ATARMAxxing · Mathematical Methods
QCE Mathematical Methods Practice Exams with Worked Solutions
20 full-length papers · worked solutions for every question
The 20 practice exams inside the QCE 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.
- Unit 3 differentiation of exponential, logarithmic and trigonometric functions (chain, product, quotient rules)
- Applications of differentiation: instantaneous rate of change, kinematics, stationary points, second-derivative test, optimisation
- Introduction to integration: antidifferentiation, reverse chain rule, definite integrals and signed area
- Discrete random variables: Bernoulli sequences, binomial distribution and expected value
- Unit 4 further integration: area between curves and numerical integration (trapezoidal rule)
- Trigonometry: sine rule, cosine rule, bearings and 2D/3D problems
- Continuous random variables and the normal distribution: z-scores, technology-based probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Real-world modelling of an exponential population for a Queensland coastal marine species, with written contextual conclusions in Complex Unfamiliar items
- Unit 3 Further Calculus: differentiation of exponential, logarithmic and trigonometric functions via chain, product and quotient rules
- Applications of differentiation: rates of change, kinematics, stationary points, concavity, optimisation and curve interpretation
- Introduction to integration: standard antiderivatives, reverse chain rule, definite integrals, area under a curve and between curves
- Discrete random variables: Bernoulli sequences, the binomial distribution and expected value
- Unit 4: numerical integration (trapezoidal rule), signed area and area between curves
- Two- and three-dimensional trigonometry: sine rule, cosine rule and bearings
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Stimulus context: a satellite navigation cosine signal-strength model analysed for rate of change, stationary points and a manufacturer performance claim
- Band A written justification, correct QCAA notation and contextual concluding statements across Simple Familiar, Complex Familiar and Complex Unfamiliar items
- Unit 3 differentiation: chain, product and quotient rules on exponential, logarithmic and polynomial functions
- Unit 3 applications of differentiation: stationary points, concavity, points of inflection, kinematics and optimisation
- Unit 3 introduction to integration: antidifferentiation, reverse chain rule, definite integrals and area under a curve
- Unit 3 discrete random variables: Bernoulli sequences, the binomial distribution and expected value
- Unit 4 integration extended: signed area, area between two curves and the trapezoidal rule
- Unit 4 trigonometry: sine rule, cosine rule, area of a triangle and 3D applications
- Unit 4 continuous random variables: the normal distribution, z-scores, technology probabilities and inverse normal
- Unit 4 inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Real-world modelling of a rainwater storage tank with a polynomial curved cross-section, optimising dimensions and computing capacity by integration
- Written justification, evaluation of reasonableness and correct QCAA notation across Simple Familiar, Complex Familiar and Complex Unfamiliar items
- Unit 3 differentiation of exponential, logarithmic and trigonometric functions via chain, product and quotient rules
- Applications of differentiation: rates of change, kinematics, stationary points, concavity and optimisation
- Introduction to integration: standard antiderivatives, reverse chain rule, definite integrals and area
- Discrete random variables: Bernoulli sequences, the binomial distribution and expected value
- Unit 4 integration extended to area between curves and the trapezoidal rule for numerical integration
- 2D and 3D trigonometry using the sine rule, cosine rule and bearings
- Continuous random variables and the normal distribution: z-score standardisation, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Real-world logarithmic modelling of bushfire spread with written contextual conclusions (Complex Unfamiliar)
- Correct QCAA notation, constant of integration, units and evaluative justification across all six assessment objectives
- Unit 3 Further Calculus: chain/product/quotient differentiation of exp, log and trig functions
- Applications of differentiation: kinematics, stationary points, concavity, points of inflection, optimisation
- Antidifferentiation: standard forms, reverse chain rule, definite integrals and the constant of integration
- Discrete random variables: Bernoulli sequences, the binomial distribution, expected value and variance
- Unit 4 integration: signed area, area between two curves, numerical integration by the trapezoidal rule
- 2D/3D trigonometry: sine rule, cosine rule and bearings
