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ESAT Cheat Sheet 2026

The 30 highest-yield ESAT facts, distilled from real exam questions. Print it, save it as a PDF, or study it here โ€” free, no sign-up.

80 questions
120 min time limit
60% to pass
  1. Which technique is most appropriate for evaluating โˆซxยทe^x dx? โ†’ Integration by parts
  2. What is the half-life concept in radioactive decay as tested in ESAT? โ†’ Time for half the nuclei to decay
  3. What is the standard electrode potential of the standard hydrogen electrode (SHE)? โ†’ 0.00 V
  4. For vectors a = (1, 2, 3) and b = (4, 5, 6), what is the dot product a ยท b? โ†’ 32
  5. If a vector a = (3, 4), what is |a|? โ†’ 5
  6. Which of the following is a reason why some universities use the ESAT in their admissions process? โ†’ To evaluate a student's proficiency in mathematics, physics, and chemistry
  7. A wave has frequency 500 Hz and wavelength 0.68 m. What is its speed? โ†’ 340 m/s
  8. What is the molar mass of water (Hโ‚‚O)? โ†’ 18 g/mol
  9. What is produced when an acid reacts with a base? โ†’ Salt and water
  10. Evaluate the definite integral โˆซโ‚€^ฯ€ sin(x) dx. โ†’ 2
  11. What does Le Chatelier's Principle state in chemical equilibrium? โ†’ A system at equilibrium will shift to oppose any imposed change
  12. Which functional group characterises an alcohol? โ†’ -OH (hydroxyl)
  13. What is the difference between mitosis and meiosis? โ†’ Mitosis produces 2 identical diploid cells; meiosis produces 4 haploid cells
  14. What are the eigenvalues of the upper triangular matrix with rows [3, 1] and [0, 2]? โ†’ 3 and 2
  15. In the chemistry section of the ESAT, which topic is LEAST likely to be included? โ†’ Classical Music Composition
  16. What is the polar form of the complex number -1 + i? โ†’ โˆš2 exp(iยท3ฯ€/4)
  17. What is the marking scheme for the ESAT? โ†’ One mark per correct answer, no penalty for wrong answers
  18. What is the gravitational potential energy of a 5 kg mass at a height of 10 m? (g = 10 m/sยฒ) โ†’ 500 J
  19. What is the volume of the solid formed when y = โˆšx (0 โ‰ค x โ‰ค 4) is rotated 360ยฐ about the x-axis? โ†’ 8ฯ€
  20. For the matrix M with rows [1, 2] and [3, 4], which entry appears in row 1, column 1 of M^(-1)? โ†’ -2
  21. What is the pH of a solution with [Hโบ] = 1 ร— 10โปยณ mol/L? โ†’ 3
  22. Which of the following subjects is most likely to be covered in the ESAT? โ†’ Organic Chemistry
  23. What is a buffer solution? โ†’ A solution that resists pH change on addition of small amounts of acid or base
  24. How long is the ESAT in total (all parts combined)? โ†’ Approximately 2 hours
  25. If z = 3 + 4i, what is |z|, the modulus of z? โ†’ 5
  26. What is the binomial expansion of (1 + x)โด? โ†’ 1 + 4x + 6xยฒ + 4xยณ + xโด
  27. What should a candidate do if they encounter a question with an unfamiliar topic in the ESAT? โ†’ Apply logical reasoning and elimination to make the best guess, then move on
  28. What type of molecule forms the phospholipid bilayer of cell membranes? โ†’ Amphipathic phospholipids with hydrophilic heads and hydrophobic tails
  29. Which of the following best describes the ESAT's role in the admissions process? โ†’ It is one component used alongside grades, personal statement, and interviews
  30. In the ESAT Mathematics section, if f(x) = 3xยฒ - 2x + 1, what is f'(x)? โ†’ 6x - 2
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