LIVETUTORIALS LEARNING LIBRARY

Tutorials and learning guides

Explore a subject, review an explained example, and practise the method with an answer you can check.

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Build selected physics, chemistry and biology foundations with original explanations, worked examples and practice answers.

Build arithmetic, algebra and logical reasoning skills with explained methods, worked examples and practice answers.

Build careful biological reasoning by distinguishing genes, alleles, genotypes and phenotypes within an explicitly stated model.

Connect particles, mass and amount of substance, then use a balanced equation to reason about chemical reaction quantities.

Learn to describe physical quantities with units, test equations using dimensions, and recognise the limits of a dimensional check.

Learn to separate assumptions from conclusions and use set diagrams and counterexamples to test deductive arguments.

Connect fractions, percentages, ratios, averages and equations through clear reference quantities and consistent units.

Calculate one-gene genotype and phenotype probabilities, interpret a test cross and distinguish expected counts from guaranteed outcomes.

Convert masses to moles, apply a balanced reaction ratio, identify a limiting reactant and check an ideal product calculation.

Test the dimensional consistency of motion formulas, convert speed units, and understand why matching dimensions do not prove a formula.

Test deductive conclusions using set containment, explicit existence and a counterexample that preserves all the premises.

Solve one-variable linear equations with balanced operations, brackets and a substitution check in the original equation.

Calculate interest and final amount using an unchanged principal, a stated rate, and time measured in matching units.

Combine group averages by reconstructing totals and weighting each group by its number of observations.

Convert ratio parts into actual shares, distinguish part-to-part and part-to-whole comparisons, and verify a proportional split.

Calculate a percentage of an amount, measure percentage change, and understand why equal increases and decreases do not cancel.