Toelatingsexamen Arts & Tandarts België (Medical & Dental Entrance Exam) · Physics and Mathematics

Electromagnetism, Modern Physics, and Differential Calculus

35 practice questions, each with the answer and an explanation.

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All 35 questions

  1. Two large parallel conducting plates are separated by a distance of 0.020 m in a vacuum. A potential difference of 200 V is applied between them. What is the strength of the uniform electric field bet…
  2. A circular wire loop of radius 0.10 m is placed perpendicular to a uniform magnetic field. If the magnetic field decreases uniformly from 0.50 T to 0.10 T in 0.020 s, what is the magnitude of the indu…
  3. An ideal electrical transformer has 500 turns on its primary coil and 50 turns on its secondary coil. If an alternating voltage of 240 V is applied to the primary coil, what is the output voltage from…
  4. In a photoelectric experiment, monochromatic light with photon energy of 4.5 eV illuminates a clean metal surface having a work function Phi = 2.5 eV. What is the maximum kinetic energy of the emitted…
  5. In the Bohr model of the hydrogen atom, the ground-state electron energy is -13.6 eV. What is the energy of the photon emitted when an electron transitions from the n = 3 state to the n = 2 state (the…
  6. What is the domain of the real-valued function f(x) = sqrt(2x - 6) / (x - 5)?
  7. What are the coordinates of the vertex of the parabola defined by the quadratic function f(x) = 2x^2 - 8x + 3?
  8. If 2^(3x - 1) = 32, what is the value of x?
  9. Given that log10(2) ≈ 0.301 and log10(3) ≈ 0.477, what is the value of log10(18)?
  10. What is the exact value of cos(2 theta) if sin(theta) = 3/5?
  11. How many solutions exist for the equation 2 * sin(x) - 1 = 0 in the interval [0, 2pi)?
  12. What is the value of the limit lim_{x -> 3} (x^2 - 9) / (x - 3)?
  13. Using L'Hôpital's rule, what is the limit lim_{x -> 0} (sin(4x) / (2x))?
  14. What is the derivative of the function f(x) = (3x^2 + 1)^4 with respect to x?
  15. What is the derivative of the product function f(x) = x^2 * e^(3x)?
  16. What is the derivative of the rational function f(x) = (2x + 1) / (x - 3)?
  17. What is the equation of the tangent line to the curve y = x^3 - 2x + 4 at the point where x = 1?
  18. A function is given by f(x) = x^3 - 6x^2 + 9x + 2. At which value of x does f(x) attain a local maximum?
  19. What is the x-coordinate of the inflection point of the cubic polynomial curve f(x) = 2x^3 - 12x^2 + 5x - 7?
  20. A farmer has 120 meters of fencing to enclose a rectangular pasture bordering a straight river (no fence needed along the river). What dimensions maximize the enclosed area?
  21. Air is pumped into a spherical balloon so that its volume increases at a constant rate of 100 cm^3/s. At what rate is the radius of the balloon increasing when the radius is 5.0 cm?
  22. What is the remainder when the polynomial P(x) = 2x^3 - 5x^2 + 4x - 7 is divided by (x - 2)?
  23. In an arithmetic progression, the first term is a1 = 5 and the common difference is d = 3. What is the sum of the first 20 terms (S20)?
  24. What is the sum of the infinite convergent geometric series 12 + 6 + 3 + 1.5 + ...?
  25. What is the coefficient of x^3 in the algebraic expansion of (2x - 1)^5?
  26. What is the complex modulus (absolute value) of the complex number z = 3 - 4i?
  27. A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers rolled is equal to 7?
  28. In how many distinct ways can a committee of 3 members be selected from a group of 8 candidate doctors?
  29. A medical screening test for a rare disease has a sensitivity of 95% and a specificity of 90%. In a population where the disease prevalence is 1%, what is the probability that an individual who tests…
  30. What is the dot product of the two vectors u = (2, -3, 5) and v = (4, 1, -2) in R^3?
  31. What is the angle between the two vectors a = (1, 0) and b = (1, 1) in the Cartesian plane?
  32. What is the area of the finite region bounded by the parabola y = 4 - x^2 and the horizontal line y = 0 (the x-axis)?
  33. What is the value of the definite integral integral_{0}^{pi/2} sin(2x) dx?
  34. What is the antiderivative (indefinite integral) of the function f(x) = (2x + 3) / (x^2 + 3x + 5)?
  35. A random variable X is normally distributed with mean mu = 100 and standard deviation sigma = 15. What percentage of the population lies within the interval [70, 130] according to the empirical rule?

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