — reducing-balance loans, annuities, recurrence/series
    • Calculus — differentiation, second derivative & curve sketching, integration and kinematics
    • Trigonometric Functions and Graphs — modelling periodic phenomena
    • Statistical Analysis — bivariate data (correlation/regression) and random variables (normal distribution)
    • Functions, exponential/logarithmic equations and rates of change
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15. Practice Exam 15100 marks · 22 questions · 2 sections
    • Statistical Analysis (Descriptive Statistics) — five-number summary, outliers, standard deviation
    • Statistical Analysis (Bivariate Data) — Pearson's r, least-squares regression, prediction and reliability
    • Statistical Analysis (Random Variables) — discrete distributions and the normal distribution / empirical rule
    • Calculus — differential (curve sketching, optimisation) and integral (area, trapezoidal rule)
    • Financial Mathematics, Trigonometric Functions and Functions (graphing techniques)
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16. Practice Exam 16100 marks · 22 questions · 2 sections
    • Functions (Graphing Techniques) — rational functions, asymptotes, area between curves, transformations, curve sketching
    • Calculus — differentiation rules, second-derivative concavity, integration, optimisation
    • Financial Mathematics — reducing-balance loan / annuity modelling
    • Statistical Analysis — normal distribution, bivariate regression, discrete random variables
    • Trigonometric Functions — exact-value equation solving and periodic (tide) modelling
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17. Practice Exam 17100 marks · 22 questions · 2 sections
    • Trigonometric Functions and Graphs (transformations, equations, identities, modelling)
    • Differential and Integral Calculus (including the second derivative and trig calculus)
    • Financial Mathematics (compound interest, annuities, reducing-balance loans)
    • Statistical Analysis (discrete random variables; bivariate regression and correlation)
    • Functions and graphing techniques (curve sketching, area and volumes of revolution)
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18. Practice Exam 18100 marks · 19 questions · 2 sections
    • Calculus emphasis: differential calculus, the second derivative, integral calculus
    • Realistic NESA Section II weighting across all Year 12 Mathematics Advanced modules
    • Multi-part modelling/application questions worth 5+ marks (tide, loan/superannuation, bivariate)
    • Full band-6 worked solutions with every numerical answer recomputed and units stated
    • Mark-by-mark criteria with per-part marks summing to each question total (overall 90)
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19. Practice Exam 19100 marks · 22 questions · 2 sections
    • Financial Mathematics — Modelling Financial Situations (annuities, reducing-balance loans, compound interest, recurrence)
    • Differential & Integral Calculus (second derivative, curve sketching, areas, volumes of revolution)
    • Statistical Analysis (normal distribution / z-scores, bivariate data & least-squares regression)
    • Trigonometric Functions and Graphs (solving equations, amplitude/period, sinusoidal modelling)
    • Functions & Graphing Techniques (trapezoidal rule applied to rates/motion)
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20. Practice Exam 20100 marks · 20 questions · 2 sections
    • Statistical Analysis — Descriptive Statistics & Bivariate Data Analysis (Q15, Q16)
    • Statistical Analysis — Random Variables: continuous PDFs and the normal distribution (Q17, Q18)
    • Calculus — differentiation, the second derivative and integration (Q11, Q13, Q19)
    • Financial Mathematics — reducing-balance loans and annuities (Q14)
    • Functions, Trigonometric graphs and exponential/log modelling (Q12, Q20)
    See what this paper covers →