Elementary Mathematics: Practicum (KPI, 2011)
A complete map of a 104-page KPI prerequisite practicum covering arithmetic, algebra, elementary functions, equations, inequalities, graphs, and trigonometry. It supplies curricular diagnostics; GTK independently reconstructs the domain-aware methods and corrects the source's damaged formulas and answers.
This 2011 department-authored practicum by Iryna V. Alieksieieva, Viktor O.
Haidei, Oleksandr O. Dykhovychnyi, and Lidiia B. Fedorova is the prerequisite
layer beneath the calculus course. All 104 physical pages were read and
visually inspected, and the archived file is byte-identical to the supplied
PDF (SHA-256
88511652148e6750baa0817ad3356d4c5868cbfa0f44bbb9cd514e09fc93b6ed).
What the practicum teaches #
The volume moves from arithmetic and absolute value through polynomial, rational, radical, exponential, logarithmic, and trigonometric functions. It then uses equations, inequalities, transformations, and graph features to diagnose whether a student has the algebraic control needed for limits and calculus.
Its durable curricular lesson is that a formula cannot be separated from its domain. Radical and logarithmic restrictions, denominator exclusions, periodicity, inverse-function branches, and extraneous roots all become proof obligations during manipulation. GTK develops that contract directly and uses new worked examples rather than reproducing exercise answers.
Reliability boundary #
Several printed expressions or answers are wrong: an absolute-value inequality loses a branch, monotonicity is asserted outside the correct interval, logarithmic conditions are omitted, a circle table contains a sphere-volume formula, and later derivative, rational, period, and geometry answers are corrupted. These defects make the practicum unsuitable as a sole reference. The retained concepts and examples were checked against OpenStax and NIST DLMF, and only those independent derivations appear in GTK.
Visual audit #
Every graph, formula table, coordinate sketch, and geometric figure was inspected at readable scale. No source visual is retained. The compact tables mix correct identities with damaged cells, while the graphs are more clearly served by a new theme-aware transformation diagram whose point-mapping formula can be checked directly.