Mathematics in fourth year of high school
La mathematics in fourth year of liceo: solid geometry in space, lines and planes, solids, polyhedra, and the consolidation of functions, trigonometry, logarithms and probability from the second biennium. Each topic has ready-made exercise templates for printable worksheets.
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What does a fourth-year high school student learn in mathematics?
In fourth year of liceo, the student takes geometry into space: mutual positions of lines and planes, parallelism and perpendicularity, the theorem of the three perpendiculars, diagonals and angles in polyhedra, surfaces and volumes of solids. It consolidates the topics of the second biennium — elementary functions and their graphs, trigonometry, exponentials and logarithms, bivariate statistics and probability — in view of the infinitesimal calculus of the fifth year.
On the programme: 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 second biennium, not year by year: the choice of topics for this class is ours. This page gathers 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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SB.AA(our numbering) · Teaching content · checked against the actAritmetica e algebra
DM 211/2010, Matematica, secondo biennio, Aritmetica e algebra
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SB.AA.1(our numbering) · Teaching contentLo studio della circonferenza e del cerchio, del numero π, e di contesti in cui compaiono crescite esponenziali con il numero e, permetteranno di approfondire la conoscenza dei numeri reali, con riguardo alla tematica dei numeri trascendenti.
our summary of the point · DM 211/2010, Matematica, secondo biennio, Aritmetica e algebra, punto SB.AA.1
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SB.G(our numbering) · Teaching content · checked against the actGeometria
DM 211/2010, Matematica, secondo biennio, Geometria
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SB.G.1(our numbering) · Teaching content · checked against the actLe sezioni coniche saranno studiate sia da un punto di vista geometrico sintetico che analitico.
DM 211/2010, Matematica, secondo biennio, Geometria, punto SB.G.1
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SB.G.2(our numbering) · Teaching content · checked against the actInoltre, lo studente approfondirà la comprensione della specificità dei due approcci (sintetico e analitico) allo studio della geometria.
DM 211/2010, Matematica, secondo biennio, Geometria, punto SB.G.2
Task templates to print
Every task type, grouped by skill. Clicking one opens the worksheet generator with it already selected.
Other task types
- Area of a circle (grade 7–8)
- Circumference of a circle (grade 7–8)
- Volume of a triangular prism (grade 7–8)
- Surface area of a triangular prism (grade 7–8)
- Surface area of a square pyramid (grade 8)
- Volume of a square pyramid (grade 8)
- What does the sample tell us about the whole school? (grade 7–8)
- Predict with a line of fit (grade 8)
- Two-way table: the missing cell (grade 8)
- Two-way table: what fraction of the group? (grade 8)
- Variance of a data set
- Drawing balls without replacement
- Decreasing exponential function (grade 10–11)
- Value of an exponential function (grade 9–11)
- Difference of logarithms (grade 9–11)
- Sum of logarithms (grade 9–11)
- Logarithm from the definition (grade 9–11)
- Logarithm of a fraction (grade 9–11)
- Exponential equation (grade 10–11)
- Compound interest — deposit (grade 9–11)
- Factoring out a monomial (grade 9–10)
- Factoring by grouping (grade 10–11)
- Sum and difference of cubes (grade 10–11)
- Remainder of polynomial division (grade 10–11)
- Dividing a polynomial by a binomial (grade 10–11)
- Quadratic inequality (grade 10–11)
- Quadratic inequality in factored form (grade 10–11)
- Quadratic equation (grade 9–11)
- The function f(x) = a/x (grade 10–11)
- Translating a graph (grade 10–11)
- Inverse of a linear function
- Composition of functions
- Vertex of a parabola (grade 10–11)
- Vertex form of a quadratic function (grade 10–11)
- Value of a quadratic function (grade 9–10)
- Intersections of a parabola and a line (grade 10–11)
- Law of sines
- Area of a triangle with sine (grade 10–11)
- Law of cosines (grade 10–11)
- Leg adjacent to an angle (grade 9–10)
- Leg opposite an angle (grade 9–10)
- Maximum of a sine curve
- Period of a sine curve
- Cosine from sine (grade 10–11)
- Tangent from sine (grade 10–11)
- Exact value of a trigonometric function (grade 10–11)
- Central angle from the inscribed angle (grade 10–11)
- Inscribed angle from the central angle (grade 10–11)
- Arc length (grade 10–11)
- Area of a sector (grade 10–11)
- Length of a chord (grade 10–11)
- Length of a tangent segment (grade 10–11)
- Area of a parallelogram with sine (grade 10–11)
- Centre of a circle from its equation (grade 10–11)
- Radius of a circle from its equation (grade 10–11)
- Length of a vector
- Linear combination of vectors
- Dot product
- Slant height of a cone
- Lateral edge of a pyramid
- Space diagonal of a cuboid (grade 9–11)
- Asymptote of a tangent graph
- Period of a tangent function from its graph
- Value of a trigonometric function from its graph (grade 11)
- How many zeros in the interval? (grade 11)
- Period of a trigonometric function from its graph (grade 11)
- Range of a sinusoid from its graph (grade 11)
- 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)
- Angle between a lateral edge of a pyramid and its base
- Angle between a lateral face of a pyramid and its base
- Angle between the diagonal of a prism and its base
- Measure of the angle between a lateral face and the base
- Exponential growth overtakes linear growth (grade 9–10)
- Angle between a section plane and the base
- Distance from a vertex to a diagonal of the base
- Sketch the graph of a quadratic function (grade 10)
- Iteration: the third approximation
- Round to significant figures (grade 8–9)
- Foci of a hyperbola
- Foci of an ellipse