Mathematics in the fifth year of high school
The mathematics of the fifth year of liceo: limits, continuity, derivatives and integrals, function study and optimization, analytic geometry of space. Each topic has ready-made exercise models for printable worksheets.
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What does a student learn in mathematics in the fifth year of high school?
In fifth year of liceo, the student acquires the concepts of infinitesimal calculus: computes limits of sequences and functions in simple cases, studies continuity and differentiability, differentiates products, quotients and composite functions, finds the tangent line, studies monotonicity and maxima and minima, and solves optimization problems. Computes integrals of polynomial functions and of other elementary functions, areas and volumes in simple cases. Using Cartesian coordinates in space, represents lines, planes and spheres.
On the syllabus: the licei follow the National Guidelines of D.M. 7 October 2010, n. 211 (G.U. n. 291 of 14 December 2010, S.O. n. 275). The specific objectives of mathematics are set for the fifth year, not year by year: the choice of topics for this class is ours. This page collects what is common to all licei; the liceo scientifico has a separate page, because it anticipates and expands many topics. The objectives, quoted verbatim, can be found in the section below.
Curriculum scope
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Q.RF(our numbering) · Teaching content · checked against the actRelazioni e funzioni
DM 211/2010, Matematica, quinto anno, Relazioni e funzioni
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Q.RF.1(our numbering) · Teaching content · checked against the actAcquisirà il concetto di limite di una successione e di una funzione e apprenderà a calcolare i limiti in casi semplici.
DM 211/2010, Matematica, quinto anno, Relazioni e funzioni, punto Q.RF.1
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Q.RF.2(our numbering) · Teaching content · checked against the actLo studente acquisirà i principali concetti del calcolo infinitesimale – in particolare la continuità, la derivabilità e l’integrabilità – anche in relazione con le problematiche in cui sono nati (velocità istantanea in meccanica, tangente di una curva, calcolo di aree e volumi).
DM 211/2010, Matematica, quinto anno, Relazioni e funzioni, punto Q.RF.2
Task templates to print
Every task type, grouped by skill. Clicking one opens the worksheet generator with it already selected.
Other task types
- Limit of a rational sequence
- Volume of a solid of revolution
- Interval of decrease
- Intervals of increase
- Local maximum
- Local minimum
- Pen against a wall with the greatest area
- Rectangle with the greatest area
- Derivative of a polynomial
- Value of the derivative at a point
- Chain rule
- Product rule
- Antiderivative
- Definite integral
- Area under a parabola
- Tangent to the graph of a function
- Limit of a function at a point
- Distance between points in space
- Point on a line in space
- Distance from a point to a line in space
- Length of a vector in space
- Linear combination of vectors in space
- Collinear vectors in space
- Equation of a plane from a point and a normal vector
- Point on a plane
- Distance from a point to a plane
- Relative position of two planes
- Position of a line relative to a plane
- Intersection of a line and a plane
- Function value from a graph (grade 9–10)
- Zeros from a graph (grade 9–10)
- A function defined piecewise (grade 9–10)
- Domain from a graph (grade 9–10)
- Range from a graph (grade 9–10)
- Where the function decreases (from a graph) (grade 9–10)
- Where the function increases (from a graph) (grade 9–10)
- Where the function is positive — from a graph (grade 9–10)
- Zeros of the derivative from the graph
- Extremum from the graph of the derivative
- Increasing and decreasing from the graph of the derivative
- Sign of the derivative from the graph