SBE MINIMAL REQUIREMENTS

Transcription

1 SBE MINIMAL REQUIREMENTS Academic year 2018/2019

2 The successful student of the SBE Bachelor Degree Program has a strong quantitative attitude and a versatile potential. A general knowledge, with special focus on both in mathematics and physics, design and visualization, general knowledge together with the ability to work with different written texts and the aptitude to abstract reasoning. It is therefore crucial that, in the case of admission, you carefully check this list in order to fill any gap in these key disciplines. If these prerequisites are not met, it may be very difficult for you to profitably attend the first year courses. English questions are aimed at verifying comprehension of written English at an elementary level. Mathematics and Physics The test aims to assess mastery of the following topics: - Sets of numbers and arithmetic (natural and negative numbers, rationals, reals; the ordering and comparison of numbers; orders of magnitude, operations, powers, roots, logarithms); algebra, Euclidean geometry (polygons, circles, lengths, surface and volume, geometric loci), analytic geometry (basics), probability and statistics (basics); - Elementary principles of mechanics: definitions of the fundamental physical quantities (displacement, velocity, acceleration, mass, momentum, force, weight, work and power); Newton's laws, inertia and the principle of action and reaction; - The basics of thermodynamics (general concepts of temperature, heat, specific heat, compressibility). General knowledge and abstract reasoning (logic) - Assessment of the ability to complete a logical argument in a way consistent with assumptions that are stated symbolically or verbally through multiple-choice questions. - The questions will focus on scientific texts or narrative essays of classical or contemporary authors, or current cuttings from newspapers or more specialized journals; they will concern cases or problems, possibly of an abstract nature, whose solution calls for various forms of logical argument. - The evaluation will be completed by questions on general cultural knowledge. In the following some exercises on these topics.

3 Mathematics and Physics 3 1. The expression log 10 x log is equal to: 2. The solutions of the trigonometric equation sinx = 1/sinx are: A. x = π/2 + kπ, for each integer value of k B. none of the other answers C. x = kπ/2, for each integer value of k D. x = 3 π/2 + 2kπ, for each integer value of k E. x = π/2 + 2kπ, for each integer value of k 3. Sort the three numbers in ascending order 7, 47, Which of the following statements is true for each pair of polynomials p (x) and q (x) of degree 3 and real coefficients, with p (x) -q (x)? A. p(x) + q(x) has degree 3 and p(x) q(x) has degree 6; B. p(x) + q(x) has degree 3 and p(x) q(x) has degree 6; C. p(x) + q(x) has degree 3 and p(x) q(x) has degree 3;

4 D. p(x) + q(x) has degree 6 and p(x) q(x) has degree 9; E. p(x) + q(x) has degree 6 and p(x) q(x) has degree 6; 5. If f(x) = x 2 x 3, then f(x-2) is: A. (3 x)(x 2) 2 B. none of the other answers C. x 2 x 3 2 D. x 2 2 x E. x 2 x Considering an equilateral triangle A with side a and an equilateral triangle B with side 2a, the surface of B is: F. greater than four times that of A G. not deducible from that of A H. four times that of A I. double that of A J. greater than that of A but still less than twice that of A 7. In a Cartesian plane, which of the following lines is parallel to the line passing through the coordinate points (1; 0) and (0; 1)?

5 8. Given two concentric spheres of radius 1 and r (with r <1), what is the value of r so that the volume of the external part of the smaller sphere is half the volume of the bigger sphere? 9. Given an angle that measures 2 radians, then: A. it s sine and his cosine have the same sign; B. the angle is acute C. its tangent does not exist D. its cosine is positive E. its sine is positive 10. The polynomial expression 12 a 2 18b 2 can be divided by:

6 11. Given the circumference g and being P a point lying in the plane included in g, different from the center. How many circumferences having center in P and tangent to g exist? 12. The Rowing Club Santerno consists of six rowers, all equally good and close as a team. The club must choose four athletes to send to the regional championships. How many different combinations can be made? 13. Given any positive real number x, then log(x 3 ) log (x 2 ) is equal to:

7 14. Given 0 x π/2, the equation 3sin 2 x + 3cos 2 x 2sinx = 0 has solution: 15. All other things being equal (material, roughness, cleanliness, etc.), less paint is needed to paint: A. a sphere of 1 meter radius B. a cube with a 1 meter side C. a pyramid where all the faces are equilateral triangles (tetrahedron) each with a 1 meter side D. A cone (right circular) 1 meter high and a 1 meter base radius E. a cylinder (right circular) with a 1 meter radius and 1 meter high 16. In a Cartesian plane, which of the following points belongs to the triangle included within the lines r1: y = 0, r2: y = 2x, r3: y = -x + 7?

