Connect the ideas.
- A density is nonnegative and has total area one. Probability is area, not a height.
- A continuous variable has probability zero at a single exact value.
- Subtract CDF values to find interval probabilities.
- Variance is the second moment minus the square of the mean.
- Normal notation here is N(mean, variance).
- Standardise using the standard deviation of the actual variable, including the smaller standard error for a sample mean.
- Independent sums add variances, not standard deviations.
- Check sampling assumptions and model limitations before interpreting a calculation.
Put it together.
Choose a paper and show your working.
Practice test 1 — areas and normal models
Build from valid densities and interval areas to normal cut-offs, independent totals and sample means.
10 questions · 41 marks · 65 minutes · Technology-assistedPractice test 2 — cumulative models and cut-offs
Use changing density shapes, CDFs, reverse normal calculations and weighted measurements.
10 questions · 42 marks · 65 minutes · Technology-assistedPractice test 3 — applications and assumptions
Connect polynomial densities with practical normal models and compare totals, averages and model choices.
10 questions · 42 marks · 65 minutes · Technology-assistedPractice test 4 — reverse calculations and comparisons
Develop density and CDF reasoning, infer normal parameters, and distinguish correlated readings from independent samples.
10 questions · 42 marks · 65 minutes · Technology-assistedPractice test 5 — modelling and interpretation
Work with a two-piece density, compare alternative normal decisions, and evaluate modelling assumptions.
10 questions · 43 marks · 75 minutes · Technology-assistedPractice test 6 — connected applications
A more demanding paper joining exact density work, normal parameter inference and independent-sample reasoning.
10 questions · 47 marks · 75 minutes · Technology-assisted
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 Mathematical Methods: continuous random variables, normal distributions and sampling distributions of sample means. Original lessons and practice.
Official curriculum source ↗