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Sustained Complex Unfamiliar modelling of a marathon runner's trigonometric velocity profile with written contextual conclusions
- Correct QCAA notation, units, signed-area interpretation and evaluate/justify written conclusions
- Unit 3 differentiation: chain, product and quotient rules on exponential, logarithmic and trigonometric functions
- Applications of differentiation: rates of change, kinematics, stationary points, curve sketching and optimisation
- Introduction to integration: antidifferentiation, constant of integration from initial conditions, definite integrals and area
- Area between two curves and the trapezoidal rule for numerical integration
- Discrete random variables: Bernoulli sequences, the binomial distribution and expected value
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- 2D and 3D trigonometry: sine rule, cosine rule and bearings
- Complex Unfamiliar modelling: exponential decay of soil pesticide concentration with written contextual conclusions
- Differentiation of exponential, logarithmic and trigonometric functions (chain, product, quotient rules)
- Applications of differentiation: stationary points, kinematics, optimisation, curve sketching
- Integration: antidifferentiation, definite integrals, signed area and area between curves
- Numerical integration via the trapezoidal rule and comparison with exact area (parabolic arch context)
- Discrete random variables and the binomial distribution (expected value, variance, probabilities)
- Continuous random variables and the normal distribution (z-scores, inverse normal)
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Two- and three-dimensional trigonometry: sine rule, cosine rule and bearings
- Real-world modelling with written contextual conclusions and correct QCAA notation
- Unit 3 Further Calculus: differentiation of exponential, logarithmic and trigonometric functions via chain, product and quotient rules
- Applications of differentiation: kinematics, stationary points, nature of stationary points, points of inflection, curve sketching and optimisation
- Introduction to integration: antidifferentiation of standard forms, reverse chain rule, constant of integration from initial conditions, definite integrals and area
- Discrete random variables: Bernoulli sequences, binomial distribution, P(X=x), P(X≥x) and expected value E(X)=np
- Unit 4 integration extension: area between two curves, signed area and the trapezoidal rule for numerical integration
- 2D and 3D trigonometry: sine rule, cosine rule and bearings (navigation problems)
- Continuous random variables and the normal distribution: z-score standardisation, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, 95% confidence intervals, margin of error and sample size
- Complex Unfamiliar synthesis: constructing a confidence interval from survey data and evaluating a conservation agency's population claim with a written contextual conclusion
- Band A communication: correct QCAA notation, dx in integrals, absolute value in log integrals, approximately-equals for decimals, units, and explicit interpretive statements
- Differentiation of trigonometric, exponential and logarithmic functions via chain, product and quotient rules
- Applications of differentiation: rates of change, kinematics, stationary points, concavity, inflection and optimisation
- Antidifferentiation, reverse chain rule, definite integrals, area under and between curves, trapezoidal rule
- Sinusoidal modelling of Brisbane daily maximum temperature (amplitude, period, phase, interpretation)
- Discrete random variables: Bernoulli sequences, the binomial distribution, expected value and variance
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Two- and three-dimensional trigonometry: sine rule, cosine rule and bearings
- Written contextual conclusions, correct QCAA notation and evaluation of reasonableness
- Unit 3 differentiation: chain, product and quotient rules on exponential, logarithmic and trigonometric functions
- Applications of differentiation: rates of change, kinematics, stationary points, concavity, points of inflection and optimisation
- Integration: antidifferentiation of standard forms, reverse chain rule, definite integrals, area under curves and between curves
- Discrete random variables: Bernoulli sequences, the binomial distribution, expected value and variance
- Continuous random variables and the normal distribution: z-score standardisation, technology probabilities and inverse normal (90th percentile delivery-time stimulus)
- Numerical integration via the trapezoidal rule and 2D/3D trigonometry (sine rule, cosine rule, bearings)
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- QCAA cognitions across Simple Familiar, Complex Familiar and Complex Unfamiliar bands with written contextual conclusions for evaluate/justify marks