8 17. In a Cartesian plane, the circumference having center C of coordinates (1,1) and tangent to the x-axis has equation: 18. Given a real number x, the following expression 2x 2 is equal to: xv The expression x A. if and only if x <-1 B. for no real value of x C. if and only if x <-2 D. if and only if x <0 E. if and only if x <1 < 0 holds

9 20. The sum of the internal angles of an irregular hexagon: A. is equal to five straight angles B. cannot be calculated without further data C. is equal to six right angles D. is equal to 360 degrees E. is equal to 4π radians 21. Consider a 5 µf capacitor connected to a 1.5 V battery. What is the charge deposited on each of the plates of the capacitor? A C B C C C D C E C 22. A 24 N force applied to a 3 kg mass produces an acceleration of: A. 72 m/s 2 B. 21 m/s 2 C. 8 m/s 2 D. 3 m/s 2 E. 3,14 m/s What is approximately the work performed by gravity on a 2 kg coconut falling from a 10- metre high palm? A. 100 J B. 5 J C. 20 J D. 200 J E. 10 J

10 24. If the temperature of a perfect gas increases from 15 C to 30 C, the pressure-volume product (PV): A. becomes 2 times bigger B. is reduced by 15% C. becomes zero D. is halved E. increases, but does not double 25. At 3:30 p.m. the odometer of a car marks 22,715. If at 5:00 p.m. the odometer marks 22,865, what was the average speed of the car? A. 100 km/h B. 150 km/h C. 50 km/h D. 10 km/h E. 200 km/h 26. A metal bar 1 metre long is suspended by its centre. At 10 cm from the left end hangs a 10 kg weight, while at the other end hangs a 12 kg weight. What must you do to balance the bar and keep it horizontal? A. Add to the weight hung on the left end another weight of 5 kg B. Add to the weight hung on the right end another weight of 5 kg C. Add to the weight hung on the left end another weight of 4 kg D. Nothing, the bar is already balanced E. Add to the weight hung on the right end another weight of 4 kg

11 Abstract reasoning 27. If you say that the statement "All of them don't work" is FALSE, it means that: A. at least one of them works B. one of them does not work C. none of them works D. all of them work except one E. all of them work 28. Which of the terms given correctly complete the following verbal proportion? X : writer = movie : Y A. X = publisher; Y = screenwriter B. X = analogic; Y = digital C. X = editor; Y = cinema D. X = book; Y = director E. X = pages; Y = film 29. The statement: "If I use my smartphone too much I will get a headache" implies that: A. if I get a headache it means that I used my smartphone too much B. if I don't get a headache, then I did not use my smartphone too much C. sometimes I don't get a headache even if I used my smartphone too much D. either I use my smartphone too much or I get a headache E. I don't have a headache although I used my smartphone too much

12 30. Which of the following series is connected by the set relation graphically represented by Diagram 1? A. {12, 2, 14, 7, 5, 8}; {1, 3, 4, 6, 2, 5}; {10, 11, 0, 9, 15, 13} B. {2, 6, 10, 0, 4, 3}; {8, 1, 9, 11, 5, 7}; {0, 6} C. {R, A, K, S, D, J}; {V, R, J, E, Q, B}; {C, L, T, Y, B, X} D. {R, M, X, B, K, D}; {S, V, T, B, K, D}; {S, E, T, M, K, D} E. {13, 17, 3, 8, 9, 5}; {7, 1, 2, 11, 12, 4}; {10, 18, 6, 14, 15, 16} 31. What part is missing to complete the solid, so as to obtain a cube? A. Figure 1 B. Figure 4 C. Figure 3 D. Figure 5 E. Figure 2

13 32. Among the pairs shown in the figure, identify the one that completes the given sequence. A. Figure 1 B. Figure 3 C. Figure 2 D. Figure 4 E. Figure Population of Bologna and Florence in all Italian censuses. Which of the following statements is certainly true? A. In 5 censuses the total population of the two cities exceeded 800,000 inhabitants B. At least once, the total population of the two cities exceeded 900,000 inhabitants C. The censuses where the population of Bologna is greater than that of Florence are more numerous than those where the population of Florence is greater D. The population of Florence is over 400,000 inhabitants in a greater number of

14 censuses than that of Bologna E. The total population of the two cities always exceeded 300,000 inhabitants 34. The missing number is: A. 14 B. 18 C. 22 D. 24 E. 36