Mathematics · 24 questions in the exam

Trigonometry

Sine, cosine and tangent: from the right triangle to the unit circle, with identities, graphs and simple equations. Trigonometry is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 5 lessons, each with the rule that solves it and a diagram.

Trigonometry in the right triangle

sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Learn the values at 30°, 45° and 60° from the two special triangles. Complementary angles swap sine and cosine, and the area of a triangle is ½ab sin γ.

Rulesin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2

The unit circle and radians

180° = π radians. On the unit circle the point at angle θ is (cos θ, sin θ), so the signs follow the quadrant: cos > 0 in I and IV, sin > 0 in I and II. Reduce any angle to its reference angle; adding 360° changes nothing.

Rulecos 120° = −cos 60° = −1/2

Trigonometric identities

sin²x + cos²x = 1 gives one value from the other, with the sign from the quadrant. Addition formulas: sin(a ± b) = sin a cos b ± cos a sin b and cos(a ± b) = cos a cos b ∓ sin a sin b; doubling gives sin 2x = 2 sin x cos x.

Rulecos 2x = 1 − 2 sin²x = 2 cos²x − 1

Graphs of sine, cosine and tangent

sin and cos have period 2π and values in [−1, 1]; tan has period π and asymptotes at π/2 + kπ. In y = A sin(Bx) the amplitude is |A| and the period 2π/|B|. Count the solutions of an equation as intersections of two graphs.

Ruley = 3 cos(4x): amplitude 3, period π/2

Inverse functions and simple equations

arcsin gives angles in [−π/2, π/2], arccos in [0, π], arctan in (−π/2, π/2). sin x = k has the solutions α and π − α, cos x = k has ±α, each plus whole turns; tan x = k repeats every π. Factor rather than divide.

Rulesin x = 1/2 in [0, 2π): x = π/6 or 5π/6

What is the Bocconi Test format?

Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.

Questions / time: 50 / 75 minutes
Distribution: 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
Scoring: +1 correct · 0 blank · −0.2 wrong
Question languages: English · Italian
Three-option questions: Some critical thinking questions have three options; a wrong answer there costs −0.33
Minimum score: Below 17 points the test is not considered for selection
AI degree: Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
Law test: A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring

Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)

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