- Differentiation of exponential, logarithmic and trigonometric functions (chain, product, quotient rules)
- Applications of differentiation: rates of change, kinematics, stationary points, optimisation
- Integration: antidifferentiation, reverse chain rule, definite integrals, area under and between curves, trapezoidal rule
- Discrete random variables: Bernoulli sequences, binomial distribution, expected value
- Continuous random variables and the normal distribution: z-scores, technology probabilities, inverse normal
- Sampling distribution of the sample proportion and confidence intervals for a population proportion (margin of error, sample size)
- 2D/3D trigonometry: sine rule, cosine rule, bearings
- Tennis-ball lifespan context: defect probabilities, warranty determination and evaluation of a marketing reliability claim with written contextual conclusions
- Differentiation: chain, product and quotient rules on exponential, logarithmic and trigonometric functions (Unit 3)
- Applications of differentiation: stationary points, inflections, concavity, kinematics and optimisation
- Integration: standard antiderivatives, reverse chain rule, definite integrals, area under and between curves, trapezoidal rule
- Discrete random variables: Bernoulli sequences, binomial distribution, expected value and variance
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- 2D/3D trigonometry: sine rule, cosine rule and bearings
- Complex Unfamiliar synthesis with written contextual conclusions, applied to a rural-intersection road-safety reaction-time study
- Unit 3 differentiation: chain, product, quotient rules on exponential, logarithmic and trigonometric functions
- Unit 3 applications of differentiation: stationary points, nature, optimisation and kinematics
- Unit 3 integration: antidifferentiation, constant of integration from initial conditions, definite integrals and area
- Unit 3 discrete random variables: Bernoulli sequences, binomial distribution, expected value and variance
- Unit 4 two- and three-dimensional trigonometry: sine rule, cosine rule and bearings in a civil-engineering pipeline-survey context
- Unit 4 continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Unit 4 numerical integration with the trapezoidal rule and area between curves
- Unit 4 inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- QCAA assessment objectives 1-6 with Simple Familiar, Complex Familiar and Complex Unfamiliar items requiring written contextual conclusions
- Correct QCAA notation, units, and evaluative justification for Band A responses
- Unit 3 Further Calculus: chain/product/quotient differentiation of exponential, logarithmic and trigonometric functions
- Applications of differentiation: rates of change, kinematics, stationary points, optimisation
- Introduction to integration: antidifferentiation, reverse chain rule, definite integrals and area
- Discrete random variables: Bernoulli sequences, binomial distribution, expected value
- Unit 4 integration extended: signed area, area between curves, trapezoidal rule
- 2D and 3D trigonometry: sine rule, cosine rule, bearings
- Continuous random variables and the normal distribution: z-scores, technology probabilities, inverse normal
- Inferential statistics: sampling distribution of sample proportion, confidence intervals, margin of error, sample size
- Stimulus context: exponential growth model of cumulative animal sightings, maximum/minimum rates via differentiation
- Complex Unfamiliar synthesis with written contextual conclusions and correct QCAA notation
- Unit 3 differentiation: chain, product, quotient rules on exponential, logarithmic and trigonometric functions
- Applications of differentiation: kinematics, stationary points, concavity, points of inflection, curve sketching and optimisation
- Introduction to integration: antidifferentiation of standard forms, reverse chain rule, definite integrals and area (with constant of integration)
- Discrete random variables: Bernoulli sequences, binomial distribution, expected value and variance
- Unit 4 integration extended: signed area, area between two curves and the trapezoidal rule for numerical integration
- Two- and three-dimensional trigonometry: sine rule, cosine rule and bearings
- Continuous random variables and the normal distribution: PDFs, z-score standardisation, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Real-world modelling of solar-array electricity output with written contextual conclusions evaluating efficiency and marketing claims
- Correct QCAA notation, evaluation of reasonableness and sustained justification across Simple Familiar, Complex Familiar and Complex Unfamiliar items
- Inferential statistics: sampling distribution of the sample proportion, margin of error, sample-size determination (n = z2p(1−p)/E2), and confidence intervals for a population proportion with precise written interpretation
- Further calculus: chain, product and quotient rules on exponential, logarithmic and trigonometric functions; stationary points, concavity, points of inflection and optimisation
- Integration: antidifferentiation of standard forms, reverse chain rule, definite integrals, signed area, area between curves and the trapezoidal rule
- Kinematics: displacement, velocity and acceleration via differentiation and integration, including distance travelled with sign changes
- Discrete random variables: Bernoulli sequences, the binomial distribution, expected value and variance
- Continuous random variables: the normal distribution, z-score standardisation, technology-based probabilities and inverse normal
- Two- and three-dimensional trigonometry: sine rule, cosine rule, area rule and bearings
- Complex Unfamiliar synthesis with written contextual conclusions linking numerical results to the Queensland study-habits survey context
- Unit 3 Further Calculus: differentiation of exponential, logarithmic and trigonometric functions via chain, product and quotient rules
- Applications of differentiation: rates of change, kinematics, stationary points, concavity, inflection, curve sketching and optimisation
- Integration: antidifferentiation of standard forms, reverse chain rule, definite integrals, signed area and area between curves
- Numerical integration with the trapezoidal rule
- Discrete random variables: Bernoulli sequences, binomial distribution and expected value
- Unit 4 trigonometry: sine rule, cosine rule, area of a triangle and bearings (navigational triangle context)
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- QCAA notation, written contextual conclusions and evaluation of reasonableness across Simple Familiar, Complex Familiar and Complex Unfamiliar items
- Unit 3 differentiation: chain, product and quotient rules for exponential, logarithmic and trigonometric functions
- Applications of differentiation: kinematics, stationary points, concavity, optimisation and curve analysis
- Integration: antidifferentiation of standard forms, reverse chain rule, definite integrals, area under curves and area between curves
- Discrete random variables: Bernoulli sequences, binomial distribution, expected value and variance
- Unit 4 trigonometry: sine rule, cosine rule, area of a triangle and bearings
- Continuous random variables and the normal distribution: z-scores, technology probabilities and inverse normal
- Inferential statistics: sampling distribution of the sample proportion, confidence intervals, margin of error and sample size
- Train kinematics context: piecewise velocity models, integration for displacement, acceleration analysis and evaluation of a timetable claim
- Numerical integration via the trapezoidal rule
- Written contextual conclusions, QCAA notation and evaluation of reasonableness across Complex Familiar and Complex Unfamiliar tasks
- Differentiation of exponential, logarithmic and trigonometric functions (chain, product, quotient rules)
- Applications of differentiation: rates of change, kinematics, stationary points, concavity, optimisation
- Integration: antidifferentiation, reverse chain rule, definite integrals, signed area and area between curves
- Trapezoidal rule for numerical integration
- Binomial distribution: Bernoulli sequences, probabilities, expected value and variance
- Normal distribution: z-score standardisation, technology probabilities and inverse normal
- Sampling distribution of the sample proportion
- Confidence intervals and margin of error for a population proportion
- Minimum sample size to achieve a target margin of error
- 2D/3D trigonometry: sine rule, cosine rule and bearings
- Evaluating reasonableness and writing contextual conclusions for compliance decisions
- Differentiation (power, product, chain, quotient rules; logarithmic and exponential derivatives)
- Anti-differentiation and definite integrals (area under curves, area between curves, average value)
- Optimisation using calculus (open-top box, minimum-surface-area cylindrical can/container, maximum profit)
- Stationary points and their classification (first/second derivative tests)
- Exponential and logarithmic equations (technology-free index laws and technology-active log solving)
- Trigonometric functions, equations and periodic modelling
- The normal distribution (probabilities, inverse-normal percentiles, finding an unknown standard deviation) in a quality-control context
- Binomial distribution (mean, exact probabilities, cumulative probabilities)
- Sample proportions and approximate confidence-interval margin of error
- Kinematics and rates of change (displacement vs distance, draining-tank rate)
Included in the QCE Mathematical Methods Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
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