THE ASCENT LIBRARY
Mathematical MethodsOne idea at a time.
Connect functions, calculus and statistics. Find your year level, then take one concept at a time.
Years 11–12 · SACE01 / YOUR YEAR LEVEL
Start where you are.
02 / EXPLORE THE TOPICS
63 lessons availableYear 12 starts here.
Develop your calculus and use probability and statistics to understand uncertainty.
63 subtopics
01
Differentiation and applications
13 subtopics1.1Review of derivatives and polynomial rules1.2Product rule1.3Quotient rule1.4Chain rule1.5Natural exponential function and its derivative1.6Exponential growth and decay1.7Derivatives of sine/cosine/tangent1.8Second derivatives and concavity1.9Inflection points1.10Stationary-point classification1.11Curve analysis1.12Optimisation1.13Rates and motion applications
Topic review6 practice tests02
Logarithmic functions
7 subtopics2.1Exponential/logarithmic inverse relationship2.2Logarithm laws and change of base2.3Solving exponential equations2.4Natural logarithms2.5Logarithmic graphs, domains and transformations2.6Differentiating logarithms and composite logarithms2.7Logarithmic modelling
Topic review6 practice tests03
Integration
12 subtopics3.1Antiderivatives and constants3.2Power/exponential/trigonometric antiderivatives3.3Antiderivatives involving reciprocal linear expressions, linked back to logarithmic derivatives3.4Initial-value problems3.5Definite integrals3.6Numerical area approximation and the integral idea3.7Fundamental theorem of calculus3.8Signed area versus geometric area3.9Areas between curves3.10Accumulated change3.11Displacement and total distance3.12Contextual integral models
Topic review6 practice tests04
Discrete probability distributions
11 subtopics4.1Random variables and probability tables4.2Probability functions and cumulative probabilities4.3Expected value4.4Variance and standard deviation4.5Effects of scale/shift4.6Sums of independent variables4.7Bernoulli trials4.8Binomial assumptions4.9Binomial probabilities and cumulative probabilities4.10Binomial mean/variance4.11Interpreting distribution results
Topic review6 practice tests05
Continuous probability and normal distributions
9 subtopics5.1Probability density functions and total area5.2Interval probabilities by integration5.3Cumulative distribution functions5.4Mean, variance and standard deviation for continuous models5.5Normal distributions5.6Standardisation and z-scores5.7Normal probabilities and inverse-normal values5.8Independent sums and sample means5.9Sampling variation and distributions of sample means
Topic review6 practice tests06
Sampling and confidence intervals
11 subtopics6.1Random sampling and bias6.2Sample means and the central-limit idea6.3Standard error6.4Confidence intervals for a population mean6.5Confidence level and interpretation6.6Effect of sample size and variability6.7Population/sample proportions6.8Sampling distribution of a sample proportion6.9Confidence intervals for a population proportion6.10Margin of error and sample-size calculations6.11Assessing claims and limitations
Topic review6 practice testsSchools may teach these topics in a different order.
A QUESTION IS A GOOD BEGINNING.
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