Grade 12 Mathematics Practice

This test applies fundamental trigonometric identities and methods for solving equations. Students write general solutions, use periodicity and select the values that belong to a specified angular interval.

This test introduces the derivative as a rate of change and applies the basic rules of differentiation. Tasks cover derivatives of constant, power, linear and quadratic functions.

This test develops the geometric and physical interpretations of a derivative. Students form tangent equations, interpret velocity and acceleration and connect the sign of a derivative with the behaviour of a function.

This test uses the first derivative to analyse a function. Tasks include finding critical points, intervals of increase and decrease, local extrema and absolute maximum or minimum values.

This test models geometric and economic optimisation situations. Students construct an objective function, determine its feasible domain, use derivatives to find an extremum and interpret the result in context.

This test covers the main relationships between lines and planes in space. Tasks apply axioms of solid geometry, identify parallelism and perpendicularity and calculate distances and angles in three-dimensional figures.

This test develops geometric reasoning and calculations with prisms and pyramids. Students find volume, lateral and total surface area, altitude and edges and analyse diagonal cross-sections.

This test covers the principal elements and properties of cylinders, cones and spheres. Tasks calculate volume, lateral and total surface area, interpret axial sections and select an appropriate formula.

Recognition and area problems for sections of cubes, prisms, pyramids, cylinders and cones.

This test develops planning of a statistical investigation and justified interpretation of data. Tasks cover populations, samples, variable types, the mean, standard deviation, outliers and the reliability of conclusions.

This test evaluates relationships between two variables using correlation and a linear model. Students interpret the correlation coefficient and R², calculate predictions and residuals and assess model suitability and the limits of causal conclusions.

Complementary, independent, dependent, incompatible events and probability trees.