Explore the skills · QCAA
Mathematical Methods
QCAA External Exam Revision · Units 3 & 4
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Differentiation of exponential and logarithmic functions
- The exponential function eˣ and its graphRevision skill
- Differentiate exponential and composite exponential functionsRevision skill
- Natural logarithms, inverse relationships and graph featuresRevision skill
- Solve exponential and logarithmic equations with base eRevision skill
- Differentiate logarithmic and composite logarithmic functionsRevision skill
- Model with exponential and logarithmic derivativesRevision skill
Differentiation of trigonometric functions and differentiation rules
- Differentiate sine and cosine functionsRevision skill
- Differentiate composite trigonometric functionsRevision skill
- Apply the chain rule to mixed functionsRevision skill
- Apply product and quotient rules to mixed functionsRevision skill
- Select and combine differentiation rulesRevision skill
Further applications of differentiation
- Interpret second derivatives and accelerationRevision skill
- Determine concavity and points of inflectionRevision skill
- Use the second derivative testRevision skill
- Sketch functions using first and second derivativesRevision skill
- Solve optimisation problems with a given objective functionRevision skill
- Develop and optimise mathematical modelsRevision skill
Introduction to integration
- Antidifferentiate standard functionsRevision skill
- Use linearity of indefinite integralsRevision skill
- Antidifferentiate linear composite functionsRevision skill
- Determine functions from derivatives and initial conditionsRevision skill
- Determine displacement from velocityRevision skill
- Determine velocity and displacement from accelerationRevision skill
- Model and solve with indefinite integralsRevision skill
Discrete random variables
- Construct and interpret discrete probability functionsRevision skill
- Estimate discrete probabilities from relative frequenciesRevision skill
- Calculate and interpret expected valueRevision skill
- Calculate discrete variance and standard deviationRevision skill
- Recognise and use Bernoulli distributionsRevision skill
- Identify valid binomial modelsRevision skill
- Calculate exact and cumulative binomial probabilitiesRevision skill
- Use binomial mean, variance and modellingRevision skill
Further integration
- Estimate area with sums and interpret definite integralsRevision skill
- Use the fundamental theorem of calculusRevision skill
- Calculate area between a curve and the x-axisRevision skill
- Calculate area between curvesRevision skill
- Approximate definite integrals with the trapezoidal ruleRevision skill
- Use definite integrals for total change and motionRevision skill
Trigonometry
- Use the sine rule including the ambiguous caseRevision skill
- Use the cosine ruleRevision skill
- Calculate triangle area using sineRevision skill
- Model 2D and 3D contexts with trigonometryRevision skill
Continuous random variables and the normal distribution
- Estimate continuous probabilities from data and histogramsRevision skill
- Use probability density and cumulative distribution functionsRevision skill
- Calculate continuous expected valueRevision skill
- Calculate continuous variance and standard deviationRevision skill
- Standardise normal values and compare samplesRevision skill
- Recognise normal-distribution models and featuresRevision skill
- Calculate normal probabilities and quantilesRevision skill
- Model and solve with normal distributionsRevision skill
Sampling and proportions
- Identify random sampling procedures and biasRevision skill
- Interpret simulated sampling distributionsRevision skill
- Use the mean and standard deviation of sample proportionsRevision skill
- Use normal approximations for sample proportionsRevision skill
Interval estimates for proportions
- Interpret interval estimates for a population proportionRevision skill
- Calculate confidence intervals for proportionsRevision skill
- Calculate and interpret margin of errorRevision skill
- Relate confidence level, sample size and margin of errorRevision skill
- Interpret confidence intervals across repeated samplesRevision skill