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Interview prep / Pure Math

Pure Math interview questions: page 2 of 3

Questions 51–100

  1. Adding the whole numbers from 1 to 100Easy
  2. Square size from a 5 by 10 box touching its incircleMedium
  3. Smallest number one short of a multiple of 2 to 10Medium
  4. Proving the area formula from the three side lengthsHard
  5. Fewest moves to shift a 64-disc Hanoi towerEasy
  6. Solving u double-prime plus u-prime plus u equals oneMedium
  7. Total cubes in a staircase pile on a 20 by 20 boardEasy
  8. Antiderivative of the secant functionMedium
  9. Closed forms for sums of integers and their squaresEasy
  10. Why primes above 3 give p squared minus 1 divisible by 24Easy
  11. Staircase routes from the origin to the point (5,5)Easy
  12. All complex sixth roots of 64Easy
  13. Limit of root of x squared plus x minus xEasy
  14. Can two neighbouring primes average to a primeEasy
  15. Limit of root of x squared plus 5x minus xEasy
  16. Binet formula for the Fibonacci numbersMedium
  17. Mean of two exponentials versus exponential of meanEasy
  18. Value of the continued fraction 2 + 2/(2 + ...)Easy
  19. Where the normal distribution function changes curvatureEasy
  20. What makes a matrix positive definiteEasy
  21. Odd-length permutation forces an even productMedium
  22. Liouville theorem via the Cauchy estimateHard
  23. Fourier transforms of sin x and cos xHard
  24. Constant bounded entire function by comparing two valuesHard
  25. Series approximations to e to the x and ln xEasy
  26. Why the harmonic series divergesEasy
  27. Derivative of x raised to the power xEasy
  28. Differentiating e to the cos x from the limit definitionMedium
  29. Derivative of x times the natural log of xEasy
  30. Antiderivative of the logarithm by partsEasy
  31. Contour integral of log x over x squared plus 2x plus 2Hard
  32. Counting domino coverings of a two-row stripEasy
  33. Base whose infinite power tower equals 2Easy
  34. Three friends or three strangers among six peopleMedium
  35. Digit-sum test for divisibility by nineEasy
  36. Score from splitting 1000 coins down to singletonsMedium
  37. Contradiction proof that root 2 is irrationalEasy
  38. Derivative of ln of x to the power ln xEasy
  39. Two indeterminate limits via L'HopitalEasy
  40. Integrating the natural log by partsEasy
  41. Definite integral of sec x from 0 to pi over 6Medium
  42. Volume shared by two crossing unit cylindersHard
  43. When the snow began, from a plough's progressHard
  44. Gaussian integral by switching to polar coordinatesMedium
  45. The value of i raised to the power iMedium
  46. Bernoulli inequality for integer powersEasy
  47. Root of 37 to three decimals by Newton's methodEasy
  48. Origin-to-plane distance with a Lagrange multiplierEasy
  49. Separable ODE y' + 6xy = 0 with y(0) = 1Easy
  50. Homogeneous first-order ODE y' = (x-y)/(x+y)Medium