Can You Pass Harvard's 1869 Entrance Exam?

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Leah Goldman

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Harvard's hallway entrance. Creative Commons CC0

The following 1869 Harvard entrance exam was supposed to be a breeze, believe it or not (via GOOD).

In those days colleges had to go out of their way to attract students. Harvard pointed out in a newspaper ad that 185 of 210 candidates passed the entrance test and were accepted in the previous year.


But those candidates had the benefit of a focused prep school education.

You will find this exam, which ranges from geography to geometry to Latin, extremely difficult. Take a stab at the answers in the comment section.

1. Prove that the perpendicular from the centre of a circle upon a chord bisects the chord and they are subtended by the chord.

Wikimedia Commons

2. Reduce the following expression to its simplest form:


(9a2b2- 4b4) (a2- b2) - (3ab - 2b2) (3a [a+ b2] - 2b [b2 + 3ab - a2])b

3. A man bought a watch, a chain, and a locket for $216.

The watch and locket together coast three times as much as the chain, and the chain and locket together cost half as much as the watch. What was the price of each?

4. Prove the formula for the cosine of the sum of two angles; and deduce the formulas for the consine of the double of an angle and the cosine of the half of an angle.

Wikimedia Commons

5. Find the amount of £50 12s. 5d. at simple interest at 8%, at the end of 5 years, 2 months, and 3 days.

6. Describe the route of the Ten Thousand, or lay it down on a map.

Thalatta! Thalatta! (The Sea! The Sea!) — painting by Bernard Granville Baker, 1901. Wikimedia Commons

7. Translate into Latin: Who more illustrious in Greece than Themistocles? Who when he had been driven into exile did not do harm to his thankless country, but did the same that Coriolanus had done twenty years before.

8. Latin grammar: Give the principal parts of cado, cacdo, tono, reperio, curro, pasco, paciscor, marking the quantity of the penult.


Give all the Infinitives and participles of abeo, ulciscor; the Present Indicative of fio; the Future indicative Active and the Present Subjunctive Passive of munio, with the quantity of all penults.

9. Greek grammar: Give an example of Elision. In what words does the accent of the elided vowel disappear with the vowel?

10. Compare Athens with Sparta.

The Acropolis at Athens. Christophe Meneboeuf/Wikimedia Commons

11. Pericles: — the Man and his Policy.


12. One metre=39.37 inches. Compute from this datum the value of 4 miles in kilometers

13. What is the logarithm of 1 in any system?

Of any number in a system of which that number is the base? In a system of which the base is 4, what is the logarithm of 64? of 2? of 8? of 1/2?

13. Leonidas, Pausanias, Lysander.

Leonidas, the Spartan king, the leader of the 300 at Thermopylae. Image by manue41350 from Pixabay

14. Show how the area of a polygon circumscribed about a circle may be found; then how the area of a circle may be found; then prove that circles are to each other as the squares of their radii.


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