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

Integral Calculus, Analytic Geometry, Statistics, and Medical Physics

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

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All 30 questions

  1. What is the value of the definite integral integral_{0}^{1} x * e^(x^2) dx?
  2. Using integration by parts, what is the antiderivative of f(x) = x * cos(x)?
  3. What is the volume of the solid of revolution formed by rotating the region under the curve y = sqrt(x) from x = 0 to x = 4 around the x-axis?
  4. In clinical pharmacokinetics, a drug is eliminated via first-order kinetics with an elimination rate constant ke = 0.1386 h^-1. If the initial plasma concentration is C0 = 40 mg/L, what will the conce…
  5. What is the center and radius of the circle defined by the equation x^2 + y^2 - 6x + 8y = 0?
  6. What is the perpendicular distance from the point P(2, 3) to the straight line given by the equation 3x + 4y - 8 = 0?
  7. Two fair coins are flipped simultaneously. If event A is 'getting at least one head' and event B is 'getting exactly two heads', what is the conditional probability P(B | A)?
  8. A binomial random variable X has parameters n = 100 trials and probability of success p = 0.20. What are the mean (mu) and standard deviation (sigma) of X?
  9. A diagnostic laboratory test correctly identifies 90 out of 100 patients with a disease (sensitivity = 90%) and correctly identifies 950 out of 1,000 healthy individuals (specificity = 95%). If the di…
  10. In medical ultrasound imaging, why does an acoustic impedance mismatch between two adjacent biological tissues cause an echo reflection at the boundary?
  11. A monoenergetic narrow X-ray beam passes through a 2.0 cm thick lead shielding block. If the linear attenuation coefficient of lead for these photons is mu = 0.693 cm^-1, what fraction of the incident…
  12. On the Hounsfield scale used in X-ray Computed Tomography (CT), what are the standard CT numbers assigned to air and pure water?
  13. In clinical Magnetic Resonance Imaging (MRI), what fundamental nuclear property of the hydrogen atom (1H) enables it to be used for imaging?
  14. What physical unit is used in radiation dosimetry to measure the absorbed dose of ionizing radiation (energy deposited per unit mass of tissue)?
  15. An alpha particle radiation weighting factor is W_R = 20. If a worker accidentally absorbs a physical dose of 0.050 Gy from an ingested alpha emitter, what is the resulting equivalent dose in Sieverts…
  16. A patient has a mean arterial blood pressure of 95 mmHg and a central venous pressure of 5 mmHg. If the patient's cardiac output is 5.0 L/min, what is the systemic vascular resistance (SVR)?
  17. A compound light microscope has an objective lens with a focal length of 4.0 mm and an eyepiece with a focal length of 25 mm. If the tube length between the focal points is 160 mm and the near point o…
  18. Why is alternating current (AC) at standard household frequencies (50–60 Hz) significantly more dangerous to the human heart than direct current (DC) of equivalent voltage?
  19. In a clinical trial, the sample mean systolic blood pressure of 100 hypertensive patients is 150 mmHg with a known population standard deviation sigma = 20 mmHg. What is the 95% confidence interval fo…
  20. What is the average value of the continuous linear function f(x) = 3x + 2 on the closed interval [0, 4]?
  21. What is the general solution to the separable differential equation dy/dx = 2x * y for y > 0?
  22. What is the distance between the two points A(1, 2, 3) and B(4, -2, 3) in three-dimensional Cartesian space?
  23. A bag contains 5 red balls and 3 green balls. Two balls are drawn sequentially without replacement. What is the probability that both balls drawn are red?
  24. What are the lengths of the semi-major axis a and semi-minor axis b of the ellipse defined by x^2 / 25 + y^2 / 9 = 1?
  25. What is the normal vector to the plane defined by the equation 2x - 5y + 3z - 11 = 0 in three-dimensional space?
  26. A random variable X has mean mu = 50 and standard deviation sigma = 8. What is the Z-score corresponding to a raw score of X = 66?
  27. What is the vascular compliance (C) of a vein segment that expands by a volume of 15 mL when venous transmural pressure increases by 5.0 mmHg?
  28. In a right-angled triangle, the adjacent side to angle theta has length 4 and the opposite side has length 3. What is the exact value of sec(theta)?
  29. What is the derivative of the natural logarithmic function f(x) = ln(x^3 + 2x) for x > 0?
  30. What is the solution to the system of linear equations: 2x + y = 7 and x - 2y = 1?